Electron energy loss spectroscopy of nanoscale materials

UNIVERSITEIT ANTWERPEN

Faculteit WetenschappenDepartement Natuurkunde

Elektronen energie verlies spectroscopie van nanoschaalmaterialen

Electron energy loss spectroscopy of nanoscalematerials

Proefschrift voorgelegd tot het behalen van de graad vanDoctor in de Wetenschappen aan de

Universiteit Antwerpen te verdedigen doorJohan VERBEECK.

Promotoren:Prof. Dr. G. Van TendelooProf. Dr. D. Van Dyck Antwerpen, 2002

A journey of a thousand miles must begin with a single step.from the Tao Te Ching 300 BC

Samenvatting

Nanoschaal materialen winnen de laatste tijd steeds meer aan belang. Ener-zijds vanwege de voortdurende reductie in afmetingen van halfgeleider bouwste-nen, maar anderzijds ook omdat allerlei technologisch en wetenschappelijk inte-ressante eigenschappen optreden bij de schaalverkleining van materialen. Nano-schaal materialen worden gedefinieerd als materialen die minstens een dimensiehebben in het nanometer gebied.

Sterke technologisch-wetenschappelijke vooruitgang heeft het mogelijk ge-maakt om artificiele nanomaterialen te groeien. De bulk eigenschappen van dezeartificiele materialen kunnen opgemeten worden, maar een karakterisatie op na-noschaal is onmisbaar om een zinvolle relatie te leggen tussen macroscopischeeigenschappen en de microscopische structuur. Zowel de kristalstructuur met mo-gelijke defecten en korrelgrenzen alsook de locale chemische samenstelling kun-nen een grote invloed hebben op de macroscopische eigenschappen en dienenonderzocht te worden.

Transmissie elektronenmicroscopie (TEM) is erg geschikt voor de microstruc-turele karakterisatie en kan aangevuld worden met elektron energie verlies spec-troscopie (EELS) om chemische en zelfs elektronische informatie op te meten vannanoschaal gebieden.

Het basisprincipe van deze techniek is als volgt: de interactie van snelle, pri-maire elektronen met de materie in een elektronenmicroscoop, kan aanleiding ge-ven tot inelastische verstrooiing. Hierbij verliest het snelle elektron een deel vanzijn energie aan de materie die hierdoor in een aangeslagen toestand komt. Stu-die van de energieverdeling van de inelastisch verstrooide elektronen leidt tot eenzogenoemd elektron energie verlies spectrum (EELS spectrum). Dit spectrum be-vat typische pieken, te wijten aan de excitatie van de materie naar welbepaaldetoestanden. De pieken worden excitatiepieken genoemd en bevatten zowel che-mische als elektronische informatie over de materie.

Het eerste deel van deze thesis behandelt de achtergrond van de EELS tech-niek. Vragen als “hoe interpreteert men de resultaten van een EELS experiment?”en “waarom is EELS zo‘n interessante techniek voor de studie van nanoschaalmaterialen?” komen aan bod.

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In hoofdstuk 1 wordt de theorie van de inelastische verstrooiing van een snelprimair elektron aan materie ingeleid. Een intuıtieve beschrijving leidt het hoofd-stuk in gevolgd door een kwantummechanische bespreking van inelastische ver-strooiing. Fundamentele begrippen als werkzame doorsnede en de angulaire ver-deling van de inelastisch verstrooide elektronen worden behandeld. Deze kortetheoretische inleiding leidt tot het opstellen van vuistregels die nuttig zijn bij hetuitvoeren van EELS experimenten. Ze geven ook een dieper inzicht in de keuzevan de microscoop parameters. Een overzicht wordt gegeven van de verschillendesoorten EELS experimenten die men kan uitvoeren met een korte beschrijving vande informatie dat ze kunnen opleveren.

Hoofdstuk 2 vergelijkt de EELS techniek met andere veel gebruikte technie-ken om materialen te karakteriseren. De vergelijking toont aan dat EELS alsenige techniek in staat is om chemische en elektronische informatie te bekomenop nanoschaal dimensie. Bovendien wordt deze techniek meestal in een elektro-nenmicroscoop uitgevoerd, waardoor de mogelijkheid bestaat om zowel micro-structurele en morphologische (conventionele TEM) als chemische en elektroni-sche (EELS) informatie te verkrijgen van nanoschaal gebieden.

In het 3de hoofdstuk komt de opbouw van de gebruikte spectrometer van hetGIF type aan bod. De verschillende gebruiksmodi worden verduidelijkt en devoor- en nadelen afgewogen. Imperfecties van de spectrometer die van belangzijn voor experimenteel werk, worden besproken.

Hoofdstuk 4 behandelt de kwantificatie van een experimenteel EELS spec-trum. De conventionele manier van kwantificeren komt eerst aan bod. Bij dezemethode is het nodig om de achtergrond van het spectrum te verwijderen tenein-de enkel de bijdrage van een bepaalde excitatie over te houden. De meervoudigeinelastische verstrooiing dient ook verwijderd te worden om een vergelijking metde theorie van enkelvoudige inelastische verstrooiing mogelijk te maken. De al-dus verkregen excitatie piek kan dan worden omgerekend naar een elementcon-centratie door gebruik te maken van een berekende of experimentele werkzamedoorsnede.

Een alternatief voor deze conventionele kwantificatie strategie, de model-ge-baseerde EELS kwantificatie, werd uitgewerkt en is gebruikt in deze thesis. Eenfysisch model van de excitatie pieken in een bepaald materiaal wordt opgestelden dit model wordt d.m.v. fitting met het experimentele spectrum vergeleken. Demethode van maximale waarschijnlijkheid wordt gebruikt om die parameters vanhet model te vinden die de hoogste waarschijnlijkheid hebben om het experimen-tele spectrum te genereren. Deze kwantificatie strategie werd uitgewerkt in eencomputer programma, EELSMODEL, dat de mogelijkheid biedt om een modelop te stellen uitgaande van een aantal componenten (excitatie pieken, achtergrondmodellen) en dat dan te vergelijking met een reeks van experimentele EELS spec-tra.

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De model-gebaseerde aanpak van het kwantificatieprobleem laat toe enkelevaststellingen te maken met betrekking tot de intrinsieke limieten die aan EELSkwantificatie verbonden zijn vanwege het deeltjeskarakter van de elektronen. Hetdeeltjeskarakter van de elektronen geeft aanleiding tot een Poisson telstatistiek.Kennis van de statistiek van het experiment kan dan gebruikt worden om eenschatting te maken van de intrinsieke precisie die onder bepaalde omstandighedengehaald kan worden. Een eenvoudig model, bestaande uit een achtergrond en eenexcitatiepiek, wordt gebruikt om dit concept te verduidelijken en om aan te tonendat er een fundamentele beperking is op de precisie die met een bepaald EELS ex-periment gehaald kan worden. De precisie wordt bepaald door de verhouding vande achtergrond t.o.v. de excitatie piek en door het aantal gedetecteerde elektronenin het spectrum.

Behalve de precisie kan ook een maat aangeduid worden voor de minimaaldetecteerbare concentratie van een bepaald element, gegeven een vereiste precisie.

Een vergelijking van de resultaten met experimentele kwantificaties toont aandat het inderdaad mogelijk is om de fundamentele precisie- of detecteerbaarheids-limiet te benaderen in zeer zorgvuldig uitgevoerde experimenten. In vele gevallenzijn er echter praktische factoren die de kwantificatie beduidend minder preciesmaken.

Hoofdstuk 5 handelt over de techniek van energie gefilterde transmissie elek-tronen microscopie (EFTEM). De EFTEM techniek laat toe om beelden te makenwaarvan de intensiteit evenredig is met de concentratie van een bepaald chemischelement. De techniek vereist het nemen van drie beelden die verkregen zijn uitinelastisch verstrooide elektronen van specifieke energie gebieden. Dit laat toeom de niet-element-specifieke achtergrond te verwijderen en een beeld te creerendat enkel element-specifieke informatie bevat.

De beeldvorming bij deze techniek wordt behandeld volgens Kohl en Rose enleidt tot het definieren van de spatiale resolutie in EFTEM beelden. Inzicht in debeeldvorming leert ons de invloed van de lens aberraties in de microscoop en hoemen de resolutiebeperkende invloed hiervan kan verminderen door het inbrengenvan aperturen.

De signaal-ruis verhouding en het optimaliseren van de microscoop parame-ters voor minimum detecteerbaarheid worden besproken.

Het tweede deel van de thesis vat de experimentele resultaten samen. Diegeven een overzicht van de mogelijkheden van EELS en EFTEM voor de studievan nanoschaal materialen.

Hoofdstuk 6 behandelt dunne film manganieten. Manganieten zijn materi-alen van de vorm AA′MnO3 met A en A′ divalente en trivalente kationen. Zehebben een perovskiet kristalstructuur die eventueel vervormd kan zijn. Bepaal-de manganieten vertonen interessante fysische eigenschappen zoals bv. metaal-isolator fase-overgangen en de kolossale magnetoweerstand (CMR) eigenschap.

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Vooral de CMR eigenschap is interessant voor technologische toepassingen zoalssensors voor magnetische velden. De eigenschappen van de huidige CMR ma-terialen verhinderen echter de massale toepassing wegens het hoge magneetveld(enkele Tesla) en de lage temperaturen (≈ 250 K) die nodig zijn voor het optredenvan dit effect.

Drie studies spitsen zich toe op materialen waarbij geprobeerd wordt om viadunne film technieken de eigenschappen van de manganieten zodanig te wijzigendat hun technologisch toepassingsgebied verbetert.

Een eerste materiaal, is een gestapelde structuur van LaMnO3 en SrMnO3 dun-ne lagen op een substraat van SrTiO3. De algemene formule van dit materiaal is(LaMnO3)2n(SrMnO3)n. Twee preparaten met n = 6 en n = 4 werden onderzochtdoor middel van EFTEM, EELS met een raster transmissie elektronen microscoop(STEM-EELS), hoge resolutie transmissie elektronen microscopie (HRTEM) enelektronen diffractie (ED). Kwantificatie van de experimenten leidde tot het voor-stellen van een model waarbij zuurstof deficientie optreedt in de SrMnO3 lagen.

Een tweede manganiet materiaal bestaat uit een gelaagde structuur met alge-mene formule ((La0.7Sr0.3MnO3)m(SrTiO3)n)15 met n = 8 en m = 5 of m = 32.Dit materiaal werd onderzocht met de EFTEM methode. Een lokale verstoringvan de chemische samenstelling van de SrTiO3 lagen werd gevonden onder devorm van mangaan rijke gebiedjes.

Het laatst beschreven manganiet materiaal is een composiet materiaal bestaan-de uit La0.77Ca0.33MnO3 (LCMO) met een dopering van MgO op een substraatvan MgO. De algemene formule is (La0.77Ca0.33MnO3)1−x : (MgO)x met x devariabele MgO concentratie. EFTEM beelden tonen aan dat vanaf x ≈ 0.3 deMgO fase een korst vormt die de LCMO korrels volledig omsluit. Beide materi-alen blijven volledig gescheiden (geen diffusie). HRTEM toont aan dat de MgOen LCMO fase volledig heteroepitaxiaal gegroeid zijn en dat er bij x ≈ 0.3 eenstructurele fase transformatie opduikt die gepaard gaat met een plotse wijzigingin de magneto transport eigenschappen.

Hoofdstuk 7 beschrijft de resultaten van een studie van Fe en Co nanodra-den en nanobuizen met een diameter van ≈ 60 nm. De EFTEM resultaten tonenduidelijk aan dat de metallische draden omgeven zijn door een oxide laag van≈ 10 nm dik. De Fe nanobuizen bestaan volledig uit polykristallijn ijzeroxide.Lokale meting van EELS spectra voor Co nanodraden toont duidelijk de veran-dering in valentietoestand van de metaalatomen door wijzigingen die optreden inde fijnstructuur van de excitatie pieken. Kwantificatie van de spectra leidde tot dedeterminatie van het cobalt oxide als Co3O4 en het ijzer oxide als Fe2O3. HRTEMen ED studies vullen de EFTEM bevindingen aan.

Het 8ste hoofdstuk beschrijft de resultaten van een EFTEM studie van cobaltnanodeeltjes in een zilver matrix. Preparaten met een verschillende warmtebehan-deling werden onderzocht. EFTEM beelden tonen duidelijk de cobalt nanodeeltjes

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met een grootte tussen 3 nm en 15 nm afhankelijk van de warmtebehandeling. Hetgrote voordeel van de EFTEM methode hier, is de sterk verhoogde zichtbaarheidvan de deeltjes in de zilver matrix vergeleken met de conventionele TEM beelden.Deze resultaten worden aangevuld met diffractie beelden en hoge resolutie TEMom een conclusie over de groei van de nanodeeltjes tijdens de warmtebehandelingte bekomen.

Tot slot wordt er in hoofdstuk 9 een overzicht gegeven van andere experimen-ten die tijdens dit doctoraat werden uitgevoerd, maar die niet werden weergegevenin het experimentele deel.

Preface

Interaction of fast primary electrons with matter in an electron microscope canlead to inelastic scattering. In that event, the primary electron loses some of itsenergy by transferring it to the material, thereby exciting it to a higher energy state.Studying the energy distribution of the inelastically scattered electrons, leads to aso-called electron energy loss spectrum (EELS spectrum). This spectrum containstypical peaks, due to excitations of the material to specific states. The peaks aretermed excitation peaks and contain information on the chemical as well as theelectronic nature of the material.

The first part of this thesis deals with the background of the EELS technique.Questions like “How to interpret the results of an EELS experiment?” and “Whyis EELS such an interesting technique to study nanoscale materials?” are dealtwith.

In chapter 1, the theory of the inelastic scattering of a fast primary electronwith matter is introduced. An intuitive description is followed by a quantum me-chanical description of inelastic scattering. Fundamental concepts like cross sec-tions and the angular distribution of the scattered electrons are treated. This shorttheoretical introduction leads to the formulation of some rules of thumb, that areuseful to perform EELS experiments. These rules give a deeper understanding ofthe parameters to choose when operating the microscope. An overview is givenof the different types of EELS experiments with a short description of the sort ofinformation they are able to give.

Chapter 2 shows a comparison of the EELS technique with other commonlyused techniques to characterise materials. The comparison shows that EELS is theonly technique able to give chemical and electronic information from nanoscaleregions. Moreover, EELS is in most cases integrated into an electron micro-scope which enables the study of crystal structure and morphology (conventionalTEM) as well as the study of chemical and electronic information (EELS) fromnanoscale regions with the same instrument.

In the 3th chapter, the construction of the spectrometer of the GIF type isdetailed. The different operation modes are explained and pros and cons are com-pared. A description of the imperfections of the spectrometer, important for ex-

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perimental work, is given.Chapter 4 describes the quantification of an EELS spectrum. The conventional

quantification scheme is described first. This method requires the removal of thebackground in the spectrum in order to obtain only that part of the spectrum thatis due to a specific excitation peak. Plural inelastic scattering needs to be removedin the second step, to enable the comparison with single scattering theory. Theexcitation peak that is obtained in this way, can be converted to elemental concen-trations by making use of calculated or experimental cross sections.

An alternative to this conventional quantification scheme is the model-basedEELS quantification, which is used in the experimental part of this thesis. Aphysical model of the excitation peaks for a material is constructed and this modelis fitted to the experimental spectrum. The technique of maximum likelihood isused to find those parameters for which it is most likely that they produced theexperimental spectrum. This quantification scheme, is implemented in a computerprogram, EELSMODEL, that enables the user to construct a model from a numberof components (excitation peaks, background models) and to fit this model to (aset of) experimental spectra.

The model based approach, enables us to make a few remarks concerning thefundamental limits of EELS quantification, due to the particle character of theelectrons. The particle character leads to a Poissonian counting statistics. Knowl-edge of the statistics can be used to estimate the intrinsic precision limits in EELS,depending on the operational parameters. A simple model, consisting of a back-ground model and one excitation peak, is used to clarify this concept and to showthat fundamental limits in precision exist. The precision is found to be dependenton the ratio of the excitation peak to the background and on the total number ofcounts in the spectrum.

Apart from the precision, a measure can be given for the minimal detectabilityof an element from an EELS experiment, given a required precision.

A comparison of these results with published experiments shows that it is in-deed possible to approach the statistical precision and detectability limit in care-fully conducted experiments. In practice, however, several factors can make thequantification considerably less precise.

Chapter 5 explains the technique of the energy filtered transmission electronmicroscopy (EFTEM). The EFTEM technique allows one to make images that areproportional to the concentration of a specific element in a sample. The techniquerequires the acquisition of three images, made up with inelastically scattered elec-trons from different energy ranges. This allows for the removal of the non-specificbackground and creates an image that only contains element-specific information.

The image formation in this technique is detailed following Kohl and Rose,which leads to a definition of spatial resolution in EFTEM images. Insight in theimage formation process is valuable to assess the influence of lens abberations

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and to minimize their resolution limiting influence by inserting apertures in themicroscope.

The signal to noise ratio and the optimization of the microscope parameters toobtain minimum detectability are described.

The second part of this thesis summarizes experimental results that give anoverview of the possibilities to study nanoscale materials with EELS and EFTEM.

Chapter 6 deals with the study of some thin film manganites. The manganitesare materials of the form AA′MnO3 with A en A′ divalent and trivalent cations.They have a perovskite crystal structure which can be deformed. Certain man-ganites exhibit interesting physical properties such as a metal-insulator transitionand/or colossal magneto resistance (CMR). The CMR property is of special tech-nological interest and can be used e.g. as a magnetic field sensor. The propertiesof the current CMR manganites, prohibit their widespread use because of the highmagnetic fields and low temperatures (≈ 250 K) that are required.

Three different materials are studied. They have in common that thin filmtechniques are used to try to tune the physical properties to improve their techno-logical applicability.

The first material is a stacked structure of LaMnO3 and SrMnO3 thin filmlayers on a substrate of SrTiO3. The general formula is (LaMnO3)2n(SrMnO3)n.Two specimen where studied, one with n = 6 and one with n = 4. The specimenare studied with EFTEM, scanning TEM-EELS (STEM-EELS), high resolutionTEM (HRTEM) and electron diffraction (ED). Quantification of the experimentsenables the proposition of a model describing the material.

The second manganite material consists of a layered structure with generalformula ((La0.7Sr0.3MnO3)m(SrTiO3)n)15 with n = 8 and m = 5 or m = 32. Thismaterial is studied by the EFTEM method. A local deviation in chemical compo-sition is found in the SrTiO3 layers as manganese rich regions.

The final manganite material is a composite material consisting ofLa0.77Ca0.33MnO3 (LCMO) doped with MgO on an MgO substrate. The generalformula is (La0.77Ca0.33MnO3)1−x : (MgO)x with x the variable MgO concentra-tion. EFTEM images indicate that from x ≈ 0.3, the MgO phase forms a grainwhich completely surrounds the LCMO grains. Both materials remain separated(no interdiffusion was found). HRTEM showed that the MgO and LCMO phasewhere grown completely heteroepitaxial and at x ≈ 0.3 a structural phase transi-tion occurs, accompanied by a drastic change in magneto transport properties.

Chapter 7 describes the results of a study of Fe and Co nanowires and nan-otubes with a diameter of ≈ 60 nm. The EFTEM results clearly indicate the ex-istence of an oxide layer (≈ 10 nm thickness) surrounding the nanowires. The Fenanotubes are made of polycrystalline iron oxide. A local measurement of EELSspectra, clearly shows the difference in valence state between the metallic core ofthe wires and the oxide layers by pronounced changes in the fine structure of the

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metallic excitation edges. Quantification of the spectra enabled the determinationof the cobalt oxide to be Co3O4 and the iron oxide as Fe2O3. HRTEM and EDstudies are used to complete these findings.

The 8th chapter describes the results of an EFTEM study on cobalt nanopar-ticles in a silver matrix. Samples with a different heat treatment are compared.The EFTEM images clearly show the cobalt particles with a diameter between 3and 15 nm depending on the heat treatment. The main advantage of EFTEM inthis case is the drastic improvement of the visibility of the cobalt particles withrespect to conventional TEM or dark field imaging. The results are supplementedwith diffraction patterns and high resolution images to make a conclusion aboutthe growth process of the particles during the heat treatment.

Finally, chapter 9 gives an overview of other experiments that were carried outduring this phd., but that were not published in the experimental part of this thesis.

Contents

I Introduction to EELS 1

1 What is EELS? 31.1 Intuitive description . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.1.1 Naming conventions . . . . . . . . . . . . . . . . . . . . 61.1.2 Things to learn from an EELS spectrum . . . . . . . . . . 61.1.3 Basic quantification . . . . . . . . . . . . . . . . . . . . . 71.1.4 Advanced EELS techniques . . . . . . . . . . . . . . . . 8

1.2 Quantum mechanical approach . . . . . . . . . . . . . . . . . . . 81.2.1 The hydrogen-like atom: orders of magnitude and rules

of thumb . . . . . . . . . . . . . . . . . . . . . . . . . . 131.2.2 Core-loss excitations in crystals . . . . . . . . . . . . . . 19

1.3 Things to learn from an EELS experiment . . . . . . . . . . . . . 221.3.1 Accessible measurement variables . . . . . . . . . . . . . 221.3.2 Types of EELS experiments . . . . . . . . . . . . . . . . 22

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2 Why EELS: comparison with other spectroscopic techniques 252.1 Primary particles . . . . . . . . . . . . . . . . . . . . . . . . . . 252.2 Detected particles . . . . . . . . . . . . . . . . . . . . . . . . . . 262.3 Absorption vs. emission . . . . . . . . . . . . . . . . . . . . . . 272.4 XANES vs. ELNES . . . . . . . . . . . . . . . . . . . . . . . . . 27Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3 Experimental setup 293.1 Spectrometer design . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.1.1 GIF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.2 Operation modes . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.2.1 EELS in diffraction mode . . . . . . . . . . . . . . . . . 313.2.2 EELS in image mode . . . . . . . . . . . . . . . . . . . . 313.2.3 EFTEM mode . . . . . . . . . . . . . . . . . . . . . . . 313.2.4 Energy filtered CBED . . . . . . . . . . . . . . . . . . . 33

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3.3 Imperfections of the spectrometer . . . . . . . . . . . . . . . . . 333.3.1 PSF of the CCD . . . . . . . . . . . . . . . . . . . . . . 333.3.2 Energy resolution and stability . . . . . . . . . . . . . . . 353.3.3 Specimen drift . . . . . . . . . . . . . . . . . . . . . . . 353.3.4 Probe stability . . . . . . . . . . . . . . . . . . . . . . . 363.3.5 Stray magnetic fields . . . . . . . . . . . . . . . . . . . . 363.3.6 Temperature of the room . . . . . . . . . . . . . . . . . . 36

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4 Quantitative EELS 394.1 Conventional EELS quantification . . . . . . . . . . . . . . . . . 40

4.1.1 Background removal . . . . . . . . . . . . . . . . . . . . 404.1.2 Multiple scattering removal . . . . . . . . . . . . . . . . 424.1.3 Conversion to chemical concentrations . . . . . . . . . . 444.1.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.2 Alternative model-based EELS quantification . . . . . . . . . . . 454.2.1 Maximum Likelihood . . . . . . . . . . . . . . . . . . . 464.2.2 How to build a model? . . . . . . . . . . . . . . . . . . . 484.2.3 EELSMODEL software . . . . . . . . . . . . . . . . . . 48

4.3 Limits to precision: Cramer Rao Lower Bound . . . . . . . . . . 504.3.1 Monte Carlo versus CRLB . . . . . . . . . . . . . . . . . 504.3.2 Precision . . . . . . . . . . . . . . . . . . . . . . . . . . 524.3.3 Detectability . . . . . . . . . . . . . . . . . . . . . . . . 534.3.4 Practical limitations . . . . . . . . . . . . . . . . . . . . 54

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

5 EFTEM 595.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595.2 Elemental mapping . . . . . . . . . . . . . . . . . . . . . . . . . 59

5.2.1 Three-window elemental mapping . . . . . . . . . . . . . 595.2.2 Jump-ratio method . . . . . . . . . . . . . . . . . . . . . 61

5.3 Colour maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 625.4 Spatial Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5.4.1 Image formation . . . . . . . . . . . . . . . . . . . . . . 625.4.2 Image of a single atom . . . . . . . . . . . . . . . . . . . 655.4.3 Resolution . . . . . . . . . . . . . . . . . . . . . . . . . 695.4.4 Implications for elemental profiles . . . . . . . . . . . . . 70

5.5 Signal to noise ratio . . . . . . . . . . . . . . . . . . . . . . . . . 735.6 Detectability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 755.7 Combining spectroscopic and spatial information . . . . . . . . . 76

5.7.1 Imaging spectroscopy . . . . . . . . . . . . . . . . . . . 76

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5.7.2 Spectrum imaging . . . . . . . . . . . . . . . . . . . . . 78Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

II Experiments 81

6 Manganite thin films 836.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 836.2 Valency measurement . . . . . . . . . . . . . . . . . . . . . . . . 866.3 LMO-SMO heterostructures . . . . . . . . . . . . . . . . . . . . 89

6.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 896.3.2 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . 916.3.3 Structural considerations . . . . . . . . . . . . . . . . . . 936.3.4 Results and discussion . . . . . . . . . . . . . . . . . . . 946.3.5 Imaging spectroscopy . . . . . . . . . . . . . . . . . . . 1046.3.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 1056.3.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . 106

6.4 LSMO-STO multilayers . . . . . . . . . . . . . . . . . . . . . . 1076.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 1076.4.2 Pulsed Liquid Injection MOCVD . . . . . . . . . . . . . 1076.4.3 Structural aspects . . . . . . . . . . . . . . . . . . . . . . 1086.4.4 Magnetic properties . . . . . . . . . . . . . . . . . . . . 1086.4.5 TEM observations . . . . . . . . . . . . . . . . . . . . . 1096.4.6 EFTEM . . . . . . . . . . . . . . . . . . . . . . . . . . . 1126.4.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . 113

6.5 Composite LCMO1−x:MgOx thin films . . . . . . . . . . . . . . . 1156.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 1156.5.2 Sample preparation . . . . . . . . . . . . . . . . . . . . . 1166.5.3 Characterisation methods . . . . . . . . . . . . . . . . . . 1166.5.4 TEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1176.5.5 EFTEM . . . . . . . . . . . . . . . . . . . . . . . . . . . 1216.5.6 Magnetotransport properties . . . . . . . . . . . . . . . . 1216.5.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . 124

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

7 Metallic nanowires 1337.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1337.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1357.3 Co nanowires . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

7.3.1 EFTEM . . . . . . . . . . . . . . . . . . . . . . . . . . . 1367.3.2 EELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

xiv CONTENTS

7.3.3 TEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1387.3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . 140

7.4 Fe nanowires and nanotubes: sample 4 . . . . . . . . . . . . . . . 1407.4.1 EFTEM . . . . . . . . . . . . . . . . . . . . . . . . . . . 1407.4.2 EELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1417.4.3 TEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1437.4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . 144

7.5 Fe nanowires: sample 6 . . . . . . . . . . . . . . . . . . . . . . . 1467.5.1 EFTEM . . . . . . . . . . . . . . . . . . . . . . . . . . . 1467.5.2 TEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1477.5.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . 147

7.6 Discussion and Conclusion . . . . . . . . . . . . . . . . . . . . . 148Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

8 Metallic nanoparticles 1518.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1518.2 Experimental procedure . . . . . . . . . . . . . . . . . . . . . . . 1528.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

8.3.1 Film microstructure and grain size . . . . . . . . . . . . . 1528.3.2 Particle structure . . . . . . . . . . . . . . . . . . . . . . 1558.3.3 Grain boundaries . . . . . . . . . . . . . . . . . . . . . . 157

8.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1578.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

9 Running projects, future 1619.1 Plasmon delocalisation . . . . . . . . . . . . . . . . . . . . . . . 1619.2 Ferrite thin films . . . . . . . . . . . . . . . . . . . . . . . . . . 1619.3 LSMO on STO(110) . . . . . . . . . . . . . . . . . . . . . . . . 1629.4 Manganite layered samples . . . . . . . . . . . . . . . . . . . . . 162

A Dipole transition rules A-1A.1 rz component . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-2A.2 r+ component . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-2A.3 r− component . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-3A.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-3Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-3

B Derivation of the cross section for the hydrogen-like atom B-5B.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-5B.2 Parabolic coordinates . . . . . . . . . . . . . . . . . . . . . . . . B-6

CONTENTS xv

B.3 Excitation of H to discrete states . . . . . . . . . . . . . . . . . . B-6B.4 Excitation of H to continuum states . . . . . . . . . . . . . . . . . B-14B.5 Combined result and hydrogenic corrections . . . . . . . . . . . . B-20Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-21

C Guidelines for experimental work C-23

D Published results and contributions D-27D.1 Published results . . . . . . . . . . . . . . . . . . . . . . . . . . D-27D.2 Oral presentations . . . . . . . . . . . . . . . . . . . . . . . . . . D-28

E List of abbreviations E-29

Index

Dankwoord

Part I

Introduction to EELS

1

Chapter 1

What is EELS?

1.1 Intuitive description

Fig. 1.1 shows schematically the interaction of a beam of fast electrons withmatter. If the sample is thin enough, most of the electrons pass the material with-out scattering. The electrons in the beam can also undergo elastic scattering,changing their direction or inelastic scattering, losing energy to the sample andalso (slightly) changing direction. When inelastic scattering occurs, the sample isexcited and this can cause secondary electrons which might leave the sample orthe generation of photons, caused by a de-excitation of the excited state. ElectronEnergy Loss Spectroscopy (EELS) is the study of the inelastically scattered elec-trons. This is in contrast with the normal operation mode of a transmission elec-tron microscope, where only elastic scattering is exploited (or inelastic scatteringis ignored). Fig. 1.2 shows the schematic overview of an inelastic scattering eventin a crystal. The initial state |i〉 (indicated as an atom core state) is excited to afinal state | f 〉 (indicated as a Bloch state). The energy required for this transitioncomes from a primary beam electron |k〉 which loses energy and becomes |k′〉. Westudy the inelastically scattered electron by means of a spectrometer consisting inits basic form of a magnetic prism and a detector. The magnetic prism creates auniform magnetic field B perpendicular to the travelling direction of the electrons.In this field B the electrons will start to travel in a circular orbit with radius R.

R =γmeveB

(1.1)

Where γ is the relativistic correction factor, me, e, v respectively the electron restmass, its charge and the velocity of the electron, B is the strength of the magneticfield. The magnetic prism is typically designed so that the electrons only travela quarter of a circle and are then captured by a detector. Electrons which havelost energy in an inelastic scattering event will travel slower and will be bent into

3

4 1.1. Intuitive description

Figure 1.1: Schematic overview of the possible interaction of the primary electron beamwith a thin sample

Figure 1.2: Schematic overview of an inelastic scattering event in a crystal

Chapter 1. What is EELS? 5

Figure 1.3: A typical EELS spectrum from an YBa2Cu3O7 high-Tc superconductor sam-ple, note the logarithmic scale on the intensity axis (from ref. [1]).

a circle with smaller radius. At the exit plane of the magnetic prism, the elec-trons are energy dispersed. The detector can measure a distribution of electronswith different energy loss, the EELS spectrum. Fig. 1.3 shows a typical EELSspectrum. The most intense feature seen in the spectrum is the zero-loss peak.This peak originates from the elastically scattered electrons. It is very intense andhas a certain width (typically 1-2 eV) caused by the non-monochromaticity of theprimary electrons and some instrumental broadening. The second peak, which isroughly an order of magnitude lower is the typical plasmon peak. Here, the beamhas excited a collective excitation of electrons in the crystal. The other peaks arecomposition related peaks; they are marked on the figure. As an example, the OK-edge lies around 530 eV and has the typical shape for a K-edge. This edgeis created by electrons which excite the O 1s core state to free states above theFermi level. The edge is about three orders of magnitude smaller than the zeroloss peak, and this signal is superimposed on a background which needs to be re-moved. This points out one of the main problems in EELS analysis, the inelasticevents of interest are rather weak and long exposure times are needed.

6 1.1. Intuitive description

1.1.1 Naming conventions

In EELS experiments, the excitation-edges are routinely indicated by the let-ters K, L, M, N followed by one or more numbers. The letter indicates the atomicshell which has been excited, K for shell 1, L for shell 2 and so on. Which orbitalin the shell is excited is indicated by a number, L1 would indicate an excitationof a 2s state, L2,3 indicates an excitation of a 2p state which is spin split into a2p 1

2(L2) and a 2p 3

2(L3) state. The spin split states are labelled by their total

angular momentum J and are (2J+1)-fold degenerate, eg. a 2p 32

state can have

j = −32 ,−1

2 , 12 , 3

2 and is therefore 4-fold degenerate. The degeneracy of a statedetermines the number of electrons that can be in that state and is important be-cause the more electrons there are in a state, the more likely an excitation fromthat state will be. Experiments show for instance that the intensity ratio betweenan L3 and an L2-edge is roughly 2:1. The following table gives an overview of themost important edges, continuation of this list for higher shells is straightforward.

Edge State DegeneracyK 1s 1

22

L1 2s 12

2

L2 2p 12

2

L3 2p 32

4

M1 3s 12

2

M2 3p 12

2

M3 3p 32

4

M4 3d 32

4

M5 3d 52

6

1.1.2 Things to learn from an EELS spectrum

We can divide the spectrum in two different parts, the low-loss region (0-100eV) and the core loss region (>100 eV). Both regions contain different types ofexcitations, but the separation between the two is arbitrary. The low loss regioncontains typically the following features:

• The zero-loss peak, contains information to calibrate the energy scale. Itswidth is related to the energy resolution of the system.


• The valence band excitations. Excitations of valence electrons to free states.For semiconductors and insulators, bandgap information is available, al-though extracting it, requires the full knowledge of the shape of the zeroloss peak because it forms a background to these valence excitations.

• The plasmon excitations. These are strong collective excitations of the va-lence electrons. These peaks are especially pronounced in metals. Apartfrom information on the plasmon energy in the sample, thickness estima-tions of the sample can be based on the relative strength between the zero-loss peak and the plasmon peak.

• Atomic excitation edges with very low energy like N- and O-edges. Theseedges can be used to identify and quantify elements, but the backgroundsubtraction is difficult because of the overlap with the plasmon excitation.

The core-loss region consists of excitations from core states of atoms in the sam-ple. The core states are localized states of an atom and can be described by asingle energy eigenvalue rather than an energy-band, even in crystals. This en-ergy eigenvalue is typically > 100 eV and is characteristic for a specific element.Bonding and electronic structure only have a marginal effect on the position ofthese peaks. It is straightforward to identify the edges by looking at their edge on-set energy and comparing it with a reference table. In unfavourable cases when theedges overlap, quantification and identification may become problematic. Once aspecific edge is identified, one can try to quantify it.

1.1.3 Basic quantification

The intensity of an edge is related to the total amount of a specific atomtype, encountered in the region of the specimen which interacted with the elec-tron beam. Knowing the exact beam diameter, the thickness of the sample, thebeam current and the exposure time, we can calculate the absolute concentrationof this element if we know the probability of the excitation. The probability for anexcitation is generally expressed as an inelastic cross section. The cross sectiongives the probability for finding an inelastically scattered electron in a solid angleΩ and in a specific energy-loss range when a primary electron beam is scatteredfrom a single atom of a certain type. The cross section is expressed as an area [m2]which has to be multiplied by the current density [1/m2s] of the primary electronbeam at the position of the scatterer.

In the case of many atoms, we find the concentration of a certain element a byusing the following simple formula:

Ca =Na

σaI0V T(1.2)

8 1.2. Quantum mechanical approach

with Ca the volume concentration of element a [1/m3], Na [/] the number of countsin the a edge taken in a certain energy interval, not counting the background. Thecross section σa [m2] is taken for the same energy interval. I0 is the current den-sity of electrons in the primary beam [1/m2s], V is the volume of the specimenwhich interacted [m3] and T is the total exposure time [s]. The knowledge ofV (including thickness of the sample), I0 and σa is problematic in real-life ex-periments. Therefore it is customary to use relative quantification between twoelements. The formula then becomes

Ca

Cb=

Naσb

Nbσa=

Na

Nbkab (1.3)

kab = σbσa

is now the only unknown term in the quantification and this can be cal-culated from models or measured from a calibration sample.

1.1.4 Advanced EELS techniques

More advanced techniques can be used to extract more information about thepossible excitations in the sample. The specific shape near the onset of an edge,contains information about the bonding and electronic structure in the materialunder study. The core state can be seen to probe locally for the unoccupied den-sity of states. These studies are termed Electron Loss Near Edge Spectroscopy(ELNES). A more detailed treatment of the sort of data ELNES provides will begiven in section 1.2.2. For some examples see ref. [1–3].

Further above the edge Extended Energy Loss Fine Structure (EXELFS) canbe seen as a very small oscillation around the ideal edge shape. This deviationis caused by interference of a secondary ejected electron wave which leaves theexcited electron and its backscattered waves from neighbouring atoms. The tech-nique can reveal data on the interatomic distances in the specimen. Some exam-ples can be found in ref. [1, 4].

By selecting inelastic electrons which leave the specimen under specific an-gles, so called angular resolved EELS can be performed. This technique allowsthe experimentalist to learn about the band structure of the material or about theplasmon dispersion curves. For examples see ref. [5–7].

1.2 Quantum mechanical approach

To describe inelastic scattering in a quantum mechanical way, we can treat asimple model system for an EELS experiment [8]. A monochromatic fast-electronwave, generated by an electron-gun, interacts with a specimen inside the vacuum


Figure 1.4: Schematic overview of position space vectors: a three electron atom with thenucleus in the origin

of an electron microscope. The specimen is taken to be a single atom for simplic-ity, but the formulas will be valid for any specimen. Initially, the system can bethought to consist of the fast electron wave |k〉 and the atom |0〉 in its ground state.We describe this state as a product of the electron wave function and the atomwave function (assuming that the beam and atomic-electrons are distinguishable).When considering the interaction of the fast electron wave with the atom, it ispossible that the electron excites the atom to a state |n〉, thereby losing some of itsmomentum to |k′〉 . Or schematically:

|k,0〉 =⇒ |k′,n〉 (1.4)

Describing both states of the system in position representation making use ofthe coordinates drawn in fig. 1.4 we get:

〈r|k,0〉 =1

L32

eik·reψ0(r1,r2, ..rN) (1.5)

〈r|k′,n〉 =1

L32

eik′·reψn(r1,r2, ..rN) (1.6)

with ψ0 and ψn the orthonormal atomic eigenstates of the atom in its groundstate and excited state. The pre-factor 1

L32

is needed for the normalization of the

plane wave in a box with dimensions L. The position vector r = (re,r1,r2, . . . ,rN)denotes a position in a 3(N +1)-dimensional space.

For fast electrons, it is reasonable to assume that the wave function will notbe influenced much by the interaction with the atom (we can regard the atom as aperturbation). Therefore, we can use the first order Born approximation [8]. Wefind in ref. [8], p.430 an expression for the differential cross section in this approx-imation. The differential cross section tells us, what is the probability to detect an


electron in a solid angle dΩ, which caused the excitation of the atom from |0〉 to|n〉. The expression is based on time dependent perturbation theory.

dσdΩ

(0 → n) =k′

kL6∣∣∣ 14π

2me

h2 〈k′,n|V |k,0〉∣∣∣2 (1.7)

With V the interaction potential between the incoming fast electron and the atom(actually it is the negative potential energy of the incoming electron caused by theatom). The interaction potential consists of two parts and can be written as:

V = −Ze2

re+

N

∑i

e2

|re − ri|(1.8)

The first part being the interaction between the fast electron and the coulomb fieldof the nucleus, the second part is the interaction between the fast electron and theN electrons in the atom. A possible complication could be the indistinguishabilityof the fast electron and one of the atomic electrons, but since the amplitude for anevent where an atomic electron is ejected with an energy in the range of the pri-mary electron is extremely small, we can neglect this possibility. We are lookingnow for the matrix element:

〈k′,n|V |k,0〉 (1.9)

Which can be written out in position space as:

〈k′,n|V |k,0〉 =∫〈k′,n|r〉〈r|V |r′〉〈r′|k,0〉d3rd3r′ (1.10)

=∫〈k′,n|r〉V (r)〈r|k,0〉d3r (1.11)

or in the separate position components

=1L3

∫d3reeik·ree−ik′·re

N

∏i=1

∫d3riψ

∗n (r1, . . . ,rN)V (r)×

ψ0(r1, . . . ,rN) (1.12)

=1L3

∫d3reeiq·re

N

∏i=1

∫d3riψ

∗n (r1, . . . ,rN)

[− Ze2

re+

N

∑i

e2

|re − ri|]×

ψ0(r1, . . . ,rN) (1.13)

With q = k−k′ the momentum transfer vector. The nuclear part of the potentialis independent of the atomic electron positions and gives:

−Ze2

re〈n|0〉 = −Ze2

reδn,0 (1.14)


which disappears for inelastic scattering (the atom is excited to a new state incontrast with elastic scattering where the atom remains in its ground state) becauseof the orthogonality of the atomic wave functions. Rearranging gives:

1L3

N

∏i=1

∫d3riψ

∗n ψ0

∫d3re

[eiq·re

N

∑i

e2

|re − ri|]

(1.15)

Substituting r′e for re − ri gives

1L3

N

∏i=1

∫d3riψ

∗n ψ0

N

∑i

e2∫

d3r′eeiq·(r′e+ri)

|r′e|(1.16)

= 4π1L3

N

∏i=1

∫d3riψ

∗n ψ0

N

∑i

e2

q2 eiq·ri (1.17)

where we used∫ eiq·r′e

r′ed3r′e = 4π

q2 .Now, we can define the inelastic form factor.

Fn(q) =1Z〈n|

N

∑i

eiq·ri|0〉 (1.18)

with Z the atom number. The total differential cross section then becomes,

dσdΩ

(0 → n) =4m2

e(Ze2)2

h4q4

k′

k|−δn,0 +Fn(q)|2 (1.19)

=4a2

0Z2

(qa0)4

k′

k|−δn,0 +Fn(q)|2 (1.20)

with a0 = h2

me2 the Bohr radius. For the elastic case (|k′| = |k| and n=0) the crosssection reduces to the Rutherford scattering case (∝ 1/q4), so the inelastic formfactor models the deviation from the Rutherford case due to the interaction of thefast electron with the bound electrons inside the target. The inelastic form factoris a property of an atom (or material) and is independent of the energy of the fastelectrons. A similar definition is that of the generalized oscillator strength (GOS)fn which is a generalization of the optical oscillator strength describing absorptionof photons by an atom. It is linked to the inelastic form factor by:

fn(q) =EZ2

R(qa0)2 |Fn(q)|2 (1.21)

or

fn(q) =E

R(qa0)2 |〈n|N

∑i

eiq.ri|0〉|2 (1.22)


with E the energy loss of the primary electron (En −E0 with En the eigen energyof state |n〉), R the Rydberg energy (≈ 13.6 eV).

In practice, the excitation spectra in EELS are continuous functions of energyand it is useful to express the cross section per unit energy interval. This requiresthe change from discrete energies to a continuous energy loss scale. Up till now,calculating the cross sections for inelastic scattering in a range of energies Estarttill Estop would require taking the sum of all cross sections dσn

dΩ for all final states|n〉 with an energy loss E0 −En in the required range.

dσE

dΩ=

n=∞

∑n=1

dσn

dΩ[Θ(Estart −En +E0)−Θ(Estop −En +E0)] (1.23)

with Θ(x) the Heaviside step function. We can rewrite this formally for a contin-uous energy scale as an integral.

dσE

dΩ=∫ Estop

Estart

d2σdΩdE

(q,E)dE (1.24)

withd2σ

dΩdE(q,E) =

4γ2

q2

RE

k′

kd fdE

(q,E) (1.25)

the so-called double-differential cross section. Note the 1/q2 dependence in eq.1.25 in comparison with the 1/q4 dependence of the elastic Rutherford scattering.We corrected approximately for relativistic effects by multiplying the electron restmass with γ , the relativistic correction factor. For a more detailed description ofthe relativistic effects see [1]. The total cross section in an energy and angularrange then becomes

σ =∫ ∫

d2σdΩdE

dΩdE (1.26)

To get more insight in the angular distribution of the inelastically scattered elec-trons, we can transform the equations to get the double differential cross sectionin function of the energy loss and scattering angle θ . Fig 1.5 shows a schematicoverview of the scattering geometry. From the figure we note:

q⊥ = k′ sinθ (1.27)

q‖ = k− k′ cosθ (1.28)

q2 = q2⊥ +q2

‖ (1.29)

= (k− k′ cosθ)2 + k′2 sinθ (1.30)

= k2 −2kk′ cosθ + k′2(cos2 θ + sin2 θ) (1.31)

= k2 −2kk′ cosθ + k′2 (1.32)

= k2(1−2k′

kcosθ +(

k′

k)2) (1.33)


Figure 1.5: Schematic overview of the scattering geometry

withk′

k=

√E0 −E

E0=√

1−2θE (1.34)

where we defined the θE = E2E0

the characteristic scattering angle.

q2 = k2(1−2√

1−2θE cosθ +1−2θE) (1.35)

Using a Taylor expansion for√

1−2θE and cos(θ) up to second order in θ andθE we get:

q2 ≈ k2(θ 2 +θ 2E) (1.36)

This makes the formula of the double differential cross section proportional to:

d2σdΩdE

∝1

θ 2 +θ 2E

d fdE

(q(θ),E) (1.37)

Which is a Lorentzian function of scattering angle if the generalized oscillatorstrength f is independent of angle.

1.2.1 The hydrogen-like atom: orders of magnitude and rulesof thumb

In order to calculate the inelastic cross section in the first order Born approx-imation, we need the initial and final states of a system. In general, this problem


can not be solved analytically except for a single hydrogen (or hydrogen-like)atom. In this section, the results for the hydrogen atom will give a basic under-standing of inelastic scattering and will provide some guidelines for the experi-mental work.

The atomic electron in the hydrogen atom can be excited to either bound orcontinuum states. In the case of an excitation to the continuum states, the atomicelectron is emitted and leaves behind an ionized hydrogen nucleus. The cross

Figure 1.6: Generalized oscillator strength d fdEdθ (derived from d f

dEdΩ with dΩ =2π sinθdθ )for a K-edge of carbon in the hydrogenic approximation (E0=300 kV) . Notethe maxima in the GOS (Bethe ridge) for energy losses much larger then the edge onset(280 eV) indicated by arrows.

section and generalized oscillator strength for excitations of a 1s core state to bothcontinuum or bound final states states are derived in appendix B. The derivationis based on early work of H. Bethe [9] and results in a complex analytical formulafor the double differential cross section. This formula is exploited in the SigmaKprogram of R.F. Egerton to calculate numerically the cross sections for any K-edgein a given energy interval and for a given solid angle [1]. The SigmaK algorithmis also implemented in the ELPTM program by Gatan.

Fig. 1.6 shows graphically the shape of the generalized oscillator strengthd f /dE for exciting a K-edge (1s core state) of carbon with 300 kV incidentelectrons as a function of scattering angle and energy loss in the hydrogen-likeapproximation. We can clearly see the GOS rapidly decaying as a function ofenergy loss. At higher energy losses, we can see two maxima appearing (marked


by arrows on fig. 1.6) in the GOS known as the Bethe-ridge [1]. The position ofthe maxima in the plot occur for those q-vectors for which:

h2q2

2me= E (1.38)

Or, the maximum occurs for excitations where the lost momentum of the primaryelectron is almost completely transferred to the secondary excited electron flyingaway from the atom 1. The fact that the GOS is non-zero away from the Betheridge, can be explained by the fact that the atomic electrons are not stationary andcarry their own momentum. Expressing this in angular variables we get for theangle θR at which the Bethe ridge occurs:

θR = ±√2θE (1.39)

Although the GOS seems to be a complicated function of θ and E, the doubledifferential cross section is well described by a Lorentzian function ( 1

θ 2+θ 2E

) in

practice, because of two reasons:

• For angles θ θR we can see in fig. 1.6 that the GOS is approximatelyindependent of θ .

• The maxima of the GOS at θR do not alter the Lorentzian shape significantlybecause in practice θE θR so the Lorentzian function is already close tozero where the deviation would be important.

Therefore we can state the following rule of thumb for a typical EELS setup(E0=100 keV - 1 MeV, E=100 eV - 2 keV):

Rule of thumb 1 The inelastic scattering cross section is a Lorentzian func-tion of scattering angle with FWHM=θE = E

2E0.

Fig. 1.7 shows the cross section for inelastic scattering into an infinitesimal ringθ to θ +dθ given by:

dσring

dE=

dσdΩdE

2πθdθ (1.40)

It is clear that the cross section drops off very rapidly with angle and has a maxi-mum for some small angle in the mrad range. Fig. 1.8 shows the cumulated cross

1like a billiard ball colliding with a stationary billiard ball. The stationary ball starts to movewith a momentum exactly equal to the momentum loss of the moving ball


section into a collection angle β for an energy at the edge onset and for 400 eVgiven by:

dσdisc

dE=∫ β

0

dσdΩdE

2πθdθ (1.41)

For all energies where the GOS is appreciable (say < 100 eV past the edge on-set) we can see that 50% of the total cross section (infinite collection angle) iscontained in a collection angle of about 3 mrad. This leads to the next rule ofthumb for estimating the collection angle which is needed for capturing most ofthe inelastically scattered electrons:

Rule of thumb 2 A collection angle β ≈ 10θE contains most of the inelasticscattering.

Fig. 1.9 shows the differential cross section as a function of energy in a certain col-lection angle β . This shows the typical shape of an excitation edge of the K-type(1s core state) which is often encountered in EELS experiments. It is clear fromfig. 1.9 that increasing the collection aperture is advantageous, since the total crosssection (area under the edge) increases. However, the increase near the onset ofthe edge is small for collection angles larger than 5 mrad in this example of a car-bon K-edge for 300 kV electrons. Far from the onset, on the other hand, the crosssection is almost double for β=10 mrad compared to β=5 mrad. In experiments,

Figure 1.7: Carbon K-edge inelastic cross section for scattering into a ring at angle θ toθ +dθ . Hydrogenic approximation for 300 kV electrons.


this contains a disadvantage, because other excitation edges (say O-K at 532 eV)are superimposed on the rapidly decreasing tail of this C-K edge. So, increas-ing the collection angle β not only increases the total cross section for the edge,but also increases the background for edges at higher energies, greatly reducingthe signal-background ratio. This leads to a decreased visibility of the edges ofhigher energy and a decreased accuracy when quantifying. This is summarized inanother rule of thumb:

Rule of thumb 3 Increasing the collection angle β increases the total crosssection for an edge. This increase however is not linear and has the dis-advantage of increasing the background for edges of higher energy (signal-background ratio decreases). Therefore it is useful to choose an intermediatecollection angle of β ≈ 10θE.

Figure 1.8: Cross section vs. collection angle for energy losses E=285eV (full) andE=400 eV (dotted) (C K-edge, 300 kV, hydrogenic approximation), relative to the crosssection with infinite collection angle. Near the onset, 50% of the inelastic scattering iscontained within an angle of ≈ 3mrad, while for higher losses, the cross section is spreadout over slightly larger angles


Figure 1.9: Differential cross section of a C K-edge (hydrogenic approximation, 300 kV)for different collection angles. Increasing the collection angle is a very effective way toincrease the cross section for angles up to about 5 mrad. Higher collection angles giveonly a small rise at the edge onset but lead to an increase of more than 100% at higherenergies. This effect reduces the signal to background ratio for edges of higher energy.


1.2.2 Core-loss excitations in crystals

In crystals, the equations for the cross section remain equally valid (withinthe first order Born approximation) but we have to reconsider the initial and finalstates |0〉 and | f 〉 for a crystal. For a schematic drawing of initial and final statesin a crystal see fig. 1.2, note also the density of states on the left side of thefigure. The initial states are generally well-localized core states and can be veryaccurately expressed in an atomic basis set centred around a certain atom in acrystal. The overlap between core states of neighbouring atoms is very small.

For the final states in crystals this is not true (think of a free electron state in ametal). The problem now is that the final state can not be decomposed uniquely inthe superposition of atomic basis-sets for each atom because this total set is not anorthogonal basis. In theory we can replace the atomic basis sets by a new orthog-onal basis set for the whole crystal (like plane waves). If we then can express theunoccupied eigenfunctions of the crystal in this set, we can calculate the matrixelements in eq. 1.22 and have a (numerical) value for the cross section of the coreexcitations in the crystal.

Unfortunately, describing the eigenfunctions of the conduction bands in acrystal by means of a plane wave basis set requires a large amount of plane wavesmaking it computationally difficult. On top of that, we can calculate the crosssection and compare this to experiments, but it is very hard to interpret the resultin terms of band structure or chemical intuition.

One of the useful ways to deal with this problem is the Augmented Plane Wavemethod (APW), where the real space of the crystal is divided into spheres aroundthe nuclei, where a spherical basis set is used, and interstitial regions where planewaves are used. This basis set is then used to express the single particle finalstates. It seems to be a more efficient basis set and has the advantage that it fitsbetter with chemical intuition gained from the study of single atoms in the atomicbasis set 2.

For infinite crystals, there is another difficulty: there is an infinite set of finalstates giving rise to the so called band-structure. A measure for the number offinal states in an energy interval is the so-called density of states. If we think ofthe excitation process in EELS as a single electron excitation 3 and we assumethat the matrix element 〈 f |eiq·r|0〉 is similar for final states with a similar energyand independent on the direction of q with respect to r, we can write the crosssection for core excitations in a crystal as:

dσdE

∝ |M(E)|2D(E) (1.42)

2The whole notion of chemical orbitals comes from the choice of that basis set3Only one electron is taken into account, the others are assumed to remain in their unperturbed

state-i.e. no relaxation effects


With M(E) the matrix element 〈 fE |eiq·r|0〉 and D(E) the density of final states atenergy E. The assumptions we made, however should be verified carefully as wasshown by Nelhiebel et al. [10]. Eq. 1.42 induces a few remarks:

• D(E) should be regarded as the unoccupied density of final states since exci-tations to occupied final states are not allowed in view of the Pauli principle.The core states are of course fully occupied.

• D(E) should be regarded as a site projected or local density of states be-cause the matrix element is only significant in a region of space where theinitial state |0〉 is non zero. The local DOS is in fact a peculiar notion be-cause it seems to be in conflict with band structure which appeared becauseof the final states being non-local. It can be understood as a rule for count-ing the density of states: take only these states into account which have aconsiderable electron density in the region of |0〉 (and all equivalent atomsin the crystal).

• D(E) should be made up of symmetry allowed states or a symmetry pro-jected DOS. This is because the matrix element M(E) follows approxi-mately the angular momentum dipole selection rule ∆l = ±1 for small col-lection angles and small energy loss (eiq·r ≈ 1 + q · r when q · r small andq2 ≈ k2(θ 2 +θ 2

E)).

Writing out the dipole selection rules (for a derivation see appendix A) explicitlywe get:

dσdE

∝ |Ml+1(E)|2Dl+1(E)+ |Ml−1(E)|2Dl−1(E) (1.43)

With Dl±1(E) the local unoccupied DOS projected onto a specific angular mo-mentum l ± 1 and l the angular momentum of the initial core state. This meansthat we have to project all the unoccupied eigenstates of the crystal onto a local(centred around a specific atom type) spherical basis set inside a sphere around theatom (chosen to completely contain the core state). We make use of the fact thatthe spherical waves form a complete basis and we can decompose any eigenstateψ f of the crystal with energy E f in that basis.

|ψ f 〉 = ∑l

∑m|E f , l,m〉〈E f , l,m|ψ f 〉 = ∑

l∑m|E f , l,m〉c f lm (1.44)

And then only take the part with a specific angular momentum l ±1 into account(i.e. take c f lm rather than 1 for that state) to calculate the density of states. ThisDOS is then called the symmetry projected local DOS.

The two matrix elements in equation 1.43 act as mixing factors combining theeffect of both l + 1 and l −1 contributions. We can combine these notions into arule of thumb for experimental work:


Rule of thumb 4 The cross section for core excitations in a crystal is ap-proximately dσ

dE ≈ |M(E)|2D(E) with D(E) the site and symmetry projectedunoccupied density of states and M(E) a matrix element that drops off slowlyas a function of energy.

It is important however to summarize the assumptions we made in getting tothis rule:

• First order Born approximation for the derivation of the cross section.

• Single particle assumption. Assume that the final states are unaltered by theexcitation of an electron from the core state.

• Dipole approximation (replace eiq·r by q · r). Only used for interpreting thecross section in terms of the local unoccupied symmetry projected DOS.The dipole approximation is not needed for numerically calculating thecross section.

• Assume that the matrix element 〈 fE |eiq·r|0〉 is similar for final states ofsimilar energy and independent on the direction of q with respect to r. Onlyneeded for the simplified rule in equation 1.43 for splitting the cross sectioninto a DOS part and a matrix element. In numerical calculations, the crosssection can be calculated without this assumption.

• The final states have an infinite lifetime. For short times, a violation ofenergy preservation is allowed and results in a so-called lifetime-broadeningof experimental edges when compared to theory.

When making theoretical calculations, we can try to find the final states | f 〉 by avariational principle. Once the single particle states | f 〉 are found to a reasonableaccuracy, we can calculate the matrix element numerically without making mostof the assumptions in eq. 1.42. This was shown by [10] and is incorporated inthe ab-initio calculation program Wien97 [11, 12]. Doing this, includes orienta-tion effects because proper integration over all allowed (selected by apertures) qdirections is taken into account. Nevertheless, eq. 1.42 is an invaluable tool forinterpreting the observed fine structure in an experimental edge in terms of atomicorbitals.

Many particle effects can be taken into account as well. See Mahan et al. [13]for an analytical approach. However, a full treatment of excitations in crystals withmany particle theory, remains far beyond the possibilities of current numericalmethods and computers.

22 1.3. Things to learn from an EELS experiment

1.3 Things to learn from an EELS experiment

1.3.1 Accessible measurement variables

The theoretical considerations thus far have included three important param-eters in the expressions for the inelastic cross section: the momentum transfer q,the energy loss E and the position(s) r of the atom(s). These variables (q,E,r) en-able various experiments to be conducted, keeping some of the variables constantwhile measuring others.

1.3.2 Types of EELS experiments

Combinations of different measurement variables lead to different experimen-tal techniques labelled by their commonly used acronym. Some of these tech-niques are:

quantitative EELS deals with EELS spectra (intensity vs. energy loss) and triesto convert these spectra to chemical concentrations. Spatial information canbe added to determine the spatial distribution of certain elements. A detaileddescription is given in chapter 4.

EFTEM (Energy Filtered Transmission Electron Microscopy) deals with spatialdata (images) selected in an energy loss range. The ultimate goal is to col-lect chemical distribution maps. The technique is described in some detailin chapter 5.

ELNES (Energy Loss Near Edge Structure) deals with the fine structure of theexcitation edges. The ultimate goal is to interpret this fine structure as asignature of the electronic structure of a crystal. The basis for this techniquewas shown in section 1.2.2.

Angle resolved EELS This technique studies the angular distribution of the in-elastic scattering (q-dependence). In specific cases it can give informationon the band structure of crystals or on the dispersion of elementary excita-tions (e.g. plasmons).

EXELFS (Extended energy loss fine structure) studies the oscillations of thecross section in a crystal with respect to the energy loss. This containsinformation on the nearest neighbour distances around specific atoms. Theexplanation relies on the backscattering of secondary emitted electrons byneighbouring atoms giving rise to interference effects in the unoccupiedDOS.


Bibliography

[1] R. F. Egerton. Electron energy loss spectroscopy in the electron microscope.Plenum Press, New York, 2nd edition edition, 1996.

[2] R. Schneider, J. Woltersdorf, and O. Lichtenberger. Phase identificationin composite materials by EELS fine- structure analysis. Journal of Mi-croscopy, 183:39–44, 1996.

[3] H. Gu. ELNES separation in spatially-resolved analysis of grain boundariesand interfaces. Ultramicroscopy, 76(4):159–172, 1999.

[4] P. Buseck, J. Cowley, and L. Eyring. High-Resolution Transmission ElectronMicroscopy and associated techniques. Oxford University Press, New York,1988.

[5] W. E. McBride, D. G. Mc Culloch, D. R. McKenzie, and D. C. Green. Plas-mon dispersion measurements in the electron microscope: Application tocarbon solids. Micron, 29(1):1–5, 1998.

[6] Z. L. Wang, J. Bentley, and N. D. Evans. Mapping the valence statesof transition-metal elements using energy-filtered transmission electron mi-croscopy. Journal of Physical Chemistry B, 103(5):751–753, 1999.

[7] P. A. Midgley. A simple new method to obtain high angular resolution ω-qpatterns. Ultramicroscopy, 76(3):91–96, 1999.

[8] J.J. Sakurai. Modern quantum mechanics. Addison Wesley, 2nd edition,1994.

[9] H. Bethe. Zur Theorie des Durchgangs schneller Korpuskularstrahlen durchMaterie. Annalen der Physik, 5:325–400, 1930.

[10] M. Nelhiebel, P. H. Louf, P. Schattschneider, P. Blaha, K. Schwarz, andB. Jouffrey. Theory of orientation-sensitive near-edge fine-structure core-level spectroscopy. Physical Review B, 59(20):12807–12814, 1999.

[11] P. Blaha, K. Schwarz, and J. Luitz. Wien1997, 1997.

[12] P. Blaha, K. Schwarz, P. Sorantin, and S.B. Trickey. Full-potential, lin-earized augmented plane-wave programs for crystalline systems. Comput.Phys. Comm., 59:399, 1990.

[13] G. D. Mahan. Many Particle Physics. Physics of Solids and Liquids. KluwerAcademic Publishers, 3rd ed edition, 2000.

24 1.3. Bibliography

Chapter 2

Why EELS: comparison with otherspectroscopic techniques

In this chapter, a comparison is made between techniques to study the in-ternal chemical and electronic structure of samples on a nanoscale. All studiesdescribed are of the transmission type1. A classification will be made with respectto the primary particles and the detected particles. It will be shown that EELSis the technique of choice for studying nanoscale structures. A more elaboratecomparison will be made with X-ray-absorption-spectroscopy (XAS) because ofthe possibility to compare EELS results with experimental XAS results of bulkmaterials. In table 2.1 an overview of different techniques is given with roughestimates of energy scale, resolution and beam size.

2.1 Primary particles

Three elementary particles are commonly used for transmission type experi-ments in solid state physics: X-ray photons, neutrons and fast electrons. The mainadvantage of electrons over neutrons or photons is the fact that electrostatic and/ormagnetic interactions can be used to control the trajectory. By analogy with lightoptics it is possible to construct electron-optical lenses, with the added advantagethat by adjusting electric fields or currents the optical elements become tunable.The “optical” elements in neutron or photon experiments are made by using scat-tering interactions with matter making them a lot less flexible. This makes elec-trons ideal to focus into a beam of small diameter which can be positioned overthe sample. Beam diameters of ≈ 0.2 nm are available in commercial electronmicroscopes. To avoid scattering and absorption, vacuum conditions are neededaround the electron optical path. Electrons interact strongly with matter making

1The primary particles are transmitted through the sample

25

26 2.2. Detected particles

them preferable over X-rays and certainly neutrons for studying small regions.The drawback of this strong interaction is possible damage of the sample and therequirement for extremely thin samples (typ. 20 nm) to ensure transparency. Elec-trons can be used to make images in electron microscopes. The combination ofimaging and chemical characterization is crucial for nanoscale analysis, becauseit enables to characterize the crystal structure and observe the overall morphol-ogy of the sample before making chemical investigations on selected areas. Adrawback of electrons is the fact that they are fermions. This makes it difficult tocreate small probes of monochromatic electrons with high current density2. Elec-trons carry a lot more momentum for the same energy compared to photons. Thismakes them more suitable to probe excitations with k = 0. Another difference be-tween X-rays and electrons is the fact that electrons are scattered by the coulombpotential, while X-rays are scattered by the electron and core density.

2.2 Detected particles

When primary electrons hit the sample, several inelastic interactions can oc-cur and will give information on the sample. Secondary electrons ejected froman atom inside the sample can be detected. The disadvantage is that they canbe re-absorbed by the specimen. X-rays can be emitted when a core hole is cre-ated by the primary electrons. An occupied state of the atom can then fall backto the empty core state exciting an X-ray photon of specific energy. Detectionof these X-rays is done by a semiconductor detector which enables to count thenumber of photons and their energy. This technique is known as energy dispersiveX-ray spectroscopy (EDX). The spectrum contains element-specific peaks at thecharacteristic energies which can be automatically quantified. EDX is not suit-able for detecting light elements because of the so-called window which separatesthe vacuum in the microscope column from the detector. X-rays are emitted as aspherical wave and only a small part of them is captured in the solid angle of thedetector, this makes the sensitivity for light elements lower compared to EELS.Detecting the primary electrons and measuring their energy loss was already de-scribed as EELS. Inelastic electrons are strongly forward scattered which has twoadvantages. First, we can collect a large part of the electrons in a small aperture,effectively using the whole cross section. This increases sensitivity. The secondadvantage is that the chance for an electron to scatter a second time within an areasome distance from the original scattering location is greatly reduced and the ex-pected resolution of this technique is higher than for EDX or secondary electrons.

2This would require all electrons to be in the same quantum mechanical state like in a conven-tional photon laser

Chapter 2. Why EELS: comparison with other spectroscopic techniques 27

2.3 Absorption vs. emission

There is a fundamental difference between techniques probing the absorptionof particles and techniques probing the emission of particles. EELS belongs tothe absorption spectroscopies and was shown to probe the unoccupied DOS sinceabsorption can only happen when a state in the sample is excited to a higher lyingstate which has to be unoccupied. Emission spectroscopies on the other hand,probe the occupied DOS because an electron from a certain state can only beejected from that state when the state is occupied.

2.4 XANES vs. ELNES

In this section, a comparison is made between X-ray absorption near edgespectroscopy (XANES) and ELNES. This comparison is important when experi-mental EELS work is to be compared to published results from bulk XANES mea-surements. XANES studies the fine-structure in XAS spectra. XAS is performedby measuring the absorption of an energetic X-ray in a sample as a function ofthe monochromatic primary X-rays. The monochromatic X-rays are made from a“white” X-ray source by putting an adjustable monochromator between the sourceand the sample. X-rays are mainly absorbed by the emission of a photoelectron.The cross section for this interaction is proportional to [1]:

dσdE

∝ |〈n|eik·rε · r|0〉|2δ (E −E f +Ei) (2.1)

With k the momentum of the primary photon and ε the polarization direction ofthe electric field. E the energy loss, E f the energy of the emitted secondary particleand Ei the ionization energy. In the dipole approximation for k · r 1 this thenbecomes:

dσdE

∝ |〈n|ε · r|0〉|2δ (E −E f +Ei) (2.2)

Which is equivalent with the EELS expression in the dipole approximation:

dσdE

∝ |〈n|q · r|0〉|2δ (E −E f +Ei) (2.3)

The momentum transfer vector in ELNES fulfils the same function as the polar-ization vector in XANES results. In the dipole approximation, both ELNES andXANES give rise to similar results, proportional to the local unoccupied symme-try projected density of states. This makes it possible to compare experimentalresults of both techniques taking into account the difference in instrumental en-ergy resolution and deviations from the dipole approximation.


technique sample source detector comments(B, T or G)a (energy) ∆E=resolution φ = beam size

electron electronEELS T 100 keV - 1 MeV 1 eV (LaB6) φ ≥ 0.2 nm

0.7 eV (Schottky FEG)0.3 eV (cold FEG)

AES B or T 2-30 keV ≈ 1% of Auger energy surface

photon photonXAS T 2-5 keV ∆E/E = 14×10−5 φ > 1 mm b

100-1500 eV c ∆E/E > 2×10−4

PL B grating grating φ > 1 µm

electron photonEDS T 100 keV - 1 MeV ∆E ≈ 150 eV φ > 0.2 nm

photon electronUPS B E=21eV 50meV surface φ > 1 mmXPS B or G E=1.5 keV 0.25 eV

neutron neutronINS B 10-200 eVd < 10 meV φ > 0.01 m

Table 2.1: Overview of different spectroscopic techniques with their acronyms (for expla-nation see the list of abbreviations on p.E-29) and rough estimates on energy, resolutionand beam size. Partly from Buseck et al. [1]

aBulk, Thin film, GasbExperiments with fresnel zone plate make φ < 1 µm possiblecBeamline I5-11 Upsalla University SwedendBT4 Filter analyzer spectrometer at NIST center for Neutron Research, USA

Bibliography


Chapter 3

Experimental setup

3.1 Spectrometer design

The spectrometer used for experiments in this work is the Gatan Imaging Fil-ter (GIF). It is a so-called post-column filter because it can be mounted belowan existing TEM microscope, without altering the optical elements of the micro-scope. Other filter topologies include the Castaing Henry and Omega filter whichare in-column filters. These spectrometers have to be placed in the optical pathof a TEM. In the next section the GIF operation is described. For other filtertopologies and more technical details see [1].

3.1.1 GIF

Fig. 3.1.1 shows a schematical overview of a Gatan Imaging Filter (GIF) [2].This spectrometer can be mounted under the microscope column, which has theadvantage that no changes in the optical path are necessary, and the normal mi-croscope mode is left unaltered. The GIF can work in both spectroscopy (EELS)and energy filtered (EFTEM) mode. Electrons of the microscope enter the GIF viathe entrance aperture which serves as a cutoff for high angle scattered electronsin diffraction mode. In image mode, the largest aperture is used. After passingthe entrance aperture, the electrons move to the magnetic prism, consisting of anarc shaped electromagnet. This magnet creates a uniform magnetic field whichbends the path of the electrons depending on their momentum. Inside the mag-netic prism, the electrons travel in a non-magnetic tube, which passes the magneticfield and enables us to cause an extra acceleration of the electrons by putting a pos-itive potential on the tube. This tube is called the drift tube. The bending radiusof the electrons in the magnetic prism will be determined by the strength of themagnetic field in the prism and the voltage applied to the drift tube. By passing

29

30 3.2. Operation modes

Figure 3.1: Schematic overview of the Gatan Imaging Filter (taken from ref. [1]).

the magnetic prism, the electrons are energy dispersed in the plane of the energyselecting slit. The slit consists of two plates with straight, sharp edges. One of theplates is fixed and the other one can be moved by a piezoelectric transducer. Theopening of this slit determines which electrons will be selected to contribute to anenergy filtered image. The opening of the slit is described as the slit width ∆ (eV).For the EELS mode, the slit is wide open to enable all electrons in the spectrum tobe captured. Behind the slit, a set of quadrupole and sextupole lenses magnify theimage in the slit (for EELS mode) or the image at the entrance aperture (EFTEMmode) to cover the CCD or the retractable TV-rate camera. To convert the fastelectrons to photons a fibre optic scintillator is used. The CCD data are stored ona computer for further processing.

3.2 Operation modes

The two operation modes of the GIF (EELS or EFTEM) can be combined withthe two operation modes of the microscope (image or diffraction mode) to get 4basic operation modes of the whole system:

EELS in diffraction mode Microscope in diffraction mode, spectrometer in EELSmode. The detector captures an EELS spectrum.

EELS in image mode Microscope in image mode, spectrometer in EELS mode.The detector captures an EELS spectrum.

EFTEM Microscope in image mode, spectrometer in EFTEM mode. The detec-tor captures an energy selected image.

Energy filtered CBED Microscope in diffraction mode, spectrometer in EFTEMmode. The detector captures an energy selected diffraction pattern.

Chapter 3. Experimental setup 31

These four basic modes will be briefly described in the next four sections. For amore detailed description of the operation modes see Reimer et al. [3].

3.2.1 EELS in diffraction mode

This mode is the most useful mode to acquire EELS spectra. The opticalpath is shown schematically in fig. 3.2. The viewing screen of the microscopecontains a diffraction pattern. The entrance aperture of the spectrometer passes allelectrons up to the collection angle, β . The knowledge of this angle is importantfor comparison of experimental spectra with theory. The angle is shown on fig. 3.2and is determined by the size of the entrance aperture and the camera length. Itcan be calibrated from samples with known lattice parameters. The so-calledconvergence angle α is determined by the condenser aperture and the beam sizeon the sample. For a focussed probe, the convergence angle can be calibrated fromknown samples by measuring CBED discs in the diffraction plane and comparingthem to the distance between known Bragg spots. The energy dispersive planeof the spectrometer at the slit position is then magnified to the CCD detector.The magnification determines the energy-dispersion expressed in eV/pixel on theCCD. Choosing a high dispersion gives a detailed view of the EELS spectrumat the expense of lower count values because the same amount of counts has tobe divided over more pixels. The energy axis in the spectrum on the CCD can beshifted by the drift tube voltage, the strength of the magnetic prism or by changingthe high tension of the microscope. The main advantage of this mode is the factthat the angles are well defined and comparison with theory is possible. Therefore,this is the mode of choice for quantitative EELS.

3.2.2 EELS in image mode

The spectrometer is in EELS mode while the viewing screen of the microscopecontains an image. The entrance aperture then selects a part of that image whichwill be EELS analysed. The collection angle is determined by the objective aper-ture. Because of the difference in trajectory of the elastic vs. inelastic electrons,the entrance aperture is not an accurate way of selecting a region in the specimen.Moreover, the angles are not well defined, especially not if no objective apertureis inserted. This mode is however, the easiest to align and can be used for quickinspection of a sample.

3.2.3 EFTEM mode

In EFTEM mode, the microscope viewing screen contains an image and thespectrometer is in energy selected imaging mode. An overview of this situation is

32 3.2. Operation modes

Figure 3.2: Microscope and spectrometer optical path in diffraction-EELS mode


given in fig. 3.3. The image is cut-off by a large entrance aperture and the energyslit selects electrons in a range E ± ∆

2 . The electrons are passed through the lensesof the spectrometer to form an image at the detector plane. The collection angleβ is determined by the objective aperture. The convergence angle α is usuallysmall and is determined by the condenser aperture and the beam convergence onthe sample. This mode is suitable for EFTEM imaging.

Since the alignment of the microscope depends on the electron energy, thehigh tension of the microscope is altered from E0 to E0 + E for the acquisitionof an image corresponding to an energy loss E. In this way, the alignment of themicroscope remains valid for the inelastic images made up of electrons with anenergy E0 +E −E = E0.

3.2.4 Energy filtered CBED

When a CBED diffraction pattern is present on the viewing screen, and thespectrometer is in EFTEM mode, energy filtered diffraction patterns can be recorded.This can be useful to study the angular distribution of scattering from the sampleas function of energy. It is also useful to filter any unwanted energies from aconventional CBED pattern, greatly increasing the visibility of the characteristiclines.

3.3 Imperfections of the spectrometer

Knowledge of the non-ideal behaviour of the spectrometer is important to un-derstand the limitations and possible errors while doing experiments. Having agood knowledge of the peculiarities of the spectrometer will help to get better andmore reliable data out of the system. Some interesting ideas on the performanceof current and experimental microscopes can be found in [4–10]

3.3.1 PSF of the CCD

The scintillator and CCD system are characterised by a point spread func-tion (PSF). This function describes how a perfect point at the entrance plane isrecorded by the CCD. We know from linear system theory that an arbitrary imagewill be convoluted with this PSF to get a blurred version of the original image.For our GIF 2000 system, the PSF was measured to have a full width at half maxi-mum of about 2.2 pixels [11]. Knowing this, it is best to choose the magnification(EFTEM or TEM mode) or dispersion (EELS mode) slightly higher than wouldbe necessary from applying the sampling theorem (i.e. take the pixel size at leasthalf of the period of the highest frequency expected in the image).

34 3.3. Imperfections of the spectrometer

Figure 3.3: Microscope and spectrometer optical path in EFTEM mode


3.3.2 Energy resolution and stability

The energy resolution is of importance for EELS work. It is normally definedas the full width at half maximum of the zero loss peak. The shape of the zero losspeak, when no sample is present is a good measure for how the system would reacton a perfect dirac-delta peak in the spectrum. The spectrum can be thought off asa perfect spectrum blurred by the instrument broadening function. The sources ofthis broadening are:

• The incoming electrons being not monochromatic. Partly because of insta-bilities in the high tension (instability in the electronics of the HT powersupply), partly because of the thermal broadening in the field emission gunand partly because of electron-electron interactions in the beam (Boerscheffect).

• Spherical abberation in the GIF will focus the EELS spectrum dependingon the incoming scattering angle. Limiting this angle with the entranceaperture helps.

• The PSF of the CCD system will further broaden the peaks in the spectrum.Choose the dispersion high enough to avoid energy resolution deteriorationdue to the PSF of the CCD.

• Fluctuations in the current of the magnetic prism and the voltage of the drifttube cause a drifting of the peak positions during spectrum acquisition.

The main limiting factor, when choosing the right setup for the spectrometer isthe energy spread of the gun. For a Schottky FEG this can be typically 0.7 eV.Instabilities in the electronics (high tension, drift tube, magnetic prism current)make this number worse. Long term drifts in the electronics will make spectrawith longer exposure times (30s to a few minutes) have a worse energy resolutionthan spectra taken at very short exposure times (milliseconds to seconds). Anenergy drift of as high as 10 eV/hour was measured on our system.

3.3.3 Specimen drift

Specimen drift is especially problematic for high resolution EFTEM. Becauseof the long exposure times required to get enough counts in the EFTEM images(typically > 10 s), the drift performance of the microscope should be as good aspossible. Making an EFTEM map with an exposure time of 60 s and a resolutionrequirement of 1nm, the drift should be smaller than 1 nm/min at least. Modernmicroscopes claim a guaranteed drift performance of 1 nm/min or 0.5 nm/minwhen factory fine-tuned. Clearly these numbers are still putting limits on thepossibilities of high resolution EFTEM.

36 3.3. Imperfections of the spectrometer

3.3.4 Probe stability

When working with a focussed probe to perform EELS of a small area of thesample, the stability of the probe is a crucial factor. Stray magnetic fields andinstabilities in the power supplies of the microscope can affect the probe position.

3.3.5 Stray magnetic fields

The magnetic prism of the spectrometer is sensitive to the magnetic environ-ment close to the spectrometer. Metal operator chairs can influence the positionof the peaks in an EELS spectrum by as much as 3eV! Other sources of magneticfields are computer monitors, pumps, ground loops etc.

3.3.6 Temperature of the room

The GIF electronics was shown to be sensitive to temperature fluctuationsin the room causing a change in the current of the magnetic prism and therebychanging the energy position in an EELS spectrum. A sensitivity estimate of -6eV/C was found. The recommended temperature stability of ± 0.1 C from themanufacturer makes this value reasonable but still high for exact determination ofedge positions.


Bibliography


[2] O. L. Krivanek, A. J. Gubbens, N. Dellby, and C. E. Meyer. Design and firstApplications of a Postcolumn Imaging Filter. Microscopy MicroanalysisMicrostructures, 3(2-3):187–199, 1992.

[3] L. Reimer, I. Fromm, and R. Rennekamp. Operation Modes of ElectronSpectroscopic Imaging and Electron Energy-Loss Spectroscopy in a Trans-mission Electron-Microscope. Ultramicroscopy, 24(4):339–354, 1988.

[4] L. M. Brown. A Synchrotron in a Microscope. In Electron Microscopy andAnalysis 1997, Proceedings of the Institute of Physics Electron Microscopyand Analysis Group Conference, pages 17–22, University of Cambridge,1997.

[5] H. Rose. Prospects for realizing a sub-angstrom sub-eV resolution EFTEM.Ultramicroscopy, 78(1-4):13–25, 1999.

[6] A. J. Gubbens, B. Kraus, O. L. Krivanek, and P. E. Mooney. An Imaging Fil-ter For High-Voltage Electron-Microscopy. Ultramicroscopy, 59(1-4):255–265, 1995.

[7] H. Hashimoto, Y. Makita, and H. Endoh. Characterization of thin film ma-terials by 400 kV electron microscope images and with an energy filter. Ma-terials Chemistry and Physics, 46(1):7–14, 1996.

[8] H. W. Mook and P. Kruit. On the monochromatisation of high brightnesselectron sources for electron microscopy. Ultramicroscopy, 78(1-4):43–51,1999.

[9] D. W. McComb and G. C. Weatherly. The effect of secondary electronsgenerated in a commercial FEG-TEM on electron energy-loss spectra. Ul-tramicroscopy, 68(1):61–67, 1997.

[10] D. Muller. private communications, 2001.

[11] P. Geuens. private communications, 2002.

Chapter 4

Quantitative EELS

Conventional quantitative EELS requires several steps in the conversion froman EELS spectrum to concentrations of chemical elements. First, the non-specificbackground has to be removed. The effect of multiple inelastic scattering1 must beremoved to compare the edge with theoretical models where only single scatteringis taken into account. Finally the strength of the edge has to be converted to achemical concentration by making use of an appropriate expression for the cross-section. All these steps will be treated in the following section.

Later sections will deal with an alternative to this conventional quantificationscheme: a model-based approach. In this approach, a parametric model, describ-ing the expectation values of the EELS observations, has to be derived. The un-known parameters are estimated/measured by fitting this model to the experimen-tal spectrum, using a criterion of goodness of fit. Parameters in these models arefor example chemical concentrations, but the exact energy-onset of a certain edgeor fine-structure changes can be taken as parameters as well.

If one would repeat this measurement several times, one would, due to thestatistical nature of the experiment, find slightly different values for the parameterestimates, which are statistically distributed around the exact value. The varianceof this distribution, or the standard deviation2, is then a measure for the precision.The final sections in this chapter deal with this statistical nature of the experimentand how they influence the highest attainable precision and the minimum detectionlimit in a given experiment. It will be shown that the counting statistics of theinelastically scattered electrons will indeed put fundamental limits to precisionand detectability.

1The primary electron undergoes more than one (inelastic) scattering event2Defined as the square root of the variance

39

40 4.1. Conventional EELS quantification

Figure 4.1: Overview of the different steps in conventional quantitative EELS analysis.EELS spectrum in the low loss energy range (A) and in the core loss energy range (B)showing the O K-edge and the Mn L2,3-edge of a sample of KMnO4 powder together withthe non-specific background. The background is removed by a standard LMS procedure.The background fitting region is indicated (B) together with the extrapolated background(dotted). The resulting Mn L2,3-edge with background removed (C) shows the typical L3and L2 white lines. Removing multiple scattering is done via the fourier-ratio method (D)making use of the low loss spectrum and the background removed Mn edge. Note that themultiple scattering correction removes the blurred repetition of the strong white lines atmultiples of the plasmon energy from their original position, reducing the cross section atenergies above the white-lines.

4.1 Conventional EELS quantification

The different steps required for conventional EELS quantification of a spec-trum are: background removal, multiple scattering removal, and conversion tochemical concentrations. They are schematically shown in fig. 4.1 and will bedetailed in this section.

4.1.1 Background removal

To separate the element-specific excitation from the non-specific backgroundcoming from the tails of all preceding edges, we have to subtract an estimate of thebackground contribution under the edge. We can only estimate this backgroundby extrapolating a model, fitted in the region preceding the edge, into the edge-

Chapter 4. Quantitative EELS 41

containing region. A commonly used model for the background is:

F(E) = AE−r (4.1)

with two parameters (A,r) to be estimated by fitting the model to the experimentin the fitting region. The conventional way to estimate these parameters is byconverting the experimental spectrum to a log(E), log(I) scale and then using theformulas for a least mean squares (LMS) fitting of a straight line. Two assump-tions are made in this step:

• The noise statistics of each pixel in the spectrum is assumed normal. Thiscan be justified by noting that the Poisson counting statistics approaches anormal distribution for a high number of counts.

• The log-log transformation of the axes does not change the noise statistics.This is a questionable assumption because of the non-linearity of the trans-formation. In reality the transformation introduces a bias due to the fact thatthe normal distribution becomes asymmetric after taking the logarithm.

The assumptions will lead to higher errors than necessary and can lead to a biasedestimate of the background under the edge. For a statistically more correct treat-ment using Poisson statistics and Maximum Likelihood estimation techniques, seeUnser et al. [1]. In principle it is advantageous to take the fitting region as wideas possible and as close as possible to the edge onset [2]. In practice however, themodel for the background does not describe the real background very well, so it isadvisable to limit the fitting regions to reasonable values, like 20 eV, close to theedge onset. For low energy excitations (regions below 100 eV) different modelsfor the background, such as exponentials or polynomials, might give a better fit.Since the background model has only two parameters, two experimental inten-sities in the fitting region are required to estimate them. This method is knownas the two-area method [3] and will be used in the EFTEM three-window tech-nique in chapter 5. The main problem with background removal is the fact thatwe have to extrapolate a model for which we have no (or little) physical justifi-cation [4] and which can be shown to fail for real experiments over large regions.The background-removal step is therefore the most accuracy-limiting3 step in thequantification of EELS spectra. The following rules of thumb give advise on howto limit the errors to reasonable values:

Rule of thumb 5 Choose the fitting region close to the edge onset, but makesure to avoid the region where the edge already creates a deviation from thebackground.

3Indeed, taking a bad model introduces systematic errors which bias the result. This limitsthe accuracy of the technique in contrast to the precision dictated by the variance of the resultsstemming from the statistical nature of the experiment.


Rule of thumb 6 Choose the fitting region as wide as possible but avoidregions with a clear deviation from the background model (e.g. precedingedges). Generally a width of 20-40eV separated 5-10eV from the real onsetworks well.

Rule of thumb 7 Make sure to capture spectra with high count numbers.This makes background removal more precise. If you have noisy spectra,consider using statistically more correct methods like Maximum-Likelihoodfor Poisson statistics, they will give an unbiased result even under very noisycircumstances.

Several authors [1–3,5–7] give estimates of the errors of background removal as afunction of position and width of the fitting region compared to different statisticalassumptions. The main limitation, however, remains the fact that the “real” modelfor the background is unknown.

4.1.2 Multiple scattering removal

In the theoretical introduction on EELS, we described the inelastic scatteringby a single scattering event. In reality, however, multiple scattering can occur. Aprimary electron can, for instance, excite a plasmon followed by a core loss ex-citation. The possibility of multiple scattering makes an experimental spectrumdifficult to interpret and to compare with theory. Therefore we would like to re-move the effect of multiple scattering from the spectrum. Two ways of treatingexperimental data are known as fourier-log deconvolution and fourier-ratio decon-volution [3].

Fourier-log deconvolution

The fourier-log method is used for low loss spectra containing the zero-losspeak4 and different plasmon peaks. It makes use of the consideration that theprobability for exciting one, two, three or more plasmons is given by a Poissondistribution, taking into account the mean-free path for plasmon excitations byprimary electrons. An analytical expression for the effect of multiple scatteringcan be deduced from these arguments and leads to an expression for the singlescattered spectrum as a function of the multiple scattered spectrum and the shapeof the zero-loss peak [3].

S(E) = I0F−1[ln(

F [J(E)]F [Z(E)]

)] (4.2)

4Energy distribution of the primary electrons without interaction with a sample


with F and F−1 the Fourier and inverse Fourier transform. J(E) is the multi-ple scattered experimental spectrum and Z(E) the zero-loss peak. I0 is the totalintensity under the zero loss peak. Z(E) can be acquired experimentally or canbe separated from the low loss spectrum by fitting its shape to a model and ex-trapolating it. The problem with equation 4.2 is the so-called noise-amplification.Fourier components of Z(E) decrease for higher frequencies and make the ratioF [J(E)]F [Z(E)] very sensitive to high-frequency noise in J(E). This can be solved byfiltering out this high-frequency noise at the expense of loosing the ability of acomplete deconvolution of the spectrum. Implementation of equation 4.2 on acomputer makes use of the discrete fourier transform which assumes a periodicinput signal. This assumption can lead to spurious high-frequency artifacts. Thelimitations of the fourier-log method for experimental work can be summarizedas follows:

• The spectrum should contain a zero-loss peak, it only works on so-calledlow-loss spectra.

• The assumption on the Poisson distribution of the plasmons does not nec-essarily hold for experimental work. For a more accurate description takinginto account the angular distribution of multiple scattered low-loss eventssee Su et al. [4].

• Use of discrete fourier transforms can lead to spurious artifacts in the de-convoluted spectrum.

All these limitations make the fourier-log method of limited use for core-loss ex-citations. It is advisable to check the deconvoluted spectra with spectra from verythin regions of the sample (little multiple scattering).

Fourier-ratio deconvolution

The fourier-ratio method is a more general technique usable for core-loss spec-tra and can be explained by viewing a multiple scattered spectrum as a single scat-tered spectrum convoluted by the low-loss spectrum as is schematically drawn infig. 4.2. Deconvolution can then be described by:

S(E) = I0F−1[F [J(E)]F [L(E)]

](4.3)

With L(E) the low-loss spectrum including the zero-loss peak and the plasmonpeaks (Z(E) only contained the zero-loss peak). Again the problem of noise-amplification limits us to completely deconvolute the experimental spectrum J(E)to an ideal S(E), corrected for multiple scattering and the instrumental broadening


Figure 4.2: Schematic overview of multiple scattering as a convolution of a single scat-tered excitation S(E) with a low-loss spectrum L(E) to obtain the multiple scattered spec-trum J(E)

caused by the finite energy resolution of the spectrometer. This problem can besolved by filtering out the noisy high-frequency components. The discrete fouriertransform can again lead to spurious artifacts and make this technique sensitive tothe exact implementation on a computer. It is advisable to compare the deconvo-luted spectra with spectra taken from very thin regions where multiple scatteringis less of a problem. In general, this technique works reasonably well for sampleswith a thickness t

λ < 1 ( with t thickness and λ the mean free path for a plasmonin the sample) or for a plasmon peak intensity in the low-loss spectrum roughlysmaller than 10% of the zero-loss intensity. The requirement to have a zero-lossspectrum creates a difficulty for experimental work. Because of the large differ-ence in zero-loss intensity and the intensity in a core-loss spectrum, we need torecord the low-loss spectrum and the core-loss spectrum with completely differentexposure times. Because of a limitation in the minimum exposure time5, one isplaced for the contradictory requirement of decreasing intensity to record the lowloss spectrum and increasing it to limit core-loss exposure times to reasonable val-ues. Improvements in the spectrometer shutter system to decrease the minimumexposure time would be helpful.

4.1.3 Conversion to chemical concentrations

After background removal and removal of multiple scattering, we can convertthe edge intensity in an energy interval Estart −Estop into a number of atoms byusing the appropriate single-atom cross-section σ for this energy range and solid

5Caused by dynamic effects in the shutter system of the spectrometer. For the Gatan ImagingFilter ≈ 10ms


angle A determined by the collection aperture.

σ =∫ Estop

Estart

∫A

dσdEdΩ

dEdΩ (4.4)

The total intensity under the edge is then by definition of the cross section:

I = I0σN (4.5)

with I0 the total number of primary electrons in the exposure time interval andN the number of atoms of the type which caused the edge in the interaction vol-ume, that is, the volume in the sample where primary electrons interacted with thesample. An absolute quantification is possible in this way.

In practice, however, several factors are generally unknown. The interactionvolume depends on the thickness of the sample and on the beam diameter on thesample, while I0 depends on the beam current and on exposure time. To cancelout these unknown or inaccurately known variables we can proceed by comparingtwo different elements in the sample. This then gives a relative concentration mea-surement which is independent on thickness, beam diameter and primary currentas shown in the next equation for two elements labelled A and B:

IA

IB=

σANA

σBNB=

σACA

σBCB=

CA

CBkAB (4.6)

with CA and CB the volume concentrations of elements A and B and kAB the ra-tio of the cross sections for edge A and B. This ratio is generally known as thek-factor and can be calculated from models for the cross-sections or it can beexperimentally derived from reference samples. The k-factor is dependent on col-lection angle and primary voltage and is therefore microscope dependent!

4.1.4 Conclusion

A number of operational parameters (fitting region, energy integration regionetc.) have to be chosen with a “looks good by eye” criterion. The accuracy ofthe quantification can strongly depend on these parameters and one should notexpect it to be better than ≈ 10% from this treatment, especially not if calculatedcross-sections are used or when comparing two regions of the sample with a con-siderable change in thickness or orientation.

4.2 Alternative model-based EELS quantification

Instead of removing background and multiple scattering for quantification ofan EELS spectrum, we can also use a model-based approach. In this way of

46 4.2. Alternative model-based EELS quantification

working, a parametric model, describing the expectations of the EELS observa-tions, has to be derived. The unknown parameters, such as concentrations, type ofelements and energy onset of the edges, are estimated by fitting this model to theexperimental spectrum, using a criterion of goodness of fit, such as for examplemaximum likelihood. Maximizing the likelihood results into parameter estimatesthat are most likely to have led to a given experimental spectrum. If the modelis correct6 and no measurement errors are present, the deviations from the “real”(inaccessible) parameters are caused by the counting statistics during the mea-surement process. This puts a fundamental limit on the precision with which onecan learn something from an EELS experiment having a finite number of collectedinelastic electrons. It also puts a limit to the minimum detectability of a certainelement in EELS if the uncertainty due to counting statistics prohibits us frommeasuring a concentration with a given precision. In this section, we outline theideas behind the model-based approach as also implemented in [7–9]. In contrastto these references however, the statistically more correct approach of maximumlikelihood is used and fundamental observations for precision and detectabilityare made.

4.2.1 Maximum Likelihood

If we regard reality as having a hidden parameter a, we can try to find outsomething about a by doing experiments. Unfortunately, the measurement onlygives us an estimate a because of the probabilistic nature of the measurement(counting statistics) and because of measurement inaccuracies. This idea is schemat-ically represented in fig. 4.3.

Because of the probabilistic nature of a measurement process we can notuniquely couple a to a but we can answer the question: ”which variable a wasmost likely to have led to this measured spectrum?”. This is what maximum-likelihood looks for. To use this, we need a model of the “probabilistic noise” inthe measurement and a parametric model describing the expectations of the mea-sured spectrum. To a good approximation, the observations are assumed to have aPoisson distribution7. For the model we need to know how the spectrum is relatedto internal parameters like concentrations of elements. How to build such a modelis detailed in the next section.

Now we try to find an expression for the probability that a certain experimentalspectrum w = [w0,w1, . . . ,wn] (n the number of energy bins (pixels) in the spec-trum) is created by a model with l parameters p = [p0, p1, . . . , pl]. Therefore, we

6If we regard nature as having a fixed set of rules behind it (physics) which enable us to predictthe outcome of an experiment (or the probability distribution)

7Modern detectors have close to single-electron counting capabilities


Figure 4.3: Schematic overview of the principle of a measurement in contrast to the hiddenreality

define the model for the spectrum fi as a function of the parameters p normal-ized to unity over the whole energy range ∑n

0 fi = 1. This fi can be viewed as thechance for finding a single electron in bin i at energy Ei when only one electron isscattered in the total energy range. Multiplying this quantity by the total amountof electrons N in the whole energy range gives:

λi = N fi = E(wi) (4.7)

with λi the expectation value for the number of electrons at Ei. This is also theexpectation value E(wi) for an experimental measurement wi. The probabilityP(w, p) for measuring a spectrum w = [w0,w1, . . . ,wn], given the parameters p ofthe model is equal to:

P(w, p) =n

∏i=0

λ wii

e−λi

wi!(4.8)

Which is for each pixel, a Poisson distribution around λi8. The total probability9 is

then the product of probabilities for each pixel. The maximum likelihood methodnow tries to maximize this probability by changing the parameters. In practice itis useful to convert equation 4.8 to a logarithm of the likelihood.

lnP(w, p) =n

∑i=0

[wi lnλi −λi − lnwi!] (4.9)

For the maximization with respect to the parameters p, we can leave out the lastterm since this is independent on p.

8If the observations are independent.9This function is called the joint probability density function of the observations.

48 4.2. Alternative model-based EELS quantification

4.2.2 How to build a model?

A reasonable model can be built from:

• A background part described by a model. The AE−r form is popular but isknown to fail for larger energy regions. We need a smooth monotonicallydecreasing function. A possible candidate is AE−r +BE−2r + . . . with more(physically meaningless) parameters.

• The excitation edges can be modelled by their differential cross-section dσdE

in a given collection angle. These can be calculated from hydrogenic mod-els, ab-initio calculations or they can even be replaced by experimental edgeshapes with a multiplication factor to represent their strength.

• The multiple scattering effect can be modelled by a convolution with anexperimental low-loss spectrum acquired with high accuracy. A theoreticalmodel for the low-loss spectrum is much more difficult than for a core-loss spectrum since plasmons, phonons, valence electrons, the physics ofthe electron gun, electron-electron interaction in the beam etc. can play animportant role. For an example fitting the multiple plasmon peaks see Dooret al. [9].

The typical parameters in a model include the concentration or number of atoms,the exact position of an excitation edge, background parameters etc. One shouldlook for a model which approximates reality reasonably well without increasingthe number of parameters too much.

4.2.3 EELSMODEL software

Working with a model-based approach requires a computer to calculate themodels and look for a maximum in the likelihood. The fitting starts from a goodguess of the parameters to finally reach those parameters which most likely ledto the recorded experiment. A software package called EELSMODEL was devel-oped in the C programming language to implement these ideas into a useful toolfor analyzing EELS spectra. A schematic overview of its function is shown infig. 4.4. A model can be built from different components and multiple scatteringcan be included by convoluting the model with an experimental low-loss spec-trum. An initial guess for the parameters has to be created by hand and then themaximum likelihood fitting can take over. Features of the package include:

• A model can be composed of different components to allow a maximumflexibility.


Figure 4.4: Schematic overview of the maximum likelihood fitting as implemented in theEELSMODEL package

• Excitation edge components can be modelled by hydrogenic cross-sectionsand/or edge shapes loaded from disk (allows any type of edge, also experi-mental edge shapes).

• Background model components including power-law, exponential and power-law + constant.

• Lorentzian and Gaussian functions can be used to model white lines or othersharp features in the spectrum.

• Automatic fit of a complete set of data after first fitting one spectrum byhand.

• Different fitting strategies: Least mean square (equals maximum likelihoodfor normal statistics) , weighted least mean square and maximum likelihoodfor Poisson statistics.

Fig. 4.5 shows the different model components in a model together with a con-verged fit of this model to the experimental data.

50 4.3. Limits to precision: Cramer Rao Lower Bound

Figure 4.5: Example of functionality of EELSMODEL: the different components in amodel together with a converged fit (green) of the model with the experimental data (red)

4.3 Limits to precision: Cramer Rao Lower Bound

The model-based approach enables us to study the precision and minimum de-tectability of quantitative EELS when assuming that we know the model behindthe experimental reality. Basically we want to know how the statistical nature ofthe experiment affects the precision of the parameter estimates. There are twoways to treat this problem. One way is to simulate a large set of synthetic spec-tra by adding statistical noise to a perfect model and then fit each of these withthe model (Monte Carlo method). Another way to is to make use of the so-calledCramer Rao Lower Bound (CRLB)10 [10,11] to answer this question numerically,without doing simulations. It will be shown that both approaches give approxi-mately the same answer but CRLB is computationally more efficient.

4.3.1 Monte Carlo versus CRLB

The Monte Carlo treatment can be regarded as a brute-force treatment. Asimulation of a large set of experiments is made and these synthetic experimentsare fitted to a model by maximizing the likelihood function for the given statistics.We find a set of estimated parameters p which will be randomly distributed aroundthe “real” parameters p if the number of observations asymptotically reaches in-

10This is a lower bound on the variance of any unbiased estimator of a parameter. An estimatoris said to be unbiased if its expectation is equal to the true value of the parameter. Stated differently,an unbiased estimator has no systematic error.


finity11. The variance of this set gives an idea on the expected deviation fromthe real parameters when only a single experiment is fitted to a model12. Thedisadvantage of the Monte Carlo approach is the time it takes to calculate and fithundreds of spectra.

An alternative to the Monte Carlo approach is the so called Cramer Rao LowerBound (CRLB). This puts a lower bound on the variance of any unbiased estimatorof a parameter. In the derivation of the CRLB, first the Fischer information matrixFp has to be derived. The elements Fpab

of the (l × l) matrix are defined as:

Fpab= −E

[∂ 2 lnP(w, p)∂ pa∂ pb

](4.10)

For the Poisson case we had an expression for P given in eq.4.9 so we can write:

lnP =i=n

∑i=0

[wi lnλi −λi − lnwi!] (4.11)

∂∂ pa

lnP =i=n

∑i=0

[wi1λi

∂λi

∂ pa− ∂λi

∂ pa] (4.12)

∂ 2

∂ pa∂ pblnP =

i=n

∑i=0

[wi[−

1λ 2

i

∂λi

∂ pa

∂λi

∂ pb+

1λi

∂ 2λi

∂ pa∂ pb]− ∂ 2λi

∂ pa∂ pb

](4.13)

For the expectation value E, we note that:

E(λi) = λi (4.14)

E(wi) = λi,since the expectations of the observationsare given by the model

(4.15)

So we get for the elements Fpabof the Fischer information matrix in the Poisson

case:

Fpab= −E(

∂ 2

∂ pa∂ pblnP) =

i=n

∑i=0

1λi

∂λi

∂ pa

∂λi

∂ pb(4.16)

The Cramer Rao Lower Bound (CRLB) is now obtained by inverting the Fischerinformation matrix. The following inequality is true for any unbiased estimator[10]

var(pi) ≤ (F−1p )ii (4.17)

With var(pi) the variance on the estimated parameter pi. It can be shown for themaximum likelihood estimator that it asymptotically reaches the CRLB limit for

11This property of a maximum likelihood estimator is called asymptotic normality.12Clearly, the error for a single fit can still be very far off and multiple experiments are therefore

advisable


a large number of observations13. In this sense, the ML estimator is the mostprecise. Applying these ideas to a real model for EELS will enable us to tellsomething about the fundamental limits of EELS quantifications.

4.3.2 Precision

Applying the CRLB or Monte Carlo technique, we can look at a simple modelfor an EELS spectrum and try to answer the question:”What is the maximumprecision obtainable from an EELS spectrum, given that we know the model ex-actly?”. The simplest model we can make is that of a power-law background withone excitation edge with cross-section σ(E). Multiple scattering is neglected forsimplicity. The model then becomes:

fi =1

N0

[A(

Ei

Ep)−r +Bσ(Ei)

](4.18)

with N0 a normalization factor so that the total sum of all fi is unity. The parameterr is explained in fig. 4.6. Ep is the position of the excitation edge, this makes surethat parameter A denotes the background intensity at the onset of the edge. Themodel contains three parameters A,B and r. Therefore, the Fischer informationmatrix becomes a 3x3 matrix:

Fp =

FpAAFpAB

FpAr

FpBAFpBB

FpBr

FprAFprB

Fprr

(4.19)

The elements of Fp must be calculated numerically since we have no analyticalexpression for σ(E)14. If we normalize σ(E) so that σ(Ep) = 1 we can define:

k =BA

(4.20)

as the signal/background ratio at the edge onset. The model is schematicallyshown in fig. 4.6. We are interested now in the relative error on B defined asBerr = σB/B with σB the standard deviation on the experimentally measured val-ues B. This gives the estimated error we make by taking B from an experimentrather than the real B. It says that in 68% (the B’s are normally distributed for alarge number of observations: asymptotic normality) of the cases the relative errorwill be smaller than Berr

15. This error will depend for a given A and r (mimicthe shape of a known experiment) on the total amount of electrons N in the whole

13This property is labelled asymptotic efficiency14We can use for example a hydrogenic cross section from appendix B15In 99.73% of the times the error will be smaller then 3Berr


Figure 4.6: Schematic overview of the simple three parameter model. The parameters Aand B are shown on the plot. The parameter r determines the steepness of the slope viathe AE−r function.

spectrum and on the signal/background ratio k. An example of such an analysisis given in fig. 4.7 where both the Monte Carlo and CRLB results are shown togive similar results. This experimentally justifies the use of the CRLB as a goodestimate of the error on the parameter estimation. It also shows how the maximumlikelihood estimator reaches the CRLB limit for a large number of observations(asymptotic efficiency).

A more elaborate calculation is then made with the CRLB method coveringthe range of dose and signal to background ratio commonly encountered in EELSexperiments and plotted in fig. 4.8. The proportionality is roughly given by Berr ∝

1√N

since B ∝ N and σB ∝√

N. For the exact numbers, the complete analysis isneeded.

4.3.3 Detectability

In practice, it is interesting to know what the minimum detectable concentra-tion of a certain element is, given a number of counts in the spectrum. In viewof the precision considerations the detectability is a subjective quantity becausewe know from the previous section that reducing the signal/background ratio (re-ducing the edge intensity while keeping the background constant) gives rise to adecreased precision. A more accurate question would be :”What is the minimumdetectable concentration if a certain precision is required”. Here we define an


Figure 4.7: Comparison of Monte Carlo (cross) and CRLB (line) results. The MonteCarlo results are calculated from a set of 200 simulated spectra for each datapoint in thegraph. The relative error on parameter B, Berr is plotted as a function of the total electroncount in the spectrum and the signal/background ratio k at the edge onset. Precisionsbelow 1% are predicted in most cases of experimental importance.

extreme case of detectability where we require that the relative error on the con-centration parameter Berr should be smaller than 100%. If we then keep A and rin the simple model constant, we can decrease B for a given N until we reach thislimit. The results for such a analysis are given in fig. 4.9. The figure gives an ideaof the minimal signal to /background-ratio that is required to detect an edge. Thenumber of atoms that corresponds to this limit can not be determined from thisplot, unless we know the primary current, the cross section for excitation and theexposure time. Ratio techniques can be used to cancel out some of these factors.

4.3.4 Practical limitations

The theoretical considerations showed that both precision and detectability de-pend on the total number of counts in the spectrum and are fundamentally limitedby counting statistics. In practice however, there are other sources of error whichprohibit us from reaching these fundamental lower boundaries of quantification:

• The models we use are never exact. The observed fine structure in excita-tion edges is very difficult to simulate and is dependent on the electronicstructure of the crystal. The shape of the background is unknown.

• Specimen preparation or oxidation of the specimen can create a thin layerof an unknown composition which will make the measured observation de-


−1.8 −1.6 −1.4 −1.2 −1 −0.8 −0.6 −0.4

6

6.5

7

7.5

8

8.5

log(k)

log(

N)

0.3

0.4

0.4

0.5

0.5

0.6

0.6

0.6

0.7

0.7

0.8

0.8

0.9

0.9

1

1

2

2

2

2

3

3

3

4

4

4

5

5

6

6

6

7

7

8

9

9

10

10

30

Figure 4.8: CRLB predictions for Berr in percent as a function of the logarithm of the totalelectron count in the spectrum and the logarithm of the signal/background ratio k at theedge onset.

viate from the ideal sample. This can be important for example for oxygen,carbon or nitrogen.

• The interaction of the primary electrons can damage the sample, changingits ideal composition or electronic structure. This should be checked bycomparing spectra with different exposure times from fresh areas of thesample.

• Multiple scattering is omitted in this simple model, but can be included asa convolution by the experimental low-loss spectrum. This introduces ofcourse also the counting errors in that spectrum.

• Elastic scattering can play an important role, especially when comparingtwo regions of a sample in different orientations. This effect is difficult tomodel unless a complete model of the primary electron waves through thesample is made, including both elastic and inelastic scattering.


Figure 4.9: Detectability plot as a function of log(k) and log(N) for and O K-edge at530eV with a power-law background (r=3.9) for a spectrum of 1024 energy-bins. A doseof 3× 108 electrons in the spectrum can detect an EELS edge with a signal/backgroundratio k > 3.2×10−4

In practice, these limitations can make the expected error at least an order of mag-nitude higher than the lower bound. Shuman et al. [12] have demonstrated thatthey could quantify experimentally small concentrations of Ca in a matrix of car-bon with a standard deviation of approximately 0.7 mmol/kg independent of theexact concentration. This amounts to a detectability of 1 Ca atom in a matrix of120.000 C atoms within a 100s exposure time16. The standard deviation on theresult is nearly independent on the small concentration, which can be understoodby the fact that the edge is small compared to the background. In that case, the to-tal dose is approximately the dose in the background alone. The effect of the doseon the standard deviation σ of quantification is much larger than the effect of thesignal/background ratio in this case. Calculation of the CRLB for a comparablesetup, gives approximately σ=0.5 mmol/kg or 30% better than the experiment.This shows that in very carefully conducted experiments, the CRLB can be ex-perimentally approached. It also shows the value of the lower bound: a target foroptimizing the experimental and data-treatment techniques to be able to make fulluse of the information in a spectrum.

16Or 3 Ca atoms in 120.000 C atoms when a 3σ confidence interval is used


Bibliography

[1] M. Unser, J. R. Ellis, T. Pun, and M. Eden. Optimal Background Estimationin EELS. Journal of Microscopy, 145:245–256, 1987.

[2] T. Pun, J. R. Ellis, and M. Eden. Optimized Acquisition Parameters andStatistical Detection Limit in Quantitative EELS. Journal of Microscopy,135:295–316, 1984.


[4] D. S. Su and E. Zeitler. Background Problem in Electron-Energy-Loss Spec-troscopy. Physical Review B, 47(22):14734–14740, 1993.

[5] D. R. Liu and L. M. Brown. Influence of Some Practical Factors OnBackground Extrapolation in EELS Quantification. Journal of Microscopy,147:37–49, 1987.

[6] R. F. Egerton. A Revised Expression For Signal Noise Ratio in EELS. Ul-tramicroscopy, 9(4):387–390, 1982.

[7] T. Pun, J. R. Ellis, and M. Eden. Weighted Least-Squares Estimation ofBackground in EELS Imaging. Journal of Microscopy, 137:93–100, 1985.

[8] T. Manoubi, M. Tence, M. G. Walls, and C. Colliex. Curve Fitting Meth-ods For Quantitative-Analysis in Electron- Energy Loss Spectroscopy. Mi-croscopy Microanalysis Microstructures, 1(1):23–39, 1990.

[9] R. Door and D. Gangler. Multiple Least-Squares Fitting For QuantitativeElectron- Energy-Loss Spectroscopy - an Experimental Investigation UsingStandard Specimens. Ultramicroscopy, 58(2):197–210, 1995.

[10] A. Van Den Bos and A. Den Dekker. Resolution Reconsidered-ConventionalApproaches and an Alternative. In P.W. Hawkes, editor, Advances in Imag-ing and Electron Physics, volume 117, pages 242–291. Academic Press, SanDiego, 2001.

[11] S. Van Aert. private communications, 2002.

[12] H. Shuman and A. P. Somlyo. Electron-Energy Loss Analysis of Near-Trace-Element Concentrations of Calcium. Ultramicroscopy, 21(1):23–32, 1987.

Chapter 5

EFTEM

5.1 Introduction

In this chapter, the technique of obtaining images of specific elements , so-called elemental maps, will be explained. The basic principles will be outlined inthe first section, while a more elaborate discussion on the image formation in thesecond section is needed to address the spatial resolution of this technique. Thispart is important to decide which apertures to use and how to interpret the imagesin the experimental part of this work. Apart from the spatial resolution, the signalto noise ratio and the detectability will be discussed. The chapter concludes withthe technique of imaging spectroscopy to combine a set of energy filtered imagesinto a dataset containing both spatial and spectroscopic data. This technique willbe shown very useful in the experimental chapters.

5.2 Elemental mapping

Energy filtered TEM images are not directly interpretable as chemical mapsbecause of the non-specific background in the EELS spectrum. Two techniquesexist to solve this problem by taking more than one image: the three-windowtechnique and the jump-ratio technique. Three images are needed in the three-window technique for elemental mapping while only two are needed for the so-called jump-ratio method.

5.2.1 Three-window elemental mapping

The method of three-window elemental mapping [1] allows us to make an im-age of which the intensity is proportional to the intensity in the EELS spectrumunder a certain excitation edge. The method makes use of three images made

59

60 5.2. Elemental mapping

up of electrons coming from three different energy regions in the spectrum. Aschematic overview of the technique is given in fig. 5.1. Two pre-edge imagesare used to estimate the non-specific background in each pixel of the image, byestimating the parameters of the background model AE−r for each pixel in thespectrum. The third image (post-edge image) is obtained from the energy re-gion which contains the excitation edge of interest. The estimated backgroundfor each pixel is subtracted from the post-edge image and an excitation-specificimage remains. The resulting image then contains an intensity per pixel which isproportional to the number of electrons that have made the specific excitation. Ifwe know the cross section for the excitation in the specimen (for given experi-mental conditions), we can use this image to estimate the absolute concentrationof a given element. To increase the signal to noise ratio in the elemental map, useis sometimes made of a so-called r-map smoothing. This technique consists ofapplying a low-pass filter to the image of the estimated background parameter r(the r-map). The idea behind this is that for regions of the same material, r doesnot vary much. On the other hand, the estimated background is very sensitive tovariations in r (steepness of the background), therefore it can be useful to filter outunwanted high-frequency noise in the r-map. In practice this works well, but theuser should be warned against using too much smoothing, especially when sharpinterfaces in the elemental map are important. Smoothing the r-map can give riseto artifacts in the region of the interface between two areas of the sample witha different r parameter. Important parameters for the use of this three-windowtechnique are:

• The position of the energy selecting windows for the three images.

• The width of the energy window.

• The number of counts in the images, as high as possible but avoid overex-posure and too long exposure times.

• The spatial and energy drift during the acquisition of the images. Driftbetween the images can be corrected by using a cross correlation technique.

• The type of excitation used. The higher the cross section for an excitationthe better the elemental mapping will work.

• Thickness of the specimen: comparing regions of comparable thickness ismore accurate and easier to interpret.

The optimal settings for these parameters depend on the goal of the experiment.The influence of apertures and choice of energy windows will be described inmore detail in the next sections.

Chapter 5. EFTEM 61

Figure 5.1: Schematic overview of the three-window technique. Two pre-edge images areused to estimate the background by fitting a background model AE−r. This backgroundestimation is subtracted from the post-edge image to obtain an elemental map. The im-ages are taken from a sample PrxCa1−xMnO3 with layers of x=1;0;0.25;0.5;0.75;1 on asubstrate of SrTiO3. The final Pr-elemental map clearly shows these layers.

5.2.2 Jump-ratio method

An alternative to the three-window technique is the so-called jump-ratio tech-nique. In this case, two EFTEM images are recorded, one pre-edge and one post-edge. Dividing the post-edge by the pre-edge image, leads to a jump-ratio image.This image gives a qualitative image of the changes in the spectrum between thepre-edge and post-edge region. No quantitative data can be extracted since the ra-tio of background to background plus edge is not directly related to the excitationedge strength but also depends on the background. The advantage of using thistechnique over the three-window method are:

• A better signal to noise ratio in the final image is obtained, since no extrap-olation or parameter estimation was needed.

• The image is less sensitive to preserved elastic contrast in the EFTEM im-ages. The ratio cancels out all elastic contrast information which is the same

62 5.3. Colour maps

for both pre and post-edge images.

• Drift problems are reduced since only two images are needed.

The disadvantage of course is the loss of quantitative information. Therefore,this technique is only used to discern real chemical changes from elastic contrasteffects by comparing the result of the jump-ratio image to the elemental image. Ingeneral it is useful to avoid zone-axis orientations in EFTEM work to limit elasticdiffraction contrast effects.

5.3 Colour maps

A convenient way to present and compare elemental maps of different ele-ments from the same sample are the so-called colour-coded maps. These imagesare prepared by overlaying up to three elemental maps using a different primarycolour for each. The total image is then a colour coded image, with mixed colorswhere more than one element is present in the same region. The advantage is thatthe correlation between the different elemental maps is much more visible, com-pared to the presentation of the different elemental maps as seperate gray-scaleimages.

5.4 Spatial Resolution

In this section the question about spatial resolution in EFTEM images willbe addressed. A quantitative definition of spatial resolution will be given. Theimage formation of energy filtered images will be studied in some detail to gaininsight in the factors affecting the spatial resolution. This insight will enable us tochoose microscope parameters for experimental work. It will clearly outline theperformance range of a modern microscope and set limits to what can be obtainedwith the EFTEM technique. This is a very important basis for evaluating theexperimental results described in later chapters of this work.

5.4.1 Image formation

The formation of an energy filtered image in the microscope can be viewedas a two step process. The first step consists of the inelastic scattering of the in-coming electrons with the sample. This leads to a function at the exit plane ofthe sample,the exit wave |Ψexit〉. This exit wave propagates through the lenses ofthe microscope to create a magnified image. The intensity for each position in theimage plane can be calculated from the probability density of |Ψimage(r)|2. The

Chapter 5. EFTEM 63

Figure 5.2: Schematic overview of the two step process of inelastic image formation.

effect of the lenses can be described with linear system theory. Fig. 5.2 showsthe two step process schematically. The image formation is very similar to theso-called central-dark-field-imaging where an inelastic image is formed by takingall Bragg beams except the 000-beam. The current density j(ri) in the two dimen-sional image plane (ri is a vector in that plane) caused by inelastic scattering to asingle atom can be calculated using the first order Born approximation accordingto Kohl and Rose [2]:

j(ri) = j0 ∑n

k f

ki

1λ f

∣∣∣∫ ∫fn,0(θ)A(θ ,δE)e−iγ(θ ,δE)eik f ri·θ d2θ

∣∣∣2 (5.1)

with j0 the current density in the image plane when no sample is present, δE(n)the energy loss relative to the center of the energy selecting slit at E determinedby the energy difference between the |0〉 and |n〉 eigenstates of the atom. Theintegral is performed in the two dimensional diffraction plane and θ is a vector inthat plane. The wavenumbers are defined as:

ki =2πλi

wavenumber of primary electrons (5.2)

k f =2πλ f

wavenumber of electron after scattering (5.3)

and A(θ ,δE) is an aperture function taking care of the cutoff in the diffractionplane up to the collection angle β as well as the energy selection by the slit (∆wide):

A(θ ,δE) =

1 if |θ | ≤ β and |δE| ≤ ∆2

0 otherwise(5.4)

The phase shift γ is due to lens aberrations and defocus and is given by [3]:

γ(θ ,δE) = k f [Csθ 4

4−∆ f

θ 2

2−Cc

δE2E0

θ 2] (5.5)

64 5.4. Spatial Resolution

with Cc and Cs the chromatic and spherical lens abberations, ∆ f the defocus andE0 the primary energy [4].

The most important factor in eq. 5.1 is the inelastic scattering amplitude fn,0for exciting |0〉 to |n〉. The only difference with central-dark-field imaging is thedifference in scattering amplitude. The inelastic scattering amplitude for a set ofatoms in a crystal can be approximated as a set of independent scatterers by notingthat the ground states for individual atoms have very little overlap and neglectingthe fine structure in the excitation edges due to solid-state effects in the final states.This approximation is justified by the fact that EFTEM images are collected withlarge energy windows which average out the fine structure details of the edges.This leads to the approximation where we regard all the atoms in the sample asindependent scattering centers and where we add the scattered waves incoherently.

If we make an image with specific excitations for element ν in an energywindow limited by E ± ∆

2 we get for the total current density jT in the image:

jT (ri) = ∑l

jA(ri − rl) (5.6)

The image is made up of the incoherent contribution of all the l atoms of type νat image positions rl. With jA(ri) the current density in the image caused by oneatom of type ν in the origin. Equation 5.6 is not valid for the central-dark-fieldmode because in that case, all scattered waves should be added coherently andinterference will arise.

The local chemical composition of a sample can be described by a continuousprojected particle density nν(r) of a specific element ν . With projected it is under-stood that we project the three dimensional particle density along the direction ofthe primary electron beam. The total image then becomes a convolution integral:

jT (ri) =∫

nν(r) jA(ri − r)d2r (5.7)

One can rewrite this in Fourier space with the following notation:

F jT (ri) = JT (Ω) (5.8)

F jA(ri) = JA(Ω) (5.9)

Fnν(ri) = Nν(Ω) (5.10)

with Ω the reciprocal position vector. We get for the total current density inFourier space:

JT (Ω) = Nν(Ω)JA(Ω) (5.11)

JA(Ω) can be written as:JA(Ω) = j0σH(Ω) (5.12)

Chapter 5. EFTEM 65

with σ the inelastic cross section for the given energy window determining the“strength” and H(Ω) a contrast transfer function determining the “shape” de-pending on the microscope and on the specific excitations which were used. Inreal space the total intensity in the image becomes a convolution product with animpulse response function h(r).

jT (ri) = j0(ri)σnν(ri)⊗h(ri) (5.13)

where we take the current density j0(ri) to be dependent on the position in theimage, to include the possibility of non-uniform illumination.

5.4.2 Image of a single atom

To calculate the impulse response function h(ri) we need to know the imageproduced by a single atom in the center. This can be calculated from 5.1 if weknow fn,0(θ). In the first order Born approximation fn,0 is defined as:

fn,0(q) = − m0

2π h2 〈k f ,n|V |ki,0〉 = − 2q2a0

〈n|eiq.r|0〉 (5.14)

With q = ki −kf the impulse transfer vector and a0 ≈ 0.529 A the Bohr radius.For small scattering angles and small energy losses, eiq·r can be approximated by1+ iq · r+O((q · r)2). This is known as the dipole approximation .

fn,0(q) ≈− 2q2a0

(〈0|n〉+ 〈n|iq · r|0〉) = − 2iqq2a0

· 〈n|r|0〉 (5.15)

We define a new vector R as:R = 〈n|r|0〉 (5.16)

which depends only on the initial and final state and has components R =(Rx,0,Rz)if we choose the axes to have z along the primary electron beam direction and xalong the projected direction of R on the plane perpendicular to the z-direction. Inthat case, we can write the inelastic scattering factor as two parts:

fn,0(q) ≈− 2iq2a0

(R⊥q⊥ cosα +q‖R‖) (5.17)

with q⊥ and q‖ the components of the impulse transfer vector projected on thex-y plane and z-axis correspondingly. α is the angle between q and the x-axis.R⊥ = Rx and R‖ = Rz are the components of R along the x-axis and z-axis corre-spondingly and contain information on the strength of the excitation. The q depen-dence is completely contained in the q⊥ cosα and q‖ factors, the R-components


Figure 5.3: Parallel (full) and perpendicular (dotted) parts of the scattering amplitude fn,0vs. scattering angle in the dipole approximation for Eloss = 540 eV. The perpendicularpart is dominant for all but the smallest angles.

lead to a constant value depending on the transition and determine the relativestrength of the q‖ and q⊥ term. Berger et al. [5] compare this scattering modelwith a central field model for different types of edges and it is shown to be verysatisfactory for scattering angles smaller than 10 mrad. Fig. 5.3 shows the

q⊥q2 and

q‖q2 parts of the inelastic scattering factor. The high angle scattering events whichcontain the localized information of the atom are almost exclusively coming fromscattering with an impulse transfer in the x-y plane.

To calculate eq. 5.1 we can make use of the assumption that the atom isspherically symmetric. Therefore we only need to know the image of the atom asa function of the distance from the center. We choose r as the distance from thecenter in the x-y plane, and convert eq. 5.1 to polar coordinates (θ ,α) with θ thedistance from the center and α the angle with the θx-axis in θ -space.

j(r) = j0 ∑n

k f

ki

1λ f

∣∣∣∫ β

0

∫ 2π

0fn,0(θ)A(δE)e−iγeik f rθ cosα)θdθdα

∣∣∣2(5.18)

= j0 ∑n

k f

ki

1λ f

∣∣∣− 2ia0

∫ β

0

∫ 2π

0

[R⊥

q⊥ cosαq2 +R‖

q‖q2

]×

Chapter 5. EFTEM 67

A(δE)e−iγeik f rθ cosαθdθdα∣∣∣2 (5.19)

Performing the α integration converts the double integral to a single integral, dras-tically improving computation speed.

I⊥ = − 2ia0

R⊥∫ β

0

[∫ 2π

0eik f rθ cosα cosαdα

]q⊥q2 A(δE)e−iγθdθ (5.20)

I‖ = − 2ia0

R‖∫ β

0

[∫ 2π

0eik f rθ cosαdα

]q‖q2 A(δE)e−iγθdθ (5.21)

which simplifies to:(see [6])

I⊥ = − 2ia0

R⊥∫ β

02πiJ1(k f rθ)

q⊥q2 A(δE)e−iγθdθ (5.22)

I‖ = − 2ia0

R‖∫ β

02πJ0(k f rθ)

q‖q2 A(δE)e−iγθdθ (5.23)

with J0 and J1 Bessel functions of the first kind. The extra imaginary unit in I⊥makes it possible to convert the total integral to:

j(r) = j0 ∑n

k f

ki

1λ f

[|I⊥|2 + |I‖|2

](5.24)

Solving this equation numerically gives the radial distribution function of an in-elastic image of an atom. This is the impulse response function h(r) which wewere looking for in eq. 5.13. For large collection angles β , it is completely dom-inated by the I⊥ part because the perpendicular part of the scattering factor aswell as the J1 function drop slower to zero as compared to the parallel part of thescattering factor and the J0 function.

Fig. 5.4 shows the results of a simulation with an ideal lens γ = 0. The spatialdistribution of the inelastic image gets broader when a smaller objective apertureis used, this can be understood from the fact that the Fourier spectrum is cut off,leading to a broader image in real space.

Introducing the effects of the non-ideal lens of a CM30 microscope with Ul-tratwin lens (300 kV, Cs=0.65 mm , Cc=1.42 mm) we get the simulated inelasticimage of an oxygen atom shown in fig. 5.5A . An energy window of 20 eV is cho-sen centered around 540 eV energy loss. To appreciate the effect of the chromaticaberration, different energy loss components are drawn separately in 5.5B. Theeffect of a slightly different energy inside the energy selecting window leads to ashift in position of the maxima in the radial distribution. A summation of thesecomponents of different energy loss leads to a heavily blurred image compared to


Figure 5.4: Radial intensity distribution in the image of a single O atom making use ofthe K-edge at 540 eV, viewed with an ideal lens for the different objective apertures in aCM30 microscope

the image with a perfect lens. Fig. 5.5A also shows a simulation for a lens withCc = 0, leaving only the spherical aberration Cs. The effect of Cs is small and is notchanged by the size of the energy selecting slit, only the objective aperture deter-mines the strength of the effect. Chromatic aberration is clearly the limiting factorin EFTEM resolution for all realistic energy windows because of the fact that wework with images made up of different energies in a lens system that was designedfor monochromatic electrons. The optimal focus for an EFTEM image is differentfrom the unfiltered because the defocus term ∆ f k f

θ 2

2 should cancel the effect of

the non-monochromatic electrons in the energy window CcδEE0

θ 2

2 in equation 5.5.

The focal spread defined as CcδEE0

should be compared to the Scherzer defocus√Csλ . The focal spread for the CM30 microscope is ≈ 50 AeV, the Scherzer de-

focus is ≈ 340 AFor realistic energy windows starting from 20 eV the focal spreadbecomes larger than the Scherzer defocus and the image is relatively insensitiveto the exact defocus. Simulations enable us to define an ’optimal’ defocus for theparameters in fig. 5.5 as ∆ f ≈ 0.5

√Csλi, although this setting is not critical.

Chapter 5. EFTEM 69

Figure 5.5: Effect of lens aberrations on an inelastic image of an oxygen atom.O-K edgeat 540 eV with energy window of 20 eV for a CM30 microscope with E0=300 kV, Cs=0.65mm, Cc=1.42 mm and θ0 = 19.2 mrad. A) Comparison between radial distribution with aperfect lens (dotted), with only Cs but no Cc (dashed) and with both Cs and Cc (full). B)Components of the image with aberrations for 10 different energies from 530 eV to 550eV. An ’optimal’ defocus was found at ∆ f ≈ 0.8

√Csλi for a lens with Cs aberration only

and ∆ f ≈ 0.5√

Csλi for a lens with both Cs and Cc

5.4.3 Resolution

Knowledge of the impulse response function enables us to define resolutionin EFTEM images. Kohl et al. [2] give a definition of resolution as the diame-ter of a disc containing 59% of the total intensity. Fig 5.6 shows the cumulatedintensity in a diameter d for imaging an oxygen atom with a 20 eV window forthe different objective apertures in a CM30 microscope. The resolution for thedifferent apertures is shown in fig. 5.6. For θ0= 19.2; 12.6; 6.7 mrad we finda resolution of roughly 3;4;5 AA complete simulation can be done for differentenergy windows, different objective apertures and for all realistic energy losses.The results are shown in fig. 5.7 and are very important for experimental work.They enable the experimenter to choose the optimal microscope parameters forvisualizing a specific sample. They also indicate the limitations of the EFTEMtechnique concerning the best attainable resolution. It should be marked however,that it is crucial to choose the microscope parameters only as good as you needfor the experiment, because improving the resolution inevitably leads to a decreasein intensity leading to extremely long exposure times (minutes) and spatial drift


Figure 5.6: Cumulative intensity in a disc with diameter d, normalized for a unit intensity.Parameters are: E0=300 kV, Cs=0.65 mm, Cc=1.42 mm, E = 540 eV and ∆E = 20 eV.Different objective apertures used: θ0 = 19.2 mrad (full), θ0= 12.6 mrad (dashed), θ0=6.7 mrad (dotted). The resolution definition is marked by arrows.

problems.

5.4.4 Implications for elemental profiles

The knowledge of the impulse response function also enables to predict theimage of a set of atoms. It is very instructive to calculate the EFTEM image of ahypothetical one dimensional line of atoms. Consider a set of oxygen atoms witha spacing of 2.75 A and take out 4 atoms in the center of the string. Now wereplace each atom by its impulse response function h(r) for the given microscopeparameters and sum all components incoherently. The result is shown in fig. 5.8.We can now appreciate the meaning of EFTEM resolution, it gives a length scaleto the visibility of a certain feature (here the gap of 4 atoms in the center) but it doesnot enable us to do a quantitative analysis of the underlying oxygen distributionunless we know the impulse response function and we have noise free data. Inpractice these two conditions are never met and deconvolution of the experimentaloxygen profile is not possible. This is a very important result for the experimentalpart of this work.

Chapter 5. EFTEM 71

Figure 5.7: EFTEM spatial resolution as function of collection angle β , energy selectingwindow ∆ and energy loss for the CM30 microscope.


Figure 5.8: Simulation of an EFTEM image of a one dimensional string of oxygen atoms.A) Indicates the position of the atoms, B) shows the individual contribution of each atomto the image, C) total image. Care is taken to include the effect of a finite pixel of 1 A 2

in the evaluation of the intensity distribution along a line centred around the atoms, Thesampling effect of the pixels and the counting noise are not included. Parameters are:E0=300 kV, Cs=0.65 mm, Cc=1.42 mm, Eloss = 540 eV, ∆E = 40 eV and θ0 = 19.2 mrad

Chapter 5. EFTEM 73

5.5 Signal to noise ratio

Apart from spatial resolution, the signal to noise ratio (SNR) in elemental im-ages is of primary importance. Optimizing spatial resolution without keeping thesignal to noise ratio to acceptable values would lead to very noisy and uninter-pretable elemental maps. On top of the counting statistics in the energy selectedimages of the three-window method, the background removal adds a consider-able amount of noise to the elemental map due to the statistical uncertainty inthe extrapolation of the background model. In most cases, the noise due to thebackground removal is much higher than the counting statistics noise. Importantparameters in the background removal step are:

• The energy ranges (position and width) used for the three energy filteredimages.

• The intensity of the images. The more counts, the more accurate the back-ground fitting will be.

• Drift of the specimen during acquisition of the images. Drift between im-ages can be corrected by a looking for a maximum in the cross correlationimage.

• The signal background ratio of the excitation edge. The higher the edgesticks out the background, the better the elemental map will be.

• Thickness of the sample. A thin specimen of uniform thickness is desirable.The thickness is generally expressed in terms of t

λ with λ the mean freepath for a plasmon excitation of the order of 100 nm depending on the ma-terial. A sample that is too thin gives a very weak signal with possibly largesurface effects. A specimen that is too thick t

λ > 1 will cause problems withmultiple scattering and the increased elastic scattering to higher angles willlimit the signal in a small objective aperture. An ideal thickness exists andis roughly t

λ ≈ 0.3 or about 30 nm.

We will address now the question on how to improve the signal to noise ratio bychanging position and width of the energy region for the energy selected images.Egerton [7] gives an expression for the signal to noise ratio as:

SNR =Ik√

Ik +hIb

(5.25)

With Ik the element specific intensity under an excitation and Ib the background in-

tensity in the region of the post-image. The parameter h is defined as h = 1+ var(Ib)Ib

74 5.5. Signal to noise ratio

Figure 5.9: SNR map for elemental mapping a Ba M4,5-edge as function of position andwidth of the post-edge energy region. The inset shows the experimental EELS spectrum.The SNR is best if the energy selecting window is chosen to include both sharp peaks inthe spectrum.

and is a measure for the inaccuracy of the background estimation. If only countingstatistics would limit the SNR, h would be 1. In practice h is dependent on positionand width of the energy regions and can easily be larger than 10. The value for hcan be numerically calculated for a specific spectrum and for different positionsand widths of the energy regions. Use is made of the assumption that after log-logtransforming a spectrum, the counting errors are normally distributed and the lin-ear least mean square fitting can be used. The result of such calculations can showa map of the SNR as a function of energy width and position of the energy regionsfor a specific experimental spectrum shape, since h is dependent on the specificshape of the spectrum. This can be of help to determine the optimum position andwidth for experimental work as shown in fig. 5.9 for a Ba M4,5-edge in a thin filmof YBa2Cu3O7. The SNR contourplot shows that it is advantageous to choosethe post-edge energy region to contain the two sharp M4,5 peaks. A wider regiondoes not pay off since most intensity is contained in the sharp peaks and a widerregion would increase the extrapolation error. As an alternative to these detailedsimulations, a few rules of thumb can be deduced from these simulations.

Chapter 5. EFTEM 75

Rule of thumb 8 Take the background fitting region as wide as possible, buttake care that the background model remains valid and no overlapping edgesoccur in the fitting region. In practice, the pre-edges are taken to be of equalenergy width as the post-edge. Choosing too wide energy regions results in aloss of spatial resolution due to chromatic abberation.

Rule of thumb 9 Increase the number of counts in the images without satu-rating the CCD. For energy losses >1000 eV exposure times can become verylarge and spatial drift can become a serious resolution limiting factor.

Rule of thumb 10 Choose the post edge region at the start of the edge, asclose to the pre-edges as possible. For spectra with pronounced peaks, makesure that these are included.

5.6 Detectability

Berger et al. [8] have investigated the optimum microscope parameters to de-tect a small amount of oxygen in grain boundaries of Si3N4. They showed thatexperimentally they could measure SiO2 grain boundaries with thicknesses of 2monolayers of oxygen in a sample approximately 35 nm thick. The main limitingfactor for detectability is the SNR. They propose several measures for optimizingthe SNR in experiments where detectability is important. If a SNR of 5 is taken asthe limit for detectability of a given element in an elemental map (by eye), a theo-retical model predicts the minimum thickness of the grain boundary to be visible.They find that a single monolayer of oxygen should be detectable in their sample(thickness 35 nm). The general operational choices for optimizing detectabilitycan be summarised as follows:

• Choose a high convergence angle α . This increases the current density inthe beam.

• Choose the collection angle β much larger than the characteristic scatteringangle θE in order to capture as much of the inelastic signal as possible. Thiscauses the resolution to decrease, smearing out the feature of interest butthe total signal is preserved.

• Choose the magnification of the microscope so that the complete intensityof a fine feature (grain boundary) is captured by one pixel.

76 5.7. Combining spectroscopic and spatial information

Figure 5.10: Schematic view of the three dimensional data cube combining spatial andspectroscopic information.

• Capture as much counts on the CCD as possible without saturating it.

• Use the optimal focus for an inelastic image. This is slightly different fromthe focus in an elastic image. Experimentally this can be done by focussingan image at 100 eV with the chosen slitwidth on the TV rate camera. Theoptimum focus for the edge under study will be close to this value.

Clearly, some of these rules are contradictory to the setting for optimal spatialresolution. It is therefore important to realise wether a certain experiment needshigh detectability or high spatial resolution or both.

5.7 Combining spectroscopic and spatial informa-tion

From an information point of view, the extra spectroscopy information we getby EELS, can be viewed as an extra dimension (energy). The total informationspace can then be viewed as a three dimensional space1, combining spatial andspectroscopic information. This idea is schematically presented in fig. 5.10 asan (x,y,E)-cube. Parts of this cube can be experimentally acquired by two dif-ferent techniques: the imaging spectroscopy technique and the spectrum imagingtechnique, briefly outlined in the next two sections.

5.7.1 Imaging spectroscopy

The technique of imaging spectroscopy was first proposed by Lavergne etal. [9] and is shown schematically in fig. 5.11. The three-dimensional data cube

1The angular dependence can also be viewed as an extra dimension making it a four dimen-sional space.

Chapter 5. EFTEM 77

is sampled by taking a large set of energy filtered images with a small energy slit.Each image is taken at a slightly different energy loss, sampling the energy lossaxis in a certain region of interest. Typically a slit of 1 or 2 eV is chosen and50 or 100 images are captured with 1 or 2 eV energy intervals. The total record-ing time can be considerable and effort should be put into keeping the exposuretime for each image as low as possible. Microscope parameters like magnifica-tion, apertures and CCD field of view should be carefully selected for the desiredperformance. The advantages of this technique are:

• Spatial resolved ELNES is added as a valuable tool to study the correlationbetween spatial information and electronic structure.

• The background subtraction technique can be done more accurately, espe-cially for overlapping edges where the conventional three-window methodfails.

• The data can be processed afterwards. This can be very interesting for back-ground removal or elemental mapping of a fine structure detail; the exactlocation of fitting region and extrapolation region for the background canbe tried out off-line.

There are also several limitations for this technique which should be kept in mindwhen applying it:

• The slit size is limited by imperfections in the mechanical flatness of theslit edge to about 1 eV. The exact width of the slit can not be accuratelycontrolled. This limits the minimal sampling of the energy dimension toabout 1 eV or 2 eV. Improvements in the slit design could help, but it isquestionable wether the increased energy resolution would be useful giventhe linear increase in exposure time needed for a decrease in slit width.

• Aberrations in the spectrometer lenses give rise to a small energy differencebetween center and edge of the energy selected images. This effect is calledisochromacity and is lower then 1 eV for a well aligned GIF (guaranteed< 3 eV).

• Spatial and energy drift limit the exposure time per image. The spatial driftbetween images can be corrected by a cross correlation technique, providedthe overlapping region in all the images remains large enough. In practice alimit of about 10 s per image gives reasonable results. A linear energy driftduring acquisition has the effect to compress or expand the energy axis. Anadvantage of this technique is that an energy drift can not cause a differencein excitation peak positions between two spatially separated regions.

78 5.7. Combining spectroscopic and spatial information

Figure 5.11: Schematic view of the two different ways to experimentally capture part ofthe three dimensional data cube. For the imaging spectroscopy technique, a large setof energy filtered images at different energy losses is recorded. The spectrum imagingtechniques scans the x-y plane with a STEM probe and captures an EELS spectrum foreach pixel

• Long exposure times make this technique less suitable for beam sensitivesamples.

It is interesting to note that the problem of long exposure times is not a funda-mental requirement of this technique. In principle, all inelastic electrons of thethree dimensional data-cube are present at the same time. Therefore we could inprinciple capture the whole data set in one single exposure solving most of the dis-advantages of this technique! This would however require some method to capturethese data on a two dimensional detector. In principle all the data could be cap-tured in the plane of the energy selecting slit if the phase and energy informationin that plane could be captured as well.

5.7.2 Spectrum imaging

Spectrum imaging approaches the problem from a different side, by capturingthe three dimensional data set line by line. A schematic drawing in fig. 5.11shows the difference with the imaging spectroscopy method. A fine STEM probeis raster-scanned over an area. For each probe position (x,y) an EELS spectrumis captured. The advantage of this technique is that the scanned region should notbe a square region. It can even be a line scanned over an interesting region in thesample. Several authors have shown that with this technique, the spatial resolutioncan be of the order of the separation between different atom columns in a zone-axis oriented sample [10–14]. The stability requirements for such experiments aretremendous but custom-build STEM microscopes are shown to achieve this [13].

Chapter 5. EFTEM 79

Bibliography


[2] H. Kohl and H. Rose. Theory of Image Formation by Inelastically Scat-tered Electrons in the Electron Microscope. In Advances in electronics andelectron physics, volume 65, pages 173–227. Academic Press, Inc., 1985.


[4] S. Amelinckx, D. van Dyck, J. van Landuyt, and G. van Tendeloo. Electronmicroscopy: principles and fundamentals. John Wiley and Sons, 1997.

[5] A. Berger and H. Kohl. Elemental Mapping Using an Imaging Energy Fil-ter - Image- Formation and Resolution Limits. Microscopy MicroanalysisMicrostructures, 3(2-3):159–174, 1992.

[6] M. Abramowitz and I. A. Stegun. Handbook of mathematical functions.Dover Publishing, 1965.

[7] R. F. Egerton. A Revised Expression For Signal Noise Ratio in EELS. Ul-tramicroscopy, 9(4):387–390, 1982.

[8] A. Berger, J. Mayer, and H. Kohl. Detection Limits in Elemental Distri-bution Images Produced By Energy-Filtering Tem - Case-Study of Grain-Boundaries in Si3N4. Ultramicroscopy, 55(1):101–112, 1994.

[9] J. L. Lavergne, J. M. Martin, and M. Belin. Interactive Electron-Energy-Loss Elemental Mapping By the Imaging-Spectrum Method. MicroscopyMicroanalysis Microstructures, 3(6):517–528, 1992.

[10] G. Duscher, N. D. Browning, and S. J. Pennycook. Atomic column resolvedelectron energy-loss spectroscopy. Physica Status Solidi A, 166(1):327–342,1998.

[11] P. E. Batson. Simultaneous STEM Imaging and Electron-Energy-Loss Spec-troscopy With Atomic-Column Sensitivity. Nature, 366(6457):727–728,1993.

[12] N. D. Browning, M. F. Chisholm, and S. J. Pennycook. Atomic-ResolutionChemical-Analysis Using a Scanning- Transmission Electron-Microscope.Nature, 366(6451):143–146, 1993.


[13] P. E. Batson. Atomic resolution electronic structure in silicon-based semi-conductors. Journal of Electron Microscopy, 45(1):51–58, 1996.

[14] P. E. Batson. Advanced spatially resolved EELS in the STEM. Ultrami-croscopy, 78(1-4):33–42, 1999.

Part II

Experiments

81

Chapter 6

Manganite thin films

6.1 Introduction

In this chapter we will deal with thin films of doped perovskite manganitesof general form AA′MnO3 with A a divalent and A′ a trivalent cation. A briefintroduction to the perovskite manganites will be given here on the crystal struc-ture and some of the most important properties. Their potential for technologicalapplications will be summarised as well as the bottlenecks preventing their break-through. Experiments will deal with a range of manganite thin films trying outnew ways to improve the properties and to understand the complex interplay be-tween structure, chemistry and electronic structure. For a more detailed overviewthe reader is referred to an excellent introduction by Rao et al. [1] or to the wealthof papers published on the subject.

The manganites are based on a perovskite unit cell with general formula ABO3as drawn in fig. 6.1. The Mn atom is situated on the B-site inside an octahedron ofoxygen atoms (fig. 6.1). The A-site is occupied by a mixture of divalent and triva-lent cations (e.g. La and Sr). The lattice parameters are approximately 0.39 nmand depending on the type of atom on the A-site, distortions from the ideal per-ovskite cell can occur. Both tilting and elongation of the octahedra can occur andleads to break down of the cubic symmetry and a change in unit cell volume [3,4].If ionic bonding is assumed it is clear that changing the divalent/trivalent cationratio A/A′ will have an effect on the Mn valency state. The parent compoundsAMnO3 (A=trivalent cation) are antiferromagnetic insulators, but doping with adivalent cation can introduce a phase transformation to a ferromagnetic metal be-low the Curie temperature Tc. The phase diagram of AA′MnO3 can be extremelycomplex. The possibility of vacancies on oxygen, cation or manganese sites in-creases the complexity even more.

The rich phase diagram (for an example see fig. 6.2)is sometimes accompanied

83

84 6.1. Introduction

Figure 6.1: ABO3 perovskite unit cell left. B-atom containing oxygen octahedron high-lighted right.

Figure 6.2: Phase diagram of La1−xCaxMnO3 as a function of concentration x and tem-perature T [2].

by interesting physical properties which make these materials technologically in-teresting. A metal-insulator transition can occur at TMI slightly below TC. Chargeordering can occur below TCO, creating an ordered lattice of Mn3+ and Mn4+ siteseven when the A and A′ sites are disordered. Colossal Magneto Resistance (CMR)is observed for some concentrations. The CMR effect consists of a drastic increaseof conductivity when applying a strong magnetic field. The magnetoresistance isdefined as MR = R(0)−R(H)

R(0) with R(0) and R(H) the resistivity at zero and non-zerofield H. The MR value is expressed in percent and can be close to 100% near TC forstrong magnetic fields (> 1 T). A simple, though not perfect model for the CMReffect is based on the Double Exchange (DE) model [5]. This model describes

Chapter 6. Manganite thin films 85

Figure 6.3: Schematic overview of the double exchange effect. The ground state of theMn4+ 3d orbitals are split by exchange interaction and octahedral crystal field splitting toa spin polarised ground state(A). The hopping of a 3d electron between a Mn4+ and Mn3+

site can take place via an intermediate O 2p orbital, only in the case of ferromagneticordering (B) and not in the case of antiferromagnetic ordering (C) since the energy gapis too high.

the hopping of a 3d conduction electron from a Mn3+ site to a Mn4+ site via anintermediate oxygen site as explained in fig. 6.3. The model predicts that this hop-ping is strong for ferromagnetic ordering of neighbouring Mn sites and weak forantiferromagnetic ordering. This serves as an explanation why the ferromagneticordering induced by an applied magnetic field would increase the conductivity inthese materials. The model however, is a very basic description and does not ex-plain the full detail of the experimental conductivity measurements. More detailedmodels also include e.g. the effect of electron-phonon coupling [6].

Technological interest in these materials is based on these properties. Venkate-san [7] gives an overview of the possible technological uses for manganites andthe bottlenecks which need to be resolved. Most important is the use as a magneticfield sensor based on the CMR effect. Most CMR manganites require tempera-tures below room temperature and strong magnetic fields making them of limiteduse until higher Curie temperatures and better low field sensitivities are obtained.The metal-insulator transition can be put to use as a bolometric IR sensor. The

86 6.2. Valency measurement

Figure 6.4: Two different approaches of white line subtraction from experimental spectradue to Pearson et al.(A) [9] and Kurata et al.(B) [10]. Throughout this work approach Bwill be used.

fact that some manganites are half metals1 can be exploited to use in fundamentalresearch as a source of polarised electrons. Combination with high Tc supercon-ducting films acting as flux concentrators may lead to an improvement in the lowfield sensitivity but requires cooling. It was found that grain boundaries improvestrongly the low field sensitivity of some CMR manganites, but at the expense oflowering TC [8].

The basic goal of the study of CMR manganites is twofold. A better under-standing of the mechanism of CMR is needed and an improvement of the TC andlow field sensitivity would open the way for technological applications. Thin filmtechnology enables us to deposit thin manganite films on a supporting substrate.The film will in some cases adapt epitaxially to the substrate creating the pos-sibility to change the lattice parameters as compared to the bulk material. Thecontrolled introduction of impurities or grain boundaries or creating multilayersof manganite or mixed manganite/insulator films are some of the possibilities thatare being tried with varying success.

6.2 Valency measurement

The DE mechanism clearly indicates the importance of local valency for theunderstanding of the CMR effect. Measurement of the Mn valency is thus ofprimary importance in experimental work on manganites. In principle, the Mn va-lency can be calculated from stoichiometry if the exact chemical formula is knownand if ionic bonds are assumed. In practice, stoichiometry can be far off from thenominal formula because of the possibility of vacancies and local changes of the

1The conduction electrons are spin polarized


A/A’ ratio. An accurate measurement of all chemical elements is necessary. Forthin films this can be done with EELS. The valency calculated in this way is anominal valency assuming complete charge transfer from Mn to O sites. In fact,valency is an ill-defined concept in view of the wave nature of the electrons. Apossible definition of the valency would include the total charge around an atominside a sphere but this still leaves the sphere radius as a free parameter.

Direct measurement of Mn valency for bulk materials can be obtained withconventional redox titration. For thin films, this is no longer possible and anothertechnique is required. EELS spectra of transition metals show strong so-called“white lines” in the L2,3 edge. These spectral features were seen in early exper-iments with X-ray absorption spectroscopy (XAS) as white lines on the photo-graphic plates containing the spectra. The white lines were attributed to strongexcitations of the spin split 2p1/2 and 2p3/2 levels to empty 3d orbitals. The ex-pected intensity ratio between the L3(2p3/2 → 3d) and L2(2p1/2 → 3d) white linesis 2:1 given the four vs. two electrons in the 2p3/2 vs. 2p1/2 initial state. EarlyEELS and XAS experiments found a deviation from this 2:1 ratio for differentelements of the 3d transition metals and the phenomenon was labelled as “anoma-lous white line ratio”. This anomalous ratio was reproduced by Waddington etal. [11] in an atomic multi configurational Dirac Fock (MCDF) calculation. Thiscalculation method approximates the all-electron atomic wave function by usingvariational principles to solve the Dirac equation. They could successfully pre-dict the anomalous white line ratio and showed that for elements in the middleof the transition element series like Mn,Fe,Cr,Co the ratio of the white lines issensitive to the charge state or valency of the elements. They also pointed outthat the simple division of L3 and L2 white lines as coming from 2p3/2 and 2p1/2initial states no longer holds exactly in the all electron view. Thole and van der

Laan [12] found general rules for the “branching ratio” defined asI(L3)

I(L3)+I(L2)with

I(L) the intensity of the white lines. They used atomic calculations and describedthe effect of adding a crystal field to the calculation. They found as a general rulethat the branching ratio is maximal for the ground state predicted by Hund’s rules.They showed that the effect of a crystal field is small unless the crystal field intro-duces a spin polarised ground state lowering the branching ratio. They describethe existence of the anomalous white line ratio to be due to the electrostatic andspin orbit coupling of the 2p core hole with the 3d final states.

Several workers made systematic studies of the effect on the white lines fordifferent ionic Mn compounds. Rask et al. [13] showed EELS O K-edges and MnL2,3-edges for several Mn compounds. They give accurate measurements of thepeak positions and white line ratios for Mn L2,3 and note that the changes are tofirst order only dependent on the Mn valency state and independent on the crystalstructure. They note a rise in L3/L2 ratio and a chemical shift of L3 and L2 to

88 6.2. Valency measurement

lower energies when the valency drops. Pearson et al. [9] showed experimentallyand theoretically that the total white line intensity is a measure of the number ofempty 3d orbitals. They also give a prescription how to subtract the white lineintensities from excitations to the continuum as schematically shown in fig. 6.4A.The method consists of fitting a line to the region preceding the L2,3-edge andextrapolating it under the white lines. The line is used to model the shape of thecontinuum excitations which form a background for the white lines. The modelconsists of a step profile with a reduced height of 2

3 of its final height between EL3and EL2 and reaches the fitted line shape from EL2 on. With EL3 and EL2 the energypositions where the maxima of the white lines are. The white line intensities arethen estimated by subtracting this model from the experimental edge and dividingthe L3 and L2 contribution at the energy between EL3 and EL2 where the intensityis minimal.

Kurata et al. [10] use a model fitting technique to measure the total white lineintensity and the L3/L2 ratio and show a strong relationship of both numbers tothe amount of 3d electrons. They model the white lines with Lorentz peaks andthe excitations to the continuum with an adapted hydrogenic cross section. Thecross section is split in two terms to represent the 2p3/2 and 2p1/2 initial statesand both are added in a 2:1 ratio. This method of subtracting the white lines fromthe rest of the spectrum is shown in fig. 6.4B and is used throughout this thesiswhen white line ratios are calculated. Wang et al. [14] combine the white lineratios with EFTEM to measure valency maps. They use a five-window technique,two pre-edge windows for the background, two for the L3 and L2 white line andone for the excitations to the continuum. They show the ability to discriminate thevalency in small grains of CoO and Co3O4 and MnO3 and Mn3O4 with a spatialresolution of 2 nm. They claim that their technique is insensitive to the thicknessof the sample.


6.3 LMO-SMO heterostructures

6.3.1 Introduction

In this section the results of a study on epitaxially grown heterostructures con-sisting of alternating layers of LaMnO3 (LMO, 8 or 12 unit cells) and SrMnO3(SMO, 4 or 6 unit cells) on a SrTiO3(100) (STO(100)) substrate are shown. Thesamples were grown in the Laboratoire CRISMAT at the Universite de Caen (F)by B. Mercey, M.Hervieu and A.M. Haghiri-Gosnet [15].

The combination of high resolution transmission electron microscopy (HRTEM),electron diffraction (ED), quantitative EELS with model fitting, EFTEM and imag-ing spectroscopy on an atomic scale was necessary for the structural, chemical andelectronic characterization of these heterostructures.

The samples are studied by a variety of techniques on different instruments.STEM experiments were performed at the Applied and Engineering Physics de-partment of the Cornell University (USA) during a visit to the lab of J. Silcox.HRTEM and ED work is performed inside the EMAT group. In view of the strongconnection between chemistry, electronic structure and crystal structure in themanganites, both techniques are essential here.

In the introduction of the chapter, it was assumed that doping AMnO3 com-pounds with divalent A′ cations changes the valency of Mn from Mn3+ to a mixedMn4+/Mn3+ state, hence these materials are called controlled valency materials.This mixed valency was found crucial for the explanation of the coupling of fer-romagnetic order with increased conductivity by the DE mechanism. However,several papers have argued against this naive ionic picture and they point out thatthe Mn-O bonds in these materials have a considerable covalent character and theintroduction of holes by divalent doping actually leads to holes with mixed O 2p- Mn 3d character in bulk La1−xSrxMnO3 [16–20]. Further complication is in-troduced by the possibility of O deficiency in these materials, which changes thegeneral formula to A1−xA′

xMnO3−δ .Experimental studies on perovskite based bulk materials of the type (A,A′)MnO3

have shown that three parameters mainly control the magnetic and electronicproperties: (a) the valence of the manganese which is determined by the ratiobetween the divalent and the trivalent cations, (b) the average A-site cationic ra-dius and (c) the difference in size between both A-site cations [21–23]. It wasfound that introducing A-site ordering increases the Curie temperature and themetal-insulator transition temperature in bulk LaBaMn2O6 as compared to thedisordered phase [24]. However, such an ordered bulk material is difficult to syn-thesize using the classical solid state synthesis methods.

Thin film laser molecular beam epitaxy (laser-MBE) growth methods offerthe possibility, utilizing a multi-target deposition process, to directly control the

90 6.3. LMO-SMO heterostructures

Figure 6.5: Schematic overview of the heterostructures indicating the nominal valencychange in the layers.

location of the different cations in an artificial superlattice. Creating this artificialsuperlattice allows the verification of the assumptions about the valency and thestudy of the electronic localization of the introduced holes. One could imaginethat introducing a spatial separation of the Sr doping in La1−xSrxMnO3 could leadto interesting new properties by keeping the lattice order high, while still addingextra holes to the system. This artificial A-site ordering allows to test some ideasabout mixed valency materials, since a nominal valency modulation is artificiallyintroduced. A schematic picture of the heterostructures and the assumed valencyordering is shown in fig. 6.5.

In the present section, two superlattices are grown in a reflective high en-ergy electron diffraction (RHEED) monitored laser-MBE system from two tar-gets, LaMnO3 (LMO) and SrMnO3 (SMO), with a nominal average compositionof La0.66Sr0.33MnO3 and a nominal sequence LMO2nSMOn. The possibility toobtain information on the electronic structure of a material by using a combi-nation of scanning transmission electron microscopy (STEM) and EELS on anatomic scale has already been shown for different materials [25–31]. Combiningthis technique with fitting methods to interpret the spectra gives an opportunityto investigate the chemistry of the present heterostructures on a unit cell scale.The detailed shape of the spectra contains information on the electronic structure,especially interesting in view of the valency assumptions. Energy filtered trans-mission electron microscopy (EFTEM) combines spectroscopic data with spatialinformation, enabling elemental distribution maps of the chemically modulatedlayers. The imaging spectroscopy technique takes EFTEM a step further andenables the spatially resolved acquisition of EELS fine structure spectra. Com-bining these spectroscopic techniques with more conventional techniques such ashigh resolution transmission electron microscopy (HRTEM) and electron diffrac-tion (ED) enables us to complement and compare the EELS data with structural


and contrast information. We show in this section, that this wide range of tech-niques leads to a narrowing of the field of interpretation, closing in on the complexstructural, chemical and electronic reality in these samples.

6.3.2 Experiment

Two samples with nominal formula SrTiO3(100)/[(LaMnO3)12]7[(SrMnO3)6]6and SrTiO3(100)/[(LaMnO3)8]9[(SrMnO3)4)]9 were prepared and will be indi-cated as LMO12SMO6 and LMO8SMO4 correspondingly. The average composi-tion of both samples is targeted to be La0.66Sr0.33MnO3 because of the interestingproperties of bulk LSMO at this composition [32]. Dense ceramic targets with thenominal formulae LaMnO3 and SrMnO3 were prepared using standard ceramicsynthesis methods. Appropriate ratios of La2O3, SrCO3 and MnO2 powders weremixed and intimately ground using a semi-planetary ball mill. The powder wasannealed twice at 900C for 12h and once at 1200C for 12h, with intermedi-ate grinding. Pellets with a diameter of 25 mm were uniaxially cold-pressed andsintered at 1500C for 24 h [15, 33].

A RHEED-monitored laser-MBE system, which allows for Reflection HighEnergy Electron Diffraction (RHEED) monitoring of the growth has been used.Briefly, the base pressure is very low (10−6 Pa) and the deposition is carried outin a pressure typically ranging between 10−2 and 5×10−2 Pa (for a more detaileddescription see [34]). The U.V. beam (λ = 248 nm, repetition rate 2 Hz) from anexcimer laser (Lambda Physics) is focused onto the sintered target to obtain anenergy density ranging between 10−4 and 2× 10−4 J/m2. Optical quality single-crystal substrates of SrTiO3 (100) were ultrasonically cleaned in acetone and inalcohol. To obtain a terraced surface, which enables a step flow growth mode, anacid etching of the substrate in a buffered NH4F/HF solution is carried out [35].To improve the quality of the surface, prior to the deposition of the superlattice,the substrate is buffered with 24 layers of SrTiO3 deposited at 720C in a dynamicvacuum of 1.5× 10−2 Pa of molecular oxygen. Care has been taken to ensurethat the STO substrate ends with a SrO layer by using a Sr2TiO4 target for thelast 2 layers. During the deposition of the superlattice, the heater was held atconstant temperature (535C) in a dynamic vacuum of 5× 10−2 Pa. To ensure acomplete oxidation of the superlattice the deposition is carried out in a mixtureof 94% oxygen and 6% ozone. After deposition, the superlattice is cooled to300C in the same pressure and atmosphere conditions as used during the growth.Between 300C and 200C, ozone production is stopped but the pressure is heldconstant. Below 200C the superlattice is cooled in low pressure (< 5× 10−5

Pa). RHEED is used to monitor the surface stability during the cooling. Growthand magnetoresistive properties of very similar samples (nominal Sr/La contentof 0.26 instead of 0.33 in our case) are described by Salvador et al. [15]. They


found a decrease in Tc, maximum MR value and low temperature conductivity forincreasing thickness of the layers in the heterostructures.

Sample preparation for TEM and HRTEM was done using a standard TEMcross section technique. Because of different ion milling effects on STO, LMOand SMO, a cross section sample for STEM was prepared using mechanical wedgepolishing.

Cross section high resolution TEM (HRTEM) images were recorded on aJEOL 4000EX operating at 400 keV and having a point resolution of 0.17 nm.For STEM EELS experiments, use was made of the Cornell VG HB501A STEMoperating at 100 keV with a cold field emission electron gun having a probe di-ameter of 0.2 nm and an energy spread of 0.6 eV [36].

Each EELS spectrum is recorded by automatically scanning the STEM probeover a region of 15.7 nm, parallel to the layers to average out possible interfaceroughness or surface contamination. The probe is manually repositioned aftereach acquisition to consecutively capture data in different perpendicular positionsof the layers. A total set of 36 spectra contains information starting from thebottom of LMO layer 4 going through SMO layer 4 and ending at the top of LMOlayer 5. EELS spectra are collected in four different energy ranges: the low loss(-60.2 eV—241.6 eV), the Mn L2,3 and O K (439.7 eV—741.6 eV), the La M4,5(739.7 eV—1041.6 eV) and the Sr L2,3 range (1839.7 eV—2141.6 eV). Recordedspectra are analyzed using a spectrum fitting technique. All edges are fitted to anexperimental reference edge from the same sample.

The fitted edge intensities serve as an estimation of the local chemical concen-tration with an estimated error of 10%. The STEM probe is calculated to spreadfrom 0.2 nm at the entrance plane to around 0.32 nm at the exit plane of the speci-men (diameter containing 80% intensity, thickness 25 nm, multislice simulation),which gives an indication on the expected blurring of the chemical profiles causedby electron scattering. The error on the probe position is of the order of 0.2 nm.Energy loss near edge spectroscopy (ELNES) is believed to give information onthe site and symmetry projected unoccupied density of states near the Fermi leveland is performed to gain insight in the electronic structure of the material. Twoedges were studied in detail: the O K-edge at (502.2 eV—590.8 eV) and the MnL2,3 edge (622.2 eV—710.8 eV), both at a 30 s exposure time. Careful inspectionof the spectra over time, showed no changes in the ELNES spectra at exposuretimes up to 120 s. This is taken as an indication that no significant beam damageeffects occurred during the acquisition of the ELNES spectra.

The spectral data are treated with a standard background removal method andthe high frequency noise is removed by convolution with a gaussian profile of0.3 eV full width at half maximum. Two spectra represent the middle part ofa LMO and SMO layer. The energy resolution of this experiment is estimatedaround 0.65 eV by a Lorenz fit to the experimental zero loss peak. Energy filtered


TEM images are recorded on a Phillips CM30 FEG equipped with a GIF2000 postcolumn energy filter. The collection angle is approximately 19.2 mrad. Elementalmaps are calculated by subtracting the non-specific background from the element-specific signal using the standard three-window technique [37]. Drift betweenimages is corrected using a cross correlation technique.

The technique of imaging spectroscopy [38] is used to collect spatial and spec-tral information with a set of 99 EFTEM images starting from 500 eV with a slitwidth and step size of 2eV. The exposure time was 10 s for each image of 128x128pixels. Drift is removed by shifting the images with respect to each other after ac-quisition. The resulting 3 dimensional dataset was reduced by integrating 100pixels parallel to the layers, this leaves a 2 dimensional set containing EELS spec-tra as a function of the position perpendicular to the layers. The background underthe O K-edge is removed with a standard least mean square procedure and the re-sulting edge was normalized to the maximum peak height. For cosmetic reasons,a 4 point interpolation in the energy dimension is performed.

6.3.3 Structural considerations

The room temperature structure of the SrTiO3 substrate is well established; itis a cubic perovskite Pm3m with lattice parameter aSTO = 0.39050 nm [39].

The structure and the phases of La-Mn-O have been the subject of manyinvestigations. The crystal structure of LaMnO3 is derived from the cubic per-ovskite type structure; it contains Mn atoms in the octahedral sites of the oxygensublattice, creating Mn-O-Mn bonds forming angles deviating somewhat from180. However, the real structure of La-Mn-O is much more complicated andstrongly depends on oxygen stoichiometry, cation deficiency, ratio between Mn3+

and Mn4+. Rotations of the MnO6 octahedrons lead to a lowering of the crystalsymmetry from the ideal cubic perovskite to e.g. orthorhombic or rhombohedralsymmetry [3,4,40,41]. The different bulk phases are discussed in the literature butmost research groups refer to the two main structures: the rhombohedral (R3c) andthe orthorhombic (Pnma) phases . The orthorhombic Pnma(62) phase has beenfound for stoichiometric LaMnO3 [42–44] with lattice parameters a = 5.582(0) A,b = 5.583(0) A c = 7.890(0) AThe non-stoichiometric La-Mn-O compound canhave an oxygen excess LaMnO3+δ or cation deficiency La1−xMn1−yO3,but both

of them show rhombohedral symmetry R3c(167) with a = 5.535(0) A c = 13.344A [44, 45, 45–48]. A. Maignan et al. reported a La0.9MnO3−δ phase with amonoclinic symmetry I2/a with a = 7.790(1) A b = 5.526(1) A c = 5.479(1)A α = 90.78. [49]

Stoichiometric SrMnO3 has two polymorphic forms: cubic and hexagonal.The cubic structure is Pm3m(221) with a = 3.805 A [50] and the hexagonal one


Figure 6.6: Low magnification image of the LMO8SMO4 sample. The SMO layers areclearly visible as 9 brighter layers.

is P63/mmc with a = 5.449 A and c = 9.0804 A [51]. Negas et al. [51] reportedthat heating SrMnO3 in air at 1525C induces oxygen deficiency (SrMnO2.69)causing a symmetry break-down to orthorhombic.

Both LMO and SMO are present in the heterostructures and misfit stress re-sulting in strain is expected. Assuming the bulk structures for SMO as well asLMO, the SMO layers are expected to be under tensile stress while the LMO willbe under compressive stress.

6.3.4 Results and discussion

TEM

A cross-section low magnification image of the LMO8SMO4 superlattice filmis shown in fig. 6.6. Fig. 6.8 shows a HRTEM image. The film is epitaxial and ex-hibits sharp, flat and well-defined interfaces between successive LMO and SMOlayers. The layers can be easily distinguished due to different contrast, inducedby different electron scattering and consequently a different composition of thelayers. Bright bands correspond to the SMO layers and dark thicker bands corre-spond to the LMO layers.

Relevant information concerning the epitaxial relationship, quality and crys-tal structure of the layers is obtained from the electron diffraction (ED) patterns(Fig. 6.7), which is a superposition of the diffraction patterns from LMO, SMOand the STO substrate. The white square indicates the positions of the LMOreflections. They can be indexed in a pseudo-cubic or a rhombohedral (R3c)structure2. No spots due to the possible presence of the orthorhombic phase are

2Pseudo-cubic means that we index the structure as if it was a perfect cubic perovskite. In factthe structure has lower symmetry, but the displacements from the ideal cubic lattice positions aresmall.


Figure 6.7: Electron diffraction pattern images for LMO8SMO4 (a) and LMO12SMO6(b) along the [001] direction of the STO substrate. The satellite spots due to long rangeorder of the layers are indicated by the fork pattern. An enlarged satellite spot patternfrom (b) is shown in (c).

observed. The perfect ED pattern confirms the epitaxial growth of the layers.Moreover, the satellites spots, due to the periodic stacking of the LMO-SMO lay-ers, are clearly visible. For the LMO12SMO6 specimen the periodicity is ≈ 81.9AThe LMO8SMO4 superlattice film exhibits the same structure perfection but thesuperperiod is ≈ 50 A (fig. 6.7a).

A cross-section HREM image of the first layers of LMO8SMO4, grown onthe STO substrate is shown in fig. 6.8. The first LMO buffer layer shows per-fect epitaxy across the interface, with no secondary phase or amorphous layerpresent along the interface. No interface dislocations, resulting from misfit ac-commodation, are seen at the STO/LMO interface. The first SMO layer growson a flat LMO surface and exhibits a sharp heteroepitaxial LMO/SMO interface.Only occasionally a perovskite unit cell step is present at the LMO/SMO interface.Surprisingly, misfit dislocations along the interface are absent although the misfitLMO-SMO for fully oxidized material would be 2.6 %. This implies that the SMOperovskite-type layer is stabilized between two LMO layers and, actually, adoptsthe pseudo-cubic structure of LMO. In this respect it is clear that the SMO layer isunder high tensile stress. The cross-section HREM image of a LMO12SMO6 film(fig. 6.9) is very similar to that obtained for LMO8SMO4. However, the first LMOlayer shows unambiguously features of orthorhombic symmetry. Discrete Fouriertransformations (FT) made from different areas of the image of the LMO/STOinterface show typical spot arrangements for [010] and [110] orthorhombic zones.Nevertheless, the following LMO layers exhibit a FT pattern which is consistentwith a rhombohedral structure.

A HREM image of the interface between the STO substrate and the first LMO


Figure 6.8: HRTEM cross-section image of the LMO8SMO4 sample, the arrow indicatesthe direction and extent of the STEM scan for EELS analysis.

Figure 6.9: HRTEM cross-section image of the LMO12SMO6 sample showing the firsttwo LMO layers on the STO substrate. Fourier transforms are made from selected regions.The first layer (regions 1 and 3) indicate an orthorhombic symmetry, while further layers(region 2) show a pattern consistent with rhombohedral symmetry.


Figure 6.10: HRTEM cross-section image of the (LMO12SMO6)6 sample near the sub-strate interface. Insets show the result of a multislice calculation for a given thickness andfocus assuming a R3c symmetry for the LMO layer and Pm3m for STO and SMO layers.

layer is shown at higher magnification in fig. 6.10. Film and substrate are per-fectly coherent. Since the crystal structures of STO and LMO are very similar(both perovskite type structures) it is reasonable to assume that the LMO layerstarts to grow so as to continue the substrate structure as much as possible. Underthe experimental defocus conditions and according to multislice image simula-tions (fig. 6.10 insets), all heavy-atom columns in the STO substrate are imaged asbright dots. In the LMO image the brightest dots represent MnO columns. Sincethe column-projected potential of Sr and Ti-O columns is very similar, no differ-ence in dot brightness between Sr and Ti-O columns can be discerned according tothe simulations. The SMO layers also have similar Sr and Mn-O column potentialsand show an intensity distribution comparable to STO. Since we prepared STO tohave a SrO terminated layer (see experiment), the following layer sequence, basedon this assumption and on the HREM evidence is most likely: bulk-TiO2- SrO-MnO2-LaO- bulk. The cross-section HREM image of fig. 6.10 reveals sharp andwell defined LMO/SMO interfaces.

The HREM images of figs. 6.8 and 6.9 clearly indicate that, across the in-terface, the brightest dot rows of the LMO layers are in phase within the wholeheterostructure film. This observation strongly suggests, that across the inter-face, the La-sublattice of one LMO layer is in register with the La sublattice of


Figure 6.11: Structure model of the heterostructure.

following LMO layers and the Mn lattice is continuous across the whole film.Therefore, the stacking sequence at the LMO/SMO and SMO/LMO interfacesshould be identical and the following layer sequence, shown in fig. 6.11, is mostlikely: bulk-TiO2-SrO-MnO2-LaO-bulk- LaO-MnO2-SrO-MnO2. This sequenceis maintained in all areas of the film and holds for the LMO/SMO as well as forthe SMO/LMO interface. The image simulations of upper and lower interfaces infig. 6.10 are based on the rhombohedral (R3c) structure for LMO (only the firstLMO layer was found to be orthorhombic), cubic (Pm3m) structure for SMO andon the model of fig. 6.11. These observations further allow us to conclude that,both LMO and SMO layers show a layer by layer growth with only unit cell heightsteps.

EFTEM

In view of a possible La-Sr interdiffusion leading to La1−xSrxMnO3 com-pounds, EFTEM analysis is performed to map the spatial distribution of chemicalelements in the heterostructure. Fig. 6.12 shows a combination of colour codedchemical maps for La and Sr (A,C) together with the conventional TEM images(B,D) for the two samples (A,B: LMO12SMO6, C,D: LMO8SMO4). This pictureshows that artificial A-site ordering is achieved and that no significant chemicaldiffusion or local concentration variation is present in the layers. The spatial reso-


Figure 6.12: EFTEM colour coded elemental maps (A,C) and conventional TEM images(B,D) for both samples (A,B LMO12SMO6, C,D LMO8SMO4)

lution in the EFTEM images can be theoretically estimated by taking into accountchromatic and spherical aberration as well as delocalisation as was shown in chap-ter 5. This gives an estimated resolution better than 1 nm for all elements with thechosen operational parameters. Due to long exposure times, significant drift canoccur, and this will deteriorate spatial resolution. Spatial resolution in EFTEMimages was defined in chapter 5 following Berger et al. [52] as the diameter of adisc containing 59% of the point spread function, which models the imaging ofa pointlike atom taking into account the inelastic scattering and the propagationof the inelastic image through the microscope lenses. This means, that with atheoretical resolution of 1 nm we can not answer questions regarding interdiffu-sion of elements between layers having thicknesses comparable to this resolution.An assumed mathematical rectangular chemical profile would require frequencycomponents up to infinity in the EFTEM image to represent the profile withoutbroadening as was demonstrated in fig. 5.8 in chapter 5. Saying that EFTEM has


Figure 6.13: EELS spectra for different positions of the STEM probe between the 4th and5th LMO layer. O K and Mn L2,3 edges are clearly visible.

a resolution limit of 1 nm in this case, only means that we can see the layers aswell separated, but not that we can determine the specific shape of the diffusionprofile directly from the EFTEM images.

STEM EELS

The result of the acquisition of EELS spectra of the LMO8SMO4 sample froma position inside the 4th LMO layer to a position in the 5th LMO layer is presentedin fig. 6.13. The O K-edge around 530 eV and the Mn L2,3 edge around 640eV are clearly visible, together with the variation of the background for differentpositions. On top of this dataset, data was also captured for the La M4,5 edge andthe Sr L2,3 edge as well as for the low loss region to allow for deconvolution andthickness estimates.

To extract chemical information from this set of spectra, a maximum likeli-hood (ML) fitting technique is used as described in chapter 4. The ML approachgives an unbiased estimate of the model parameters when the counting statisticsare taken into account properly. This is especially important for noisy spectra likefor the Sr L2,3 edge at ≈ 2 kV, which requires long exposure times because of theextremely small inelastic cross section at these high energies. The model F(E)consists of a standard background model AE−r and experimental cross sectionsfor the excitation edges.

F(E) = AE−r +C1M1(E)+C2M2(E)+ . . .


The fitting procedure results in a set of parameters, which we can use as estimatesof the real parameters of the experiment. We can use the proportionality constantsC1,C2, . . . as estimates of the chemical concentration of the different elementsmodelled by the experimental cross section M1(E),M2(E), . . . A convolution withlow loss spectra to include multiple scattering is not carried out because we as-sume that the difference in low loss spectra is small because of the delocalisationof the plasmon excitations. Recording the low loss spectra required that the elec-tron beam current was largely reduced to avoid overexposure of the detector andmade it difficult to position the beam on the layers with only a very weak darkfield STEM image as a guide. Using convolution in the model is possible andcould improve the fit, but we argue that the uncertainty in the position of the lowloss spectra makes the quantification worse in this case. However, the low lossspectra enable us to estimate a thickness profile which was found to be a lineardecreasing profile with a variation of less than 10% over the range of the scan( t

λ ≈ 0.4 with λ the inelastic mean free path for a plasmon excitation).To cancel out problems with varying thickness and elastic scattering, we as-

sume that the Mn content in the sample is constant and we divide all elementalcontributions to the spectra by the Mn L2,3 signal. The result of this process isshown in fig. 6.14. The relative values in the plot are chosen to fit approximatelywith the nominal values in the LMO layers. This way, we circumvented most ofthe problems with absolute quantification by keeping only the relative quantifica-tion from place to place. We have decreased significantly the uncertainty of thedifferent factors like thickness, absolute cross sections, multiple scattering andelastic scattering by assuming that they have approximately the same effect on allexcitation edges under study.

The profiles show a complementary La-Sr signal, and an oscillating O signal.The O-signal drops approximately 15%, and the drop is centered around the SMOlayer. The resolution and signal to noise with STEM-EELS is clearly higher ascompared to the EFTEM results, but still the resolution is limited by beam broad-ening inside the sample, slight misorientation and/or steps in the interface plane,sample drift and delocalisation. An improvement by deconvolution of these fac-tors is possible in principle when the effect of all these factors is known precisely,but even then, noise amplification (see chapter 4) prevents us from recoveringsuppressed high resolution information in practice.

ELNES

The energy loss near edge structure (ELNES), of both the O K-edge and theMn L2,3-edge are studied from the spectrum of the middle of a LMO and a SMOlayer, and the results are shown in fig. 6.15.


Figure 6.14: Result of fitting procedure: Chemical profiles of O-K, La M4,5 , Sr L2,3 andMn L2,3 divided by Mn L2,3 edge signal to cancel out elastic scattering and thicknesseffects. Positions are calibrated from the layer to layer distance as observed in HRTEMimages.

O K-edge The O K-edge shows the excitation of the O 1s core state to unoccu-pied states near the Fermi energy. The dipole selection rules apply approximatelyand favour the excitation to O 2p-like states. The actual shape of ELNES can onlybe compared to theoretical calculations or compared with other known compounds(fingerprinting).

Fig. 6.15A shows the O K-ELNES for the center of an LMO and SMO layer.Three peaks can be distinguished and were attributed by Abbate et al. [17] bymeans of electronic structure calculations (crystal field model) to be excitationsto the O 2p state hybridized with Mn 3d (a), La 5d or Sr 4d (b) and Mn 4sp (c).From this labelling of the peaks, we can conclude that the change of La by Sr ingoing from LMO to SMO, leads to an increase in the number of O 2p holes whichare hybridized with Mn 3d and a shift of peak (b) by 1eV to higher energies,indicating that the hybridized O 2p-La 5d band lies about 1 eV lower in energy asthe O 2p-Sr 4d band. Peak (a) rises by ≈ 20% in the SMO layer. Both the shiftof peak (b) and the rise of peak (a) seem to be correlated, i.e. both effects followapproximately the same curve when plotted in function of position in the sample.Zampieri et al. [53] have shown that for bulk CaMnO3−δ the oxygen deficiencydecreases peak (a) of the O K-ELNES, a similar effect as seen for changing Laby Sr in La1−xSrxMnO3 [17]. If we extrapolate this result, we would expect thatthe O deficiency would have an equally important effect on peak (a) of the O K-ELNES as changing the A site cations. This makes it difficult to separate the effectof the measured O deficiency from the effect of the change in A-site cations.

The O K-ELNES is in qualitative agreement with experimental [17, 54] and


Figure 6.15: ELNES from center of the layers for O K-edge (a) and Mn L2,3-edge (b)

theoretical [17, 55] results for bulk La1−xSrxMnO3 or La1−xCaxMnO3. There ishowever a disagreement in the relative height of the peaks for SMO. The ELNESof La0.1Sr0.9MnO3 in [17] shows a much stronger peak as compared to our ex-periments. This could be attributed to differences in crystal orientation, XAS vs.EELS or instrumental resolution.

To our knowledge, no systematic spectroscopic study (XAS or EELS) wasperformed on SrMnO3−δ . Therefore we have to look at “similar” compounds toget a feeling of the behaviour with varying oxygen deficiency. Zampieri et al. [53]have shown XAS spectra for the O K-ELNES of CaMnO3−δ and a consistentdrop of the prepeak with oxygen deficiency was observed. Extending this trend toSMO could explain the observed small peak (a) in the O K-ELNES of the SMOlayer to be due to a significant oxygen deficiency.

Mn L2,3-edge The Mn L2,3-edge is shown in fig. 6.15b and is attributed to ex-citations from the spin split Mn 2p core states to higher unoccupied states of Mn3d character. The difference between the Mn L2,3 ELNES of SMO and LMO isvery small, indicating that there is almost no measured difference in the unoccu-pied states of Mn 3d character between LMO and SMO within the experimentalresolution. This is surprising since it is assumed that the valency of Mn changes


nominally from Mn4+ for SMO to Mn3+ for LMO.Studies of ionic manganese oxides have shown that there is a significant change

in the Mn L2,3-edge, which can be correlated with the nominal Mn valency. TheMn L-edge is expected to shift to higher energies, increase in intensity and alterthe intensity ratio of the L3 to L2 peak with increased Mn valency [10, 13, 56]. Itis clear that an extrapolation of these ideas to the experimental data of the layersunder study gives rise to difficulties.

It can be argued that because changes can be seen in the O K-edge, the Mn-O bonds have a considerable covalent character. The idea of hybridized Mn 3dand O 2p states is supported by experimental evidence from XPS [20], XPS andXAS [18],XAS [17] and EELS [19]. A systematic study of different controlled-valency materials [16] shows that the manganites are an intermediate case betweenthe behaviour of the titanates and vanadates where the holes go to the transitionmetal site, and the cuprates and nickelates where holes go to the oxygen sites.

On the other hand, assuming an oxygen deficiency in the SMO layer as ob-served in the EELS spectra, would make the nominal valency in the SMO layerdrop and thus decrease the expected difference in the Mn L2,3-edge.

6.3.5 Imaging spectroscopy

Fig. 6.16 shows the results of the imaging spectroscopy technique combined toshow the change of fine structure in the O K-edge from the substrate to the layers.The waterfall plot is superimposed with an intensity plot for better visibility of theposition of the peaks. The 3 peaks in the O K-edge fine structure can be clearlyseen. A change of the fine structure can be seen as a rise of the first peak and ashift to higher energies of the second peak in the SMO layers, compared to theLMO layers. This change is consistent with the ELNES results obtained withSTEM, but the image series technique shows the results of all the layers together.Again, the shift of peak (b) and the rise of peak (a) are correlated. Following theinterpretation of the peaks of Abbate et al. [17], we can conclude that O 2p holesin the SMO layers are well localized.

It is also interesting to note the extra peak at the interface between the STOsubstrate and the first LMO layer. This prepeak is probably due to the terminatingSrO layer of the substrate, connecting to a MnO2 layer in LMO. This creates alocal oxygen environment, similar to that in SMO. The result of the image seriesof the LMO12SMO6 sample shows similar results as in LMO8SMO4 with STEMELNES, and shows the ELNES changes to be consistent over all layers.


Figure 6.16: Result of imaging spectroscopy technique. ELNES of O K-edge for substrateand layers in the LMO12SMO6 sample. The arrow above the spectrum indicates theprepeak seen at the interface between the STO substrate and the first LMO layer.

6.3.6 Discussion

We will try to propose a model that combines all experimental evidence. Themodel can be described by the general formula(LaMnO3)2n(SrMnO3−δ )n/STO(100) for n=4,6 , with an estimated oxygen defi-ciency δ ≈ 0.5 as measured from the experimental chemical concentration profile.

The HRTEM images clearly show a layer-by-layer growth (as also seen on theRHEED patterns during growth [57]) of the layers with sharp interfaces betweenthe layers. Perfect epitaxy and a distinct intensity distribution for different layers,consistent with multislice image simulations is seen. This confirms the separationof La- and Sr-containing layers while it can be shown that the simulated image isinsensitive to an oxygen deficiency of about 15% in the SMO layer.

The model is confirmed by the chemical profiles obtained from a parameteri-zation of the EELS spectra. A good La/Sr separation and an O-deficiency in theSMO layer are seen when a constant Mn concentration is assumed. The hypothe-sis for a constant Mn concentration has been verified by noting that the intensitychange in the Mn signal for both layers can be explained by preservation of elasticdiffraction contrast.

The ELNES of the Mn L2,3 edge is in agreement with the proposed model

since for δ ≈ 0.5 the nominal valency of Mn is fixed to Mn3+ for both the LMOand the SrMnO3−δ layer. Even for an O-deficiency different from 0.5, only asmall change of the Mn L-edge is expected, in agreement with experiment. The


fine-structure inside the Mn L3 and L2 peak is attributed to multiplet splittingand is expected to be different for both layers, explaining the tiny difference inshape of the white lines. The O K-edge on the other hand shows a very differentfine-structure for both layers. Comparison with experimental results for SrMnO3shows a discrepancy in the strength of the first peak of the O K-ELNES. Com-parison with a similar compound CaMnO3−δ showed that the effect of oxygendeficiency is a strong decrease in the strength of the first O K-ELNES peak. Thisseems to suggest that the observed ELNES for the SMO layer is likely to comefrom SrMnO3−δ rather than SrMnO3 which fits to our proposed model.

The EFTEM results as well as the imaging spectroscopy technique agree withthe STEM observations pointing out an interesting consequence. The STEM re-sults were obtained from a mechanically polished sample, while the TEM resultswere obtained from a conventional ion-milled sample. The fact that both resultsagree so well, rules out the possible influence of sample preparation on the ob-served electronic structure. STEM and TEM experiments used different primaryelectron energies of 100 kV and 300 kV, giving extra support for the absence ofbeam damage because both results are consistent. Both samples, LMO8SMO4and LMO12SMO6, lead to comparable observations, pointing out that apart fromdifferent scales and different total layer thickness, there is no significant differencein chemical or structural observations at the experimental accuracy.

Electronic structure calculations could further improve the interpretation of theobserved ELNES peaks. The reason for the oxygen deficiency, which remarkablybalances the nominal Mn valency to approximately Mn3+, is related to tensilestress in the SMO layer creating oxygen vacancies.

6.3.7 Conclusion

In this section we illustrated how a combination of HRTEM, diffraction tech-niques, STEM EELS, ELNES, EFTEM and imaging spectroscopy can solve nanoscalecharacterization problems. We investigated (LMO)2n(SMO)n heterostructuresand showed that oxygen deficiency in the SMO layers leads to an adapted for-mula (LaMnO3)2n(SrMn3−δ )n with δ ≈ 0.5. This model was shown to fit to allexperiments. We found good chemical separation of the A-site cations La andSr and the structure shows an artificial crystal with unbroken Mn lattice. TheSMO layers are stabilized between two LMO layers, but tensile stress leads toweakly ordered oxygen vacancies increasing the number of 3d electrons in Mn toresemble the Mn3+ state of LMO. The O K-ELNES however, points out that theMn-O bonds have a considerable covalent character and electronic structure cal-culations are needed to fully interpret the electronic structure of such a complexheterostructure.


6.4 LSMO-STO multilayers

6.4.1 Introduction

Heterostructures of La0.7Sr0.3MnO3 and SrTiO3 are grown on a SrTiO3 (100)substrate to obtain a sequence of 15 layers described as:((La0.7Sr0.3MnO3)m(SrTiO3)n)15. The layers are grown with a pulsed liquid in-jection metalorganic chemical vapour deposition (pulsed liquid injection MOCVD)technique by Dubourdieu et al. from the Laboratoire des Materiaux et du GeniePhysique (F). The deposition technique is described in detail in reference [58] andwill only briefly be described in this section.

The interest in these heterostructures lies in the possibility to tune the latticemismatch induced strain by choosing the thickness (via m and n) of the layers.This gives the opportunity to tune the lattice parameter in the LSMO layer betweenthe bulk value (≈ 3.875 A ) and the value for bulk STO (≈ 3.905 A ) creating newways to optimize the magnetic and electronic properties of the LSMO manganitesfor technological applications.

In this section, the growth and magnetic properties of a set of((La0.7Sr0.3MnO3)m(SrTiO3)n)15 samples with n=8 and m between 5 and 32 willbe shown. Only two “extreme” samples from this set, m=5 and m=32, are stud-ied by EFTEM and TEM. A brief overview of the TEM results will be giventogether with some preliminary findings on the chemical differences found in twoend members of the set of samples, studied by EFTEM.

6.4.2 Pulsed Liquid Injection MOCVD

The technique of the pulsed liquid injection metalorganic chemical vapour de-position is described by Dubourdieu et al. [58] and is based on the injection ofsmall droplets of a liquid precursor in a low pressure deposition chamber (0.67kPa). The liquid immediately vaporizes and forms a stable gas phase which con-denses on a heated substrate (STO 700C). The liquid injection is controlled viamicrovalves and the number of injected droplets can be correlated to the thicknessof the deposited layer. A set of microvalves with different liquid precursors allowsfor the growth of alternating layers of different materials. It was shown that goodquality heterostructures could be produced in this way even for layers of only 3perovskite unit cells thick.

After the deposition, the samples were annealed at 800C for 15 min. in anoxygen pressure of ≈ 105 Pa.

The quality of the heterostructures was checked with X-ray diffraction andtypical satellite spots are found as proof of the long range stacking periodicity ofthe layers. It should be noted however that X-ray diffraction only estimates the

108 6.4. LSMO-STO multilayers

Figure 6.17: Curie temperature Tc of the set of samples with m = 5,8,12,16 and 32. Twovalues are given for Tc as explained in the text.

overall quality of the film; local imperfections can still exist. A TEM study wasperformed to further investigate the quality of the films.

6.4.3 Structural aspects

Dubourdieu et al. [58] showed by X-ray diffraction that the average latticeparameter of the superlattice changes continuously between the bulk lattice pa-rameters of STO (3.905 A ) and LSMO (3.875 A ) depending on the thickness ofthe STO and LSMO layers.

Kreisel et al. [59] showed by a Micro-Raman study that a structural phasetransition in LSMO takes place, from bulk rhombohedral in thick LSMO layers(10 nm LSMO, 12.4 nm STO) to orthorhombic in thin LSMO layers (3.6 nmLSMO, 9 nm STO). They propose that an intermediate range of layer thicknessesexist where orthorhombic and rhombohedral regions co-exist.

6.4.4 Magnetic properties

The magnetic properties of a set of ((La0.7Sr0.3MnO3)m(SrTiO3)n)15 are in-vestigated by Dubourdieu et al. [60] and a plot of the Curie temperature Tc versusLSMO layer thickness is shown in fig. 6.17. The Tc is calculated from the mea-sured magnetization curve obtained with a SQUID magnetometer in a field of 5mT perpendicular to the layers for different temperatures. The Tc is derived intwo ways because the ferromagnetic phase transition is not abrupt. One way is totake the inflection point of the magnetization curve and the other way is to takethe intersection of the tangent at the inflection point with the horizontal line of the


Figure 6.18: Low magnification TEM image of a cross section sample with m = 5. Notethe darker contrast regions perpendicular to the substrate. The inset shows a magnifiedDP showing the characteristic satellite spots due to the stacking periodicity.

magnetization in the paramagnetic state. Both methods give identical results for asharp phase transition , but can deviate for a slow transition. The results of bothmethods are shown in fig. 6.17.

Fig. 6.17 shows a large drop in the Curie temperature, when the LSMO layerthickness decreases. This huge change in Tc from the bulk value ≈ 350 K to below200 K proves the sensitivity of the magnetic properties to the crystal structure andthe value of the lattice parameter.

6.4.5 TEM observations

TEM observations were made to check quality and the local crystal structureof the superlattices. The low magnification cross section images of the two “ex-treme” samples are shown in fig. 6.18 for m = 5 and in fig. 6.20 for m = 32.

Fig. 6.18 shows darker regions running perpendicular to the substrate fromthe substrate to the top of the film, together with a selected area diffraction pattern(DP). The DP shows satellite spots due to the periodic stacking of the LSMO-STOlayers. The satellite spots are shown magnified as an inset of the HRTEM imagein fig. 6.19. The HRTEM image shows the perfect epitaxial growth of the filmwith sharp interfaces. Some blurred regions are indicated by arrows and might beindicative for local chemical imperfections.

The low magnification image for the m = 32 sample in fig. 6.20 does not showthe darker contrast regions that were observed for the m = 5 sample. The insetsshows a selected area diffraction pattern. The satellite spots are less visible nowsince the stacking period is 40 unit cells for m = 32 compared to the 13 unit cellsfor m = 5. The film also shows some waviness and the top of the film is lessflat than for m = 5. A HRTEM image for m = 32 is shown in fig. 6.21. Thesame epitaxial growth as for the m = 5 sample is observed and blurred regions of


Figure 6.19: HRTEM image of the m = 5 sample. Note the high quality of the epitaxialgrowth. Note also the blurred regions indicated by arrows. The inset shows a magnifi-cation of the satellite spots from the selected area diffraction pattern due to the periodicstacking of the layers.


Figure 6.20: Low magnification TEM image of a cross section sample with m = 32. Theinset shows a selected area diffraction pattern.

Figure 6.21: HRTEM image of a cross section sample with m = 32. Note the blurredregion inside and below the STO layer indicated by an arrow.

similar size as found in fig. 6.19 are seen to be localised inside and slightly belowthe STO layer as marked by the arrow on fig. 6.21. These regions do not show adisruption of the structure and the contrast is believed to be due to a chemicallydifferent secondary phase. The composition of these regions will be studied withEFTEM.


6.4.6 EFTEM

EFTEM elemental maps together with zero-loss images for both “extreme”samples are shown in fig. 6.22 and fig. 6.23 for a sample with m = 5 and m = 32correspondingly. The elemental maps are taken with a collection angle of β ≈19.2 mrad with a heavily focussed beam. The focussed beam improves the signalto noise ratio in the images as well as decreasing the required exposure time atthe expense of non-uniform illumination observed in some of the elemental maps(especially Sr maps). The non-uniform illumination prevents us from doing areliable quantification in the elemental maps. The colour coded maps containhowever some interesting qualitative information.

The m = 5 sample in fig. 6.22 shows an almost perfect chemical separationbetween the LSMO and STO layers. The layers are slightly waving. Small imper-fections in the chemical separation are found near the interface as Mn containingregions in an STO layer. These regions are indicated by arrows in fig. 6.22B. Theregions are Mn rich as evidenced from the red colour and from the Mn elementalmap. The regions contain no sign of La and the Sr content seems to be depletedalthough the Sr elemental map is rather noisy. The oxygen contrast is also slightlyreduced but this is probably due to a difference in elastic contrast. The qualitativeconclusions of the elemental maps of the m = 5 sample can be summarised as:

• The LSMO and STO layers are well separated on a nanometer scale

• Small regions of a chemically different phase disrupt mainly the first STOlayer near the substrate interface. The phase is manganese and oxygen richand seems to contain no La or Sr. A quantification of the exact chemicalconcentrations in the regions should be made with quantitative EELS.

The zero-loss image of the m = 32 sample in fig. 6.23A shows spot-like re-gions inside and below the STO layers that are ordered perpendicular to the sub-strate. The elemental maps of Ti, La and Mn are combined in a colour map infig. 6.23B showing qualitatively the nature of these regions. The regions are Mnrich as evidenced by the strong contrast in the Mn elemental map. This contrast issurprising because of the expected smaller volume of the anomalous regions andpoints probably to a chemical phase with a Mn volume concentration higher thanin LSMO. Most regions are ordered and form a continuous string from the sub-strate to the top of the layers. The regions are localised inside the STO layers, butcontinue for some distance in the LSMO layer below it. The regions contain no orvery little La as evidenced from the reduced intensity regions in the La elementalmap. The Sr elemental map shows no evidence of Sr in the anomalous regions.The oxygen map finally, shows no clear evidence of the regions suggesting thatthe oxygen volume concentration in the anomalous regions is similar to that ofboth STO and LSMO.


Figure 6.22: EFTEM analysis for a cross section sample with m = 5: Zero-loss image(A), colour coded elemental map image (B) and Mn, La, Sr and O elemental maps. Mnrich regions in the first STO layer are indicated by arrows in B.

It is worth noting that the waving of the layers is strongly correlated with theappearance of the anomalous regions. This is especially apparent in the topmostlayers of fig. 6.23.

6.4.7 Conclusion

This study illustrates once again the importance of EFTEM and conventionalTEM techniques to study the structure and chemistry of thin films on a nanoscale.It is interesting to note that the anomalous contrast regions observed with TEMand qualitatively characterised with EFTEM went unnoticed in previous studieswith X-ray diffraction and Micro-Raman spectroscopy [58, 59]. The exact chem-ical formula of the regions could not be obtained unambiguously from EFTEMbecause of the difficulty to interpret and quantify the elemental maps on this scale.The elemental maps however strongly point to the direction of a manganese ox-ide (MnO?) with a high volume content of manganese. The correlation with themagnetic and electric properties is not straightforward but it should be clear thatthe possible influence of these anomalous regions could be large in LSMO.

A future STEM EELS study combined with fitting a parametrized model could


Figure 6.23: EFTEM analysis for a cross section sample with m = 32: Zero-loss image(A), colour coded elemental map image (B) and Mn, La, Sr and O elemental maps. Mnrich regions are clearly visible in (B) as red lines running from the substrate to the top ofthe film.

shed light on the exact composition of the regions and on the film growth process.


6.5 Composite LCMO1−x:MgOx thin films

6.5.1 Introduction

In this section we discuss the composite LCMO1−x:MgOx thin films whichhave some interesting structural and magnetotransport properties. The films arestudied by a combination of TEM, EFTEM, X-ray diffraction and magnetotrans-port measurements and only a brief overview of the results is given here, whilewe will focus on the nanoscale EFTEM investigation. For a more detailed reviewof the structural aspects, see Lebedev et al. [61]. For a detailed report on themagnetotransport properties, see Moshnyaga et al. [62].

The films are prepared by Shapoval et al. from the Institute of Applied Physicsin Moldova.

Recently, composite bulk samples of La0.7Ca0.3MnO3(LCMO)/SrTiO3(STO)and La0.7Sr0.3MnO3(LSMO)/borosilicate glass were shown to be appropriate sys-tems to study the possibility of nanostructural engineering by adding a secondaryphase to a doped manganite material. This secondary phase induces lattice strain,and has a comparable effect as applying hydrostatic or chemical pressure to themanganite. The properties of the manganites are known to be very sensitive to thelattice parameters [1] and therefore, such composite systems may be able to tunethe properties to fit better with technological needs.

A possibility to enhance low field magnetoresistance (MR) for a LSMO/glasscomposite at room temperature was demonstrated [63]. The low field MR, how-ever not larger than 2%, as well as the CMR-values were maximal for concentra-tions of the second phase in the vicinity of the percolation threshold in conduc-tivity. Typical values of the percolation threshold of 25% of borosilicate glass forthe LSMO/glass composite [63] and of 40% of STO in a LCMO/STO compos-ite [64] were observed. A similar increase of the MR at the percolation thresholdwas observed earlier for granular ferromagnetic metal (FM)/metal(or insulator)composites [65, 66].

LC(S)MO/oxide thin film composites seem to be promising not only for therealization of a low field MR but also as a model system consisting of 3D mangan-ite clusters imbedded in an appropriate oxide matrix. In such a system an artificialelectronic phase separation of the metal-insulator type can be realized and its pa-rameters can be controlled by the processing conditions. Electrical transport andmagnetic properties can then be compared with those recently observed in “nat-ural” FM/antiferromagnetic insulator phase separated systems [67]. This showsthat the properties of a perovskite manganite can be controlled to a large extentby a surrounding second phase component. This becomes particularly interestingwhen both phases can be grown epitaxially on a substrate.

116 6.5. Composite LCMO1−x:MgOx thin films

6.5.2 Sample preparation

(La0.77Ca0.33MnO3)1−x : (MgO)x ((LCMO)1−x : (MgO)x) films were preparedby a metalorganic aerosol deposition described elsewhere [68]. This is a solutionbased technique which uses a mixture of the corresponding metal-chelate precur-sors dissolved in an organic solution. The deposition of oxide films occurs as aresult of a heterogeneous pyrolysis of a finely dispersed aerosol/vapour phase ofmetalorganic precursors on the heated substrate. To obtain composite films anappropriate amount of Mg-precursor is added to the basic solution used for thepreparation of LCMO films. Thus, a simultaneous growth of LCMO and MgOphases from a single precursor solution is realized. The nominal concentration“x” of the insulating MgO phase in the composite films corresponds to the mo-lar concentration of the Mg-precursor in the precursor solution. Freshly cleavedMgO(100) single crystalline plates are used as substrates. The substrate tempera-ture during the film deposition was 700 C and the deposition rate was about 40nm/min. The final thickness of the films is in the range 150-200 nm.

6.5.3 Characterisation methods

The macrostructure of the films is characterized by X-ray diffraction (XRD)using CuKα radiation, on a ”Siemens D5000”diffractometer. The microstructureof the films is studied by TEM and high resolution electron microscopy (HREM)for plan view and cross section geometries of the samples. Electrical transportproperties are measured by the 4-probe d.c. method in a temperature range from4.2 K to 300 K and under magnetic fields ranging from 0 to 5 T. A commer-cial He-cryostat equipped with a superconducting solenoid ”Cryogenics Ltd.”isused. Magnetization measurements are carried out by means of a vibrating sam-ple magnetometer (VSM) as well as by a commercial SQUID magnetometer atT=1.8-300 K with the magnetic field aligned parallel to the substrate. Transportmeasurements and X-ray results are given in more detail by Moshnyaga et al. [62].

TEM investigations are carried out with a JEOL 4000EX microscope operatedat 400 kV. The point resolution of the microscope is of the order of 0.17 nm.Cross-section as well as plan-view specimens for TEM study are prepared bythe standard techniques: mechanical polishing till a thickness of about 15 µmfollowed by ion-milling under grazing incidence.

The EFTEM technique is used to create elemental maps of Mg with the stan-dard three-window technique [37]. EFTEM images are captured using a GatanGIF2000 coupled to a Philips CM30 FEG. Maps of the Mg K-edge, La M4,5-edge, Mn L2,3-edge, Ca K-edge and O-K edge are acquired to confirm the chem-ical composition of the sample. Both cross-section and plan-view specimens arechecked with EFTEM. The collection angle β =19.2 mrad and the exposure time


for the Mg K-edge is 60 s. The sample orientation is chosen to be slightly off-axisto reduce problems with diffraction contrast. Drift between the 3 window imagesis corrected by cross-correlation.

6.5.4 TEM

Cross-section multibeam bright field images of (LCMO)1−x : (MgO)x com-posite films for x = 0 and x = 0.5 are shown in fig. 6.24. Films are epitaxial at allMgO concentrations and exhibit sharp well defined film/substrate interfaces. Thethickness of the film is 120-150 nm. All films show the presence of a columnarmicrostructure with columns parallel to the interface normal, but the grain bound-ary and surface structure of the films vary with the MgO composition. A pureLCMO film (x = 0) exhibits an almost uniform domain size around 40 nm withvery little contrast between the domains (fig. 6.24a). The uniform contrast of thedomains and domain boundaries suggests that no secondary phase is present at theboundaries. The surface of the film is not flat and pyramid-like grains separatingdifferent domains are clearly visibly. The origin of this shape is believed to be dueto mismatch stress between substrate and domains and is described in more detailby Lebedev et al. [61].

The microstructure of composite films (x > 0) changes with x. The film sur-face grows flatter with increasing MgO content and the domain size changes. Atthe column boundaries Moire patterns appear (fig. 6.24b). They start from the in-terface film/substrate and run through the film to the surface. These Moire patternsare related to the presence of MgO as a second phase. The LCMO-MgO domainsoverlap along the viewing direction and because of the lattice mismatch Moirepatterns are formed. The width of the Moire regions increases with increasingMgO content.

Diffraction patterns from cross-section specimens are a superposition of diffrac-tion patterns produced by film and substrate; they clearly show a variation withincreasing MgO content as seen from Fig. 6.25. All patterns can be indexed as acomposite of two materials: LCMO and MgO. The ED pattern obtained from thepure LCMO film (x = 0) (Fig. 6.25a) can be indexed with respect to an orthorhom-bic lattice (Pnma, ao = ap

√2, bo = 2ap, c = ap

√2). Two different domain ori-

entations ([010]* and [101]*) are present within the selected area. Increasing theMgO concentration to x = 0.1 does not lead to visible changes of the ED patterns(Fig. 6.25b).

The reciprocal rows, indicated by white arrows in Fig. 6.25a,b, however dis-appear for x ≥ 0.33 (Fig. 6.25c,d). This suggests a different space group. Thediffraction conditions for R3c were found to be consistent with all observationsfor high MgO concentrations (Fig. 6.25c,d).

Further study of the diffraction patterns revealed a change in the spot splitting


Figure 6.24: Low magnification multibeam images of cross-section samples of as-grown(La0.77Ca0.33MnO3)1−x : (MgO)x/MgO(100) with different MgO concentration: (a) x=0;(b) x=0.33.

between spots coming from the MgO substrate and spots from the LCMO film.This spot splitting can be used to measure the change in lattice parameters betweenthe substrate and the film. It was found that the lattice parameters of the film arerather independent of MgO concentration for x < 0.3 and show a drastic increasefor x > 0.3. The lattice parameters were more accurately measured by X-raydiffraction but the same trend is observed (see table 6.1).

HRTEM images reveal an epitaxial growth of the LCMO domains on the sub-strate, with an atomically flat LCMO/MgO interface for x = 0. As the MgO con-centration increases, the structure of the film changes. At low concentration of theMgO (x=0.1) no significant differences with the pure LCMO film are noticed andthe structure remains perfectly coherent and free from secondary phases. Increas-ing the MgO concentration (x=0.33-0.5) leads to buckling of the film/substrateinterface (fig. 6.26) resulting from the epitaxial growth of MgO islands on the


Figure 6.25: Electron diffraction patterns of cross-section samples for different MgO con-centrations: (a) x=0; (b) x=0.1; (c) x=0.33; (d) x=0.5. The white arrows in (a) and (b)indicate reflections specific for the Pnma space group. These spots are absent in (c) and(d) consistent with the R3c space group.

MgO substrate surface. The MgO layers start from the interface, grow along theoriginal domain boundaries and extend all the way through the film up to thesurface. It is evident from the HRTEM image (Fig. 6.26) that the MgO layer isepitaxially intergrown between the LCMO domains with the same orientation asthe MgO substrate. No amorphous phase is observed in the domain boundaries.

Plan-view HRTEM observations confirm the epitaxial intergrowth of MgOalong the domain boundaries as shown in fig. 6.27. The interface between theLCMO grain and the MgO layer is not straight and has no specific crystallographicorientation.


Figure 6.26: Cross-section HREM image of the interface (LCMO)1−x −(MgO)x/MgO(100) for x = 0.5 Note the heteroepitaxial growth of MgO columnsalong a domain boundary in the direction parallel to the normal of the interface.

Figure 6.27: Plan view HRTEM image of the interface (LCMO)1−x−(MgO)x/MgO(100)for a sample with x=0.5. Note the epitaxial growth of the MgO layer around LCMOgrains.


Table 6.1: Characteristics of (LCMO)1−x : (MgO)x composite filmsx 0 0.01 0.05 0.1 0.33 0.5 0.67 0.8TMI(K) 257 260 205 149 - - - -TC(K) 260 245 197 145 228 216 210 208CMR(%@ Tc) - 700 1400 15000 90000 - - -c (nm) 0.385(8) 0.386(3) 0.386(7) 0.387(4) 0.388(0) 0.389(3) 0.391(4) 0.394(8)

6.5.5 EFTEM

Fig. 6.28b shows the Mg elemental map for a plan-view specimen (x = 0.5)with the accompanying zero-loss filtered image (Fig. 6.28a). The elemental mapshows a good localisation of the Mg signal in the bright ring-like features of thezero-loss image. An integrated line scan across an MgO layer (Fig. 6.28c) showsthat the Mg signal drops rapidly to zero on both sides of the MgO layer. As a roughestimate for the upper limit of Mg in the LCMO grain, we calculate the standarddeviation in the region outside and inside the wall from the profile in Fig. 6.28. Wetake into account the bright field intensity difference between the two regions andget an estimate for an upper bound of around 7% for the Mg volume concentrationin the LCMO layer as compared to the MgO wall. This accuracy is on the orderof what is to be expected from the three-window elemental mapping technique.Acquiring EELS spectra from different regions in the sample should be able tomake a more precise statement in view of the discussion in chapter 4 and can bedone in the future with a STEM/TEM combination.

From the EFTEM results, we conclude that there is no observable diffusionof Mg into the LCMO domains within the expected error of the three-windowtechnique. This result is in accordance with the fact that to our knowledge nostructural data have been published on Mg substituted LCMO phases.

The Mg elemental map of a cross section sample in fig. 6.29 also shows theMgO tube-like structure, but because of the overlap of LCMO and MgO regions, itis hard to quantify the phase separation between MgO and LCMO in cross section.

6.5.6 Magnetotransport properties

The magnetotransport properties are summarised in table 6.1 for different val-ues of x. With TMI the metal insulator transition temperature, Tc the Curie tem-perature, taken as the inflection point from the magnetization curves and CMR =100%R(0)−R(5T )

R(5T ) with R(5T ) the resistivity of the sample when applying a mag-netic field of 5 T perpendicular to the film and R(0) the resistivity when applyingno magnetic field. The table also contains the pseudo cubic c-lattice parame-ter measured by X-ray diffraction. A pure LCMO (x = 0) film is characterized by


Figure 6.28: Zero-loss filtered TEM image (A) and the elemental Mg map (B). The inte-grated line scan across the MgO layer in the white rectangle and in the direction indicatedby the arrow is shown in (C).


Figure 6.29: EFTEM elemental maps for the cross section sample. Zero-loss image (ZL)and Mg, Mn, Ca, O, La elemental maps.

TMI ≈ TC=260 K typical for the La-Ca-Mn-O manganite with a Ca-doping of 0.33.These data along with the low residual resistivity ρ(4.2K) ≈ 10−4 Ohm×cm ofthe pure LCMO film allow us to conclude that the films prepared by the metalor-ganic aerosol deposition technique behave as an intrinsic LCMO material similarto the epitaxial films prepared by a pulsed laser deposition method. Moreoverthe value of the c-lattice parameter c=0.385(8) nm is close to the correspondingbulk value and indicates no mechanical stress in pure LCMO films. Upon increas-ing the MgO concentration in the region 0 < x < 0.3 the values of TMI and TCfor composite films decrease systematically, while the CMR value becomes ex-tremely pronounced, reaching about 105%. Such a magnetotransport behaviour isin a good accordance with that found previously for coherently strained LCMOfilms deposited on SrTiO3 or LaAlO3 substrates [69–71]. The c-lattice parameterincreases slightly up to 0.388(8) nm for x=0.33, indicating the development ofstress in composite films with increasing MgO content.

At x≈ 0.3 the percolation threshold in conductivity takes place, at which an in-finite insulating MgO cluster forms around the LCMO domains, yielding a drasticincrease of the electrical resistance for films with x > 0.3. The value of the per-colation threshold is in good agreement with that observed in LSMO-glass bulkcomposites [63].

It is remarkable, that the Pnma-R3c structural phase transition takes place alsofor x ≈ 0.3; i.e. the structural phase transition is coupled to the percolation thresh-old. The reason seems to be a drastic increase of the 3D stress contribution when


Figure 6.30: The dependence of the Curie temperature, TC (K)(triangle), and the metal-insulator transition temperature, TMI (K)(square), and room temperature resistance, R,((Ω) right scale, circle) on the concentration, x, of the MgO phase in composite films.

all the LCMO domains are surrounded by epitaxially grown MgO layers at thepercolation threshold.

The magnetotransport data for composite films are summarized in a phasediagram shown in fig. 6.30, which illustrates the relationship between the micro-scopic structure and the macroscopic properties (resistance and magnetization).Note that TC has a non-monotonous dependence on x with a minimum at xC = 0.3and a further increase in the R3c phase.

6.5.7 Conclusion

(La0.77Ca0.33MnO3)1−x : (MgO)x composite films on a (100) MgO substratewere found to have remarkable microstructure and magnetotransport propertiesdepending on the MgO concentration. The films consist of two phases MgO andLCMO which were found to be chemically separated by EFTEM. For x > 0.3 theMgO domains form a layer around the LCMO domains which has two dramaticeffects:

• The conduction path is broken by the infinite insulating MgO layer and the


resistivity shows a drastic increase. At this percolation threshold the CMRvalue is highest.

• The LCMO grains surrounded by the MgO layer undergo a phase transfor-mation from Pnma to R3c due to the sudden increase in tensile 3D-stresscaused by epitaxial intergrowth of MgO.

Contrary to the expectations based on other composite manganites, the low-fieldMR was not found to increase.

This study showed that composite materials may hold promises for nanoscaleengineering of manganite materials. The introduction of uniform tensile stress isespecially interesting since this can not be achieved with hydrostatic pressure.


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Chapter 7

Metallic nanowires

7.1 Introduction

Metallic nanowires form an interesting subset of the field of nanomaterials.They have a diameter in the nm range and a large length/diameter ratio (aspectratio). Because of their nm scale, metallic nanowires can show very interestingand technologically important properties.

Ferromagnetic nanowires show interesting magnetisation behaviour when thediameter of the wire becomes comparable to the thickness of a magnetic domainwall. In this regime, the wire contains only a single magnetic domain and theprocess of magnetization reversal of the single domain is of fundamental interest[1]. Intuitively, the magnetic domain can only change magnetization by flippingover as a whole, requiring relative large magnetic fields. This makes these wiresideal permanent magnets with a high remanent magnetic field, a high coercivefield and an almost square hysteresis loop. These properties make ferromagneticwires interesting for use in so-called perpendicular storage media where a groupof ferromagnetic wires is stacked with the wire axis and magnetization directionperpendicular to the storage media plane ensuring extremely high storage densitiesand good thermal stability [2].

Electrical properties of nanowires are equally promising. The effect of anisotropicmagnetoresistance (AMR) is found in Co nanowires [3,4] where the conductanceof the wire is dependent on the angle of the electric current with the magneti-zation direction. The resistance of the wire is thus different for a current flow-ing in the direction of the magnetization as opposed to a current flowing per-pendicular to the magnetization. The effect is small with a magnetoresistance

AMR =Ralligned−Rperpendicular

Ralligned≈ 1%. Thin wires can show quantum transport and

adding an insulating gate to a wire or tube may lead to field effect transistor asfound in carbon and V2O5 nanotubes [5].

133

134 7.1. Introduction

Figure 7.1: Different steps in the growth of metallic nanowires with template synthesis.

Densely packed arrays of Co nanowires show a Giant Magnetoresistance (GMR)

effect with MR =RB=0−RB=0

RB=0≈ 60% the relative change in resistance of the set of

wires with and without a magnetic field B [6].Another interesting property of the nanowires is their high surface/volume

ratio making them ideal as catalysts for instance in organic solar cells.Their shape makes them possible candidates to create an array of field-emission

tips in future display technology. Metallic nanowires can be efficiently producedby the so-called template electrodeposition technique [6]. The different steps areoutlined in fig. 7.1.The technique is based on electrolysis through the holes of aso-called template. An isolating template with nm sized holes can be obtained byradiating a polycarbonate (PC) film with high-energy heavy ions. These ions dam-age the internal structure of the membrane on their way. The so-called damage-tracks can be etched away, leaving small holes in the PC film with a radius de-pending on the etching time. One side of the membrane is covered with a Au filmacting as a cathode for the electrolytic deposition. A salt of the desired metal isdissolved in water and the assembly is put into a potentiostat. The potentiostatadjusts the electrolytic current by keeping the voltage between the Au-cathodeand a reference anode constant. The deposition of the desired metal takes place in

Chapter 7. Metallic nanowires 135

the holes of the membrane until the current suddenly increases indicating that theholes are filled. Dissolving the membrane (or keeping it as is - a highly orderedfilm of metallic wires) leaves the wires behind.

Advantages of this technique are the cheap, and relatively uncomplicated setupand the fast growth. This makes the technique highly preferable over vacuumdeposition techniques for cases where it is usable.

Disadvantages are the need of an isolating membrane and the fact that a sol-uble salt is needed for the metal of interest, limitting the possible choices of ma-terials that can be used. The template can be made with lithographic techniquesas well if the scale allows. By switching the potential in the potentiostat, a choicebetween deposition of two dissolved elements can occur giving rise to interest-ing possibilities like creating a Co/Cu multilayer nanowire with GMR effect fora current along the axis of the wire, creating an extremely small magnetic sen-sor device [4]. In this chapter, the composition and valency effects of Co and Fenanowires made by template electrodeposition are studied by EELS and EFTEM.

7.2 Experimental

The metallic nanowires are prepared by G. Tourillon from the Laboratoire deCristallographie at the CNRS, Grenoble (F), making use of the template electrode-position method. Cobalt and iron nanowires (or nanotubes) were electrodepositedin the pores of commercially available track-etched polycarbonate membranes 6µm thick with quoted pore diameter of 30 nm and a pore density of ≈ 6× 108

cm−2 (Poretics). A thin gold layer was evaporated on one side of the membraneto serve as the working electrode in a standard three-electrode electrochemicalcell with a platinum grid as counter electrode and a saturated calomel electrode asreference. The electrolyte used to grow the nanowires or nanotubes was preparedfrom reagent grade chemicals and purified water. It consisted of 0.1 M H3BO3and 5× 10−2 M CoSO4 or FeSO4. The electrolyte was degassed by an argonflow for 10 minutes and the electrodeposition of Co and Fe took place at roomtemperature. Deposition was performed in the potentiostatic mode by applyinga sequence of potential pulses. Typically during the pulse sequence, the deposi-tion potential was -1.3 V/SCE for 0.3 s followed by a relaxation potential of -0.8V/SCE for 3 s, in order to renew the electrolyte inside the pores by diffusion,which is helped through magnetic stirring of the solution. At this latter potential,it has been checked that no dissolution occurred. It takes 15-20 minutes to fillthe pores of the membrane with nanowires. A shorter deposition time producedmainly nanotubes in the case of iron. After sample preparation, extraction of thenanowires or nanotubes from the template was made in two steps. First the goldlayer was removed by rubbing it with a cottoned head stick in water. Second, the

136 7.3. Co nanowires

polycarbonate membrane was dissolved in dichloromethane. Several drops of thesolution were then placed on a carbon-coated Cu TEM microscope grid. Threesamples were prepared in this way. The conditions for each sample are summa-rized in the following table together with their name that will be used throughoutthis chapter:Sample name Growth conditions Metal

Co1 15 min. growth CoFe4 10 min. growth FeFe6 15 min. growth Fe

TEM investigations are performed on a JEOL 4000EX, operating at 400 kVand having a point resolution of 0.17 nm.

EFTEM and EELS investigation was performed on a Philips CM30 operatingat 300 kV with a GIF 2000 energy filter.

EFTEM images are taken with a collection angle of β = 19.2 mrad and aver-aging of several images is used to improve the signal to noise ratio if spatial driftperformance allowed this. Zone axis orientations are avoided to limit the effect ofdiffraction contrast.

EELS is performed in diffraction mode with a collection angle β ≈ 10 mradand convergence angle α ≈ 2 mrad. EELS spectra are recorded together witha low-loss energy spectrum before and after the core-loss spectrum to check forbeam damage (change in plasmon) and energy drift (change in zero loss posi-tion). All spectra are calibrated to the position of the zero loss peak ensuring arelative energy scale accuracy better then 0.3 eV. EELS spectra are maximum like-lihood fit to a model consisting of hydrogenic cross sections with lorentz shapesto model the Fe or Co L2,3 white lines. Obtainable parameters with this model arethe energy positions of the white lines, their width and height and the chemicalconcentration of the elements.

7.3 Co nanowires

7.3.1 EFTEM

EFTEM elemental maps together with zero loss images of the Co sample areshown in fig. 7.2. The Co and O map are combined to give a colour coded imagefor clarity. Fig. 7.2A shows the tip of a Co wire having a distinct intensity in thezero loss image. The colour coded map 7.2B reveals that the tip contains bothCo and O and the wire is surrounded by a cobalt oxide layer. Fig. 7.2C and Bshow two wires crossing, one ending in an oxide tip and the other one ending in arounded oxide layer. From these images we can roughly estimate the thickness of


Figure 7.2: Zero loss images (A,C) and colour coded maps (B,D) of Co sample 1. Thesample contains mainly nanowires which end in a cobalt oxide tip. Note the oxide skinsurrounding the needle. To verify the composition of the oxide tip, EELS spectra are takenfrom regions 1 and 2 marked in C by the red circles.

the wire and of the oxide layer to be 60 nm and 10 nm correspondingly. Most wiresare cigar-shaped indicating that the template holes are considerably wider insidethe membrane as compared to the surface as was also noted by Schonenberger etal. [7].

7.3.2 EELS

The composition of the oxide tip is measured by EELS spectra from the two re-gions indicated on fig. 7.2C containing the oxide-tip (2) and the wire body (1). Theresults are shown in fig. 7.3. In the low loss spectrum fig. 7.3A the Co M4,5-edgeis visible for both regions, but clearly stronger for the nanowire body. Fig. 7.3Bshows the core loss spectrum containing a carbon and oxygen K-edge and theCo L2,3 edge. The scale is logarithmic to increase the visibility of the three edges.

138 7.3. Co nanowires

Clearly the Co/O ratio is higher in the body as compared to the tip. A large amountof carbon is always present; this is because of the overlap of the wire with a pieceof carbon grid. The overlap makes an accurate O/Co ratio determination difficultsince the carbon grid contains oxygen as well (cellulose acetate+ evaporated car-bon, contains at least C,H,O). An unrealistic O/Co ratio of ≈ 2.4 is seen in area 2.We can however still use the fine structure of cobalt to determine the nature of thecobalt oxide at the tip. Fig. 7.3C shows the ELNES of the Co L2,3 edge. A chemi-cal shift is observed as well as a shift in relative white line intensity. Both changesare indicative for a change in Co valency as expected for a cobalt oxide. Reganet al. [8] published a set of XAS spectra for standard samples among which Coand CoO, they note a chemical shift of -0.25eV of the L3 edge position in CoO ascompared to the Co metal. Pearson et al. [9] showed a linear correlation betweenthe number of 3d electrons in the transition metal series and the ratio of the whitelines L3/L2. Wang et al. [10] used this valency effect in the fine structure to distin-guish CoO and Co3O4 regions with EFTEM. They note a chemical shift of +1.15eV for Co3O4 as compared to CoO and they give a graph showing the L3/L2 whiteline ratios for different cobalt containing elements using the technique of Pearsonet al. [9]. Making use of these observations in the literature, we can discriminatebetween the two possible cobalt oxides Co3O4 and CoO by inspecting the finestructure of the cobalt L2,3 edge. By fitting a Lorenz function to each white line,we can estimate the energy position of these lines. A positive energy shift of theposition of the L3-line of ≈ 0.8 eV between the oxide tip and the wire body is ob-served. This contradicts with the negative shift for CoO, but is in agreement withCo3O4 which is expected to lie approximately −0.25 + 1.15 = 0.9 eV above theCo metal L3 edge. Calculating the white-line ratio L3/L2 using the prescriptionby Pearson et al. [9] we find a ratio of L3/L2 = 3.02 and L3/L2 = 3.63 for theCo wire and the oxide tip correspondingly. The value for the oxidized tip is inreasonable agreement with the published value of ≈ 3.3 for Co3O4 and disagreeswith the value of ≈ 5 for CoO making use of the same method for quantifyingthe ratio. From these observations, we conclude that the oxide tip of the cobaltnanowires consists of Co3O4. We could derive this results only from the ELNESof the Co L-edge making use of the fact that the white lines are sensitive to theoxidation state for elements in the center of the transition metal series.

7.3.3 TEM

Confronting this result with TEM diffraction patterns and HRTEM data showsa good fit. The selected area diffraction pattern from a cobalt nanowire and an oxi-dised tip are shown in fig. 7.4A and 7.4B. The cobalt nanowire is seen to be singlecrystalline cobalt metal with a hcp crystal structure (space group P63/mmc). Theoxide tip DP is shown in fig. 7.4B and is also single crystalline. The diffraction


Figure 7.3: ELNES spectra of position 1 and 2. Low loss region (A) core loss region(logarithmic scale to improve visibility)(B) and ELNES of Co L2,3 (C) and O K-edge (D).

Figure 7.4: Selected area diffraction patterns for the body of a Co nanowire(A) and theoxidized tip(B).

pattern is in agreement with structural data for Co3O4 (space group Fd3m).The HRTEM image in fig. 7.5 shows the interface between the Co metal and

the oxide tip. Both regions contain fringe contrast and Moire fringes are seen inthe Co region because of the overlap of the oxide surrounding with the Co interior.Optical diffraction patterns from small regions in the image are shown as insetsin fig. 7.5 and agree with the hexagonal symmetry for the Co metal phase (1) andthe cubic pattern for the Co3O4-phase (2 and 3).

140 7.4. Fe nanowires and nanotubes: sample 4

Figure 7.5: HRTEM image of the interface between the Co metal body and the oxidizedtip of a Co nanowire. The insets show optical diffraction patterns indicative of a hcp Cometal phase (1) and a cubic Co3O4 phase (2 and 3)

7.3.4 Conclusion

The Co nanowire sample shows the existence of monocrystalline Co nanowireswith a typical diameter of 60 nm. All wires are surrounded by a Co3O4 oxidelayer, and some wires end in a Co3O4 tip. The Co metal and the oxide layer showan epitaxial relationship: (001)Co3O4//(0001)Co; [110]Co3O4//[1010]Co.

7.4 Fe nanowires and nanotubes: sample 4

7.4.1 EFTEM

Fig. 7.6 shows an overview of Fe-sample 4. Two different types of wires canbe discerned in the zero loss image 7.6A. The colour coded map 7.6B reveals thatthe darker wires are Fe nanowires with a small oxide skin while the brighter wires


contain both iron and oxygen and show the typical chemical profile of a hollowtube. A series of TEM images was taken at different angles to prove that they areapproximately round and hollow. Fig. 7.6C and D show an enlargement of twohollow iron oxide nanotubes. The tubes are closed at the end. Fig. 7.6E and Fshow an enlargement of a region containing both the iron oxide nanotubes and thesolid iron nanowires. The wires are covered with a small oxide skin. The diameterof the wires and tubes is similar and roughly 60 nm on the average. The oxide skinor tube wall has an approximate thickness of 10 nm. The ratio of nanotubes versusnanowires is approximately 1:2.

7.4.2 EELS

To study the chemical composition and the Fe valency, EELS spectra are takenfrom a solid Fe nanowire and from a hollow iron oxide nanotube. Fitting the EELSspectra to a simple model enables us to determine the composition. The resultsare summarised in the following table:

position O/Fe [/] L3/L2 [/] EL2−EL3

[eV] EL3[eV]

tube 1.55 8.21 13.5 711.15wire 0.108 3.29 13.7 710.49

The O/Fe ratio from the table holds evidence that the nanotubes consist of Fe2O3although the TEM results in the next section will propose the Fe3O4 compound oncrystallographic grounds. The difference in oxygen content between Fe2O3 andFe3O4 is ≈ 12 %. The higher oxygen content found with EELS is probably due tothe fact that some of the oxide is in an amorphous phase. This affects the diffrac-tion pattern only slightly because the crystalline phase information is collected indistinct diffraction spots, while the diffraction information of an amorphous phaseis spread out in diffraction rings, that are less visible.

Further evidence can be seen from the ELNES spectra in fig. 7.7. The Fe L2,3-edge is shown in fig. 7.7C and clearly indicates a chemical shift and a change inwhite line ratio. This positive chemical shift and rise of white line L3/L2 ratio isqualitatively consistent with published XAS results for Fe2O3 but also for Fe3O4[8]. With the given energy resolution it is not possible to distinguish betweenα −Fe2O3(hcp) or γ −Fe2O3(spinel) although this is shown to be possible withan energy resolution < 0.5 eV by Paterson et al. [11] from both the O K-edge andthe Fe L2,3-edge. The Fe L2,3-edge is rather insensitive to the changes in oxidationwhen compared to the strong sensitivity for Co or Mn. We can only eliminate FeOfrom the list of iron oxides on the basis of our experimental Fe L2,3-edge.

The O K-edge however shows a typical fine structure for each iron oxide com-pound. Wu et al. show experimental XAS spectra together with multiple scatter-ing calculations for the O K-edge of FeO, Fe2O3 and Fe3O4 [12]. Comparing our


Figure 7.6: Zero loss images and colour coded maps of the Fe sample 4. Note thenanowires with an iron core and iron oxide shell and the hollow nanotubes made of ironoxide. The red structure is the carbon grid which supports the needles.


Figure 7.7: EELS spectra from a Fe-nanowire(1) and an iron oxide nanotube (2) fromsample 4. Low loss spectrum(A), O K-edge spectrum (B) and Fe L2,3-edge.

results to their Fe2O3 and Fe3O4 spectrum, reveals a slightly better fit with thefine structure of Fe3O4. The O K-edge of Fe2O3 contains two prepeaks at ≈ 530eV with a separation of 1.3 eV which is not seen in our experimental spectrum.The visibility of this feature with our experimental energy resolution however isdoubtful, and both Fe3O4 and Fe2O3 remain possible. The quantitative EELScontained evidence for Fe2O3, but we made use of hydrogenic cross sections forwhich the error can be as high as 20%. The final determination however, can beobtained from ED and HRTEM.

7.4.3 TEM

Fig. 7.8 shows a selected area diffraction pattern for a nanotube (A) and ananowire (B). The nanowire is single crystalline and shows the typical sixfold


Figure 7.8: Selected area diffraction patterns from Fe sample 4 showing the polycrys-talline pattern of a nanotube(A) and the single crystalline sixfold pattern of a hcp Fenanowire(B).

pattern for fcc iron (space group Im3m). The nanotube diffraction pattern consistsof a complex overlay of diffraction patterns from different oriented grains. Thedistances in the DP match to the structural data for Fe3O4. A HRTEM image ofa hollow nanotube is shown in fig. 7.9 together with a selected area diffractionpattern from that nanotube. The tube is made up of randomly oriented crystalliteswhich gives rise to the ring-like diffraction pattern. The distances in the diffractionpattern where found to match to structural data for Fe3O4 (space group Fd3m).

7.4.4 Conclusion

Sample 4 contained both hollow nanotubes made up of polycrystalline Fe3O4and nanowires made up of monocrystalline hcp iron surrounded by a 10 nm oxidelayer. The ELNES structure for the Fe L-edge as well as for the O K-edge showsrather subtle changes for the different iron oxides and a full determination of theoxide phase is not possible from the fine structure alone with the experimentalenergy resolution. Quantitative EELS points into the direction of Fe2O3 althoughFe3O4 is still within the error expected for the use of hydrogenic cross section.On the other hand, in view of the polycrystalline nature of the nanotubes, it cannot be excluded that Fe2O3, FeO and Fe3O4 are present in small crystalline oramorphous grains. TEM diffraction patterns are shown to fit the structural datafor Fe3O4, which indicates the average composition of the crystalline part of theoxide. A deviation of the oxygen in the sample is possible in small amorphousregions, possibly leading to the higher oxygen content measured with EELS.

A systematic and more detailed EELS study of these wires and tubes couldgive a better insight in their chemistry at local scale as complementary data forthe EFTEM images.


Figure 7.9: HRTEM image of the end of a hollow nanotube from Fe sample 4. The insetshows a selected area diffraction pattern indicating the polycrystalline nature of the tube.The DP was found to fit to the structural data of Fe3O4.

146 7.5. Fe nanowires: sample 6

Figure 7.10: Zero loss image (A) conventional tem image (B) and colour coded map (C)of the Fe sample 6. Sample 6 contains mainly nanowires like the one shown here. An ironoxide skin surrounds the iron needle, some carbon material is present at the left. Insetsshow details. A disruption of the wire by an oxidelayer is seen in the first inset, the tipcontains a gold cluster which is black in the ZL and TEM images.

7.5 Fe nanowires: sample 6

7.5.1 EFTEM

No hollow iron oxide nanotubes are observed in Fe sample 6. A representa-tive nanowire from this sample is shown in fig. 7.10 with insets having slightlyhigher spatial resolution. The oxide skin is approximately 10 nm thick while thenanowires have a diameter of 60 nm on the average. The particle at the tip of thewire in fig. 7.10 is a gold particle from the cathode.


Figure 7.11: Low magnification TEM image of Fe sample 6. Inset show a selected areadiffraction pattern of single nanowire. The diffraction pattern shows the single crystallinenature of the wires and the hcp Fe structure.

7.5.2 TEM

A low magnification image of sample 6 shows a large set of metallic nanowires.The inset shows a selected area diffraction pattern indicating the single crystallinenature of each wire.

7.5.3 Conclusion

The nanowires found in sample 6 are very similar to those found in sample4 with the notable exception that no nanotubes where observed. The wires aresingle crystalline hcp Fe and are surrounded by a thin layer of iron oxide.

148 7.6. Discussion and Conclusion

7.6 Discussion and Conclusion

We determined the structural and chemical composition of Fe- and Co-nanowiresand tubes and showed the existence of an oxide layer on all nanowires. Also, theexistence of hollow polycrystalline Fe3O4 nanotubes for sample 6 and Co3O4 tipson some Co wires were found.

The thickness of the oxide top layers was found to be ≈ 10 nm for all samples.The fine structure of both Fe and Co L2,3-edges contained the signature of va-

lency changes typical for the oxidation process, but the Co L2,3-edge was moresensitive to the specific oxidation state. An improved energy resolution (0.5 eVor better) could be helpful for a more decisive distinction of compounds from theELNES fine structure, but conventional TEM techniques such as electron diffrac-tion and high resolution imaging are also very well suited to discern between alimited set of compounds proposed by EELS.

Fitting the EELS spectra enabled us to quantify the chemical composition ofthe oxide regions.

The scale and composition of these wires makes them ideally suited for EFTEMinvestigations giving excellent signal to noise ratio. EFTEM provides a quick andeasy to use qualitative view on the chemical nature of the wires and tubes. Fora more detailed chemical investigation, it should be combined with a elaboratestudy of the EELS spectra from a high number of regions in the sample. Animproved accuracy would be obtained when using experimentally derived crosssections from reference samples, taken under similar conditions.

In this chapter, it has been shown that EELS and EFTEM are powerful tech-niques to contribute to the exciting field of metallic nanowires, even when scalesgo below the 10 nm range. Important properties such as chemical compositionand spatial distribution of the elements, plasmon energies, transition metal va-lency, bond lengths and unoccupied density of states are in principle availablefrom EELS. The 3d transition metals are ideally suited for study with EELS be-cause of the favourable energy position of their strong L2,3 edges and the sensitiv-ity of their white lines to chemical bonding.


Bibliography

[1] P. M. Paulus, F. Luis, M. Kroll, G. Schmid, and L. J. de Jongh. Low-temperature study of the magnetization reversal and magnetic anisotropy ofFe, Ni, and Co nanowires. Journal of Magnetism and Magnetic Materials,224:180–196, 2001.

[2] Yang Shaoguang, Hao Zhu, Yu Dongliang, Jin Zhiqiang, Tang Shaolong,and Du Youwei. Preparation and magnetic properties of Fe nanowire array.Journal of Magnetism and Magnetic Materials(222):97–100, 2000.

[3] B. Hausmanns, T.P. Krome, G. Dumpich, E.F. Wassermann, D. Hinzke,U. Nowak, and K.D. Usadel. Magnetization reversal process in thin Conanowires. Journal of Magnetism and Magnetic Materials, in press, 2002.

[4] A. Fert and L. Piraux. Magnetic nanowires. Journal of Magnetism andMagnetic Materials, 200:338–358, 1999.

[5] S. Roth, M. Burghard, V. Krstic, K. Liu, J. Muster, G. Phillip, Gyu TaeKim, Jin Gyu Park, and Yung Woo Park. Quantum transport in molecularnanowires transistors. Current Applied Physics, 1:56–60, 2001.

[6] W. Schwarzacher, O.I. Kasyutich, P.R. Evans, M.G. Darbyshire, Ge Yi, V.M.Fedosyuk, F. Rousseaux, E. Cambril, and D. Decanini. Metal nanostructuresprepared by template electrodeposition. Journal of Magnetism and MagneticMaterials, 198-199:185–190, 1999.

[7] C. Schonenberger, B. M. I. van der Zande, L. G. J. Fokkink, M. Henny,C. Schmid, M. Kruger, A. Bachtold, R. Huber, H. Birk, and U. Staufer. Tem-plate synthesis of nanowires in porous polycarbonate membranes: Electro-chemistry and morphology. Journal of Physical Chemistry B, 101(28):5497–5505, 1997.

[8] T. J. Regan, H. Ohldag, C. Stamm, F. Nolting, J. Luning, J. Stohr, and R. L.White. Chemical effects at metal/oxide interfaces studied by x-ray- absorp-tion spectroscopy. Physical Review B, 64(21):4422–+, 2001.

[9] D. H. Pearson, B. Fultz, and C. C. Ahn. Measurements of 3d State Occu-pancy in Transition-Metals Using Electron-Energy Loss Spectrometry. Ap-plied Physics Letters, 53(15):1405–1407, 1988.

[10] Z. L. Wang, J. Bentley, and N. D. Evans. Valence state mapping of cobalt andmanganese using near-edge fine structures. Micron, 31(4):355–362, 2000.


[11] J. H. Paterson and O. L. Krivanek. ELNES of 3d Transition-Metal Oxides:2. Variations With Oxidation-State and Crystal-Structure. Ultramicroscopy,32(4):319–325, 1990.

[12] Z. Y. Wu, S. Gota, F. Jollet, M. Pollak, M. Gautier-Soyer, and C. R. Natoli.Characterisation of iron oxides by X-ray absorption at the oxygen K-edgeusing a full multiple-scattering aproach. Physical Review B, 55(4):2570–2577, 1997.

Chapter 8

Metallic nanoparticles

8.1 Introduction

Magnetic granular films are artificially structured solids consisting of nanos-tructured magnetic granules embedded in an immiscible metallic or insulator ma-trix. They have drawn great attention due to their giant magnetoresistance (GMR)properties [1,2]. The GMR property is considered to be caused by spin-dependentscattering at the interface between the ferromagnetic grains and non-magnetic ma-trix as well as scattering within the ferromagnetic grains [1–4]. The GMR of thesegranular films strongly depends on their composition and microstructure which iscontrolled by the synthesis procedure and the post-annealing conditions [5–7]. Itis important to study structural and chemical details such as grain size, defects,interfacial structure, chemical profiles etc., in order to understand their magneticproperties.

Of those structural study methods, electron microscopy is effective and pow-erful for this task since it can give a direct insight on the small particles. It willbe shown that energy filtered TEM (EFTEM) can be of great help for makingelement specific images, improving the visibility of the granules in the matrix.Ag-Co granular film is a prototypical GMR material and its GMR property hasbeen extensively investigated.

Granular films were prepared by the co-evaporation technique and annealed atdifferent temperatures. By investigating the film microstructure, the growth of Coparticles in the Ag matrix is understood and the GMR properties can be related tothis.

In this chapter we will focus on the results obtained from the chemical investi-gation with EFTEM and give only a brief outline of the results obtained with othertechniques. For a full report on this study see Lei et al. [8].

151

152 8.2. Experimental procedure

8.2 Experimental procedure

Granular Co/Ag films with nominally 18 atomic percent Co were prepared bythe co-evaporation technique, i.e., Co and Ag were co-evaporated on an amor-phous SiO2 (about 800 nm thick) covered (001) Si substrate at room temperature.The typical film thickness is about 30nm. The granular films were simultaneouslyco-evaporated on two kinds of substrates: 3 mm discs for microstructural investi-gation and 10 by 10 mm substrates for magnetotransport and Mossbauer studies.

Plan view samples for TEM and EFTEM are thinned to electron transparancyby ion-milling. To avoid the structural variation due to ion-beam heating, thespecimen is cooled by liquid nitrogen during ion milling.

The microstructural study was carried out on the Philips CM20, CM30 FEGand Jeol 4000EX microscopes. Energy Filtered TEM (EFTEM) images are ob-tained from a CM30 FEG microscope with post-column Gatan GIF2000 filter.The GIF is operated in EFTEM mode with a slit width of 40 eV, a collection angleof β = 19.2 mrad, and energy windows at 714 eV, 754 eV and 799 eV. The the-oretical spatial resolution can be calculated (as outlined in chapter 5) to be betterthan 1.0 nm. In practice this theoretical value will be deteriorated by specimendrift.

8.3 Results

8.3.1 Film microstructure and grain size

Figs. 8.1A, 8.1B, 8.1C and 8.1D present the bright field plan view imagescorresponding to the as-grown (RT), 300 C, 400 C, and 500 C films, respec-tively. They show obvious differences in both grain size and shape. The as-grownfilm shows an almost homogenous contrast except for local Moire contrast. Noobvious grain boundaries or grain shapes are observed, indicating that both Agand Co grains are very fine and are mixed homogeneously. The 300 C sampleshows a microstructure similar to the as-grown film except for a different scale(note different scale bars used in two images). Different from the as-grown film,the 300C sample shows more fringe contrast and more contrast difference, indi-cating a structure change due to the annealing step. The grains grow larger withincreased annealing temperature as can be seen from fig. 8.1. Well-defined triple-junction grain boundaries and various grain shapes can be seen, particularly forthe 500C sample. The Co particles have grown larger appreciably and are clearlyseparated from the Ag grains due to their immiscibility in Ag. It is rather difficultto reveal the grain size and shape of Co particles by means of conventional darkfield techniques due to two facts.

Chapter 8. Metallic nanoparticles 153

Figure 8.1: Bright field images of Co/Ag granular films of (A) as-grown (B) 300 C (C)400 C and (D) 500 C samples.

• Both Ag and Co grains are of such a small size that it is difficult to obtaindiffraction patterns from isolated Co particles, in particular for the as-grownand the 300C samples.

• The lattice parameters of Ag and Co are too close to exclude Ag reflectionfrom the objective aperture when making dark field images.

Fortunately, the elemental mapping technique (see chapter 5) can help to distin-guish the Co and Ag particles. Since the Co L2,3 edge is well separated from anyother edges in the spectrum (such as Ag, Si, C, O) no systematic errors due tooverlapping edges are expected and the elemental mapping technique is straight-forward. Figs. 8.2B, 8.2D, 8.2F show the Co elemental map recorded from the300 C, 400 C and 500 C films, respectively, using the normal three-windowtechnique described by Egerton [9]. These maps reveal the size and shape of theCo particles in the annealed sample. No elemental map for the as-grown sample isobtained since the Co particles are expected to be smaller than 2nm which is near

154 8.3. Results

Figure 8.2: Zero loss images (A,C,E) and Cobalt elemental maps (B,D,F) for samplesannealed at 300 C (A,B), 400 C (C,D), 500 C(E,F) showing the growing Co particlesizes upon annealing


the limit of the expected spatial resolution limit of our setup taking into accountthe inevitable spatial drift of the specimen stage. In Fig. 8.2, white regions markregions with a high projected Co concentration, while black regions mark the ab-sence of Co. From fig. 8.2B it can be deduced that the Co particles of the 300C sample are homogeneously distributed in the Ag matrix and that their sizes areusually less than about 3 nm. Sometimes 5 nm particles can be seen, probably dueto local anomalous growth or overlap. The Co grain size of the 400 C film shownin fig. 8.2D varies from about 6 to 10 nm, about twice as large as for the 300 Cparticles. Both 300 C and 400 C Co particles approximately show a sphericalshape, indicating a homogeneous growth.

Fig. 8.2F shows the Co-map of the 500 C sample, the average size of the Co-particles is in the range of 12-15 nm. Some Co particles display an elliptic shape,indicating inhomogeneous growth. Since elemental maps give a distribution ofthe projected concentration of Co particles embedded in the film, the area ratiobetween bright and dark regions in Fig. 8.2 is substantially higher than 18%, thenominal atomic Co percentage.

8.3.2 Particle structure

The crystal structure of the Co particles can statistically be deduced fromrecorded diffraction patterns of areas containing lots of randomly oriented Ag/Cograins. These diffraction patterns consist of rings1 due to the random orientationof the different grains, with a specific diameter for each grain with different latticeparameters or crystal structure. Figs. 8.3a-8.3d present the recorded diffractionrings from as-grown, 300 C, 400 C and 500 C samples respectively; they wererecorded using the same objective aperture size. The left parts of the images infig. 8.3 are recorded with normal exposure time while the right-top quadrant isover-exposed with a fine beam showing more detail. The right-bottom quadrantshows simulated rings for Ag (solid), Co fcc (dotted) and Co hcp (dashed).

First, one can deduce some information about the Co particle size by compar-ing the diffraction rings. The as-grown and 300 C diffraction rings are continuousand homogeneous in both Co and Ag rings, indicating that both Ag and Co parti-cles are very fine. The Ag rings in fig. 8.3a are broad and indistinguishable fromthe Co rings, indicating the small size of the particles2. In this case it is thereforevery difficult to determine the Co structure.

For the 400 C and 500 C samples, the diffraction rings become discontinu-ous, revealing an appreciable growth of both Ag and Co grains.

1The rings are made up of spots from the small crystalline particles2Small crystallites give broad diffraction spots and relaxation at the grain boundaries will make

the lattice parameter difference smaller. Both effects lead to blurred overlapping rings

156 8.3. Results

Figure 8.3: Diffraction rings of Co/Ag granular films of (A) as-growth (B) 300 C (C) 400C and (D) 500 C samples, revealing a crystalline of Co particles of hcp at 300 C andfcc structure at 400 C and 500 C. The simulated diffraction rings are shown as inset forAg (full), Co fcc (dotted) and Co hcp (dashed).

Silver has an f.c.c. structure with lattice parameter aAg = 0.4086nm [10].Cobalt in equilibrium can exist in two isomorphic structures, fcc (aCoF = 0.3548nm) or hcp (aCoH = 0.2507nm, cCoH = 0.4069 nm) depending on temperature[10]. According to the above lattice parameters and extinction rules, the first fiverings on the diffraction patterns should correspond to planar distances given intable 8.1. The 0.1480 nm(102) ring is very weak in the JSPD card [10]. Twoimportant diffraction rings for Co particles are (200)fcc and (101)hcp; one candistinguish Co fcc from Co hcp by means of these two rings. With the Ag ringsas a reference, it is easy to index the diffraction rings shown in Fig. 8.3. The in-dexed rings are schematically shown in the right-bottom quadrant of each figure.It follows that Co particles mainly exhibit an f.c.c. structure in the 400 C and 500C samples. The (101)h.c.p. diffraction spots from Co particles should be locatedbetween the (111)fcc and (200)fcc rings of silver. Stronger (101)hcp reflections


Table 8.1: Important reflections for Ag and Co fcc and hcp.Ag fcc Co fcc Co hcp

0.2359 nm(111) 0.2047 nm(111) 0.2165 nm(100)0.2044 nm(200) 0.1772 nm(200) 0.2023 nm(002)0.1445 nm(220) 0.1253 nm(220) 0.1910 nm(101)0.1231 nm(311) 0.1069 nm(311) 0.1480 nm(102)0.1180 nm(222) 0.1023 nm(222) 0.1252 nm(210)

can be seen on the 300C diffraction pattern. It is therefore concluded that Coparticles display both hcp and fcc structure at 300 C.

8.3.3 Grain boundaries

A full description of the grain boundary structure studied with high resolutionTEM (HRTEM) is given by Lei et al. [8]. Here only the results are outlinedto give a complete picture of the characterisation of the samples. The HRTEMstudy reveals rough and unsharp grain boundaries between Co/Ag and Ag/Ag forthe as-grown and 300 C samples. Stacking faults and dislocations take up themismatch stress. The 400 C and 500 C samples show well defined sharp grainboundaries and large Ag grains consisting of twinned sub-grains. Co particles arefound mostly in tri-grain junctions.

8.4 Discussion

The magnetic properties of Ag/Co granular films show that the films displayGMR properties below 350 C [11]. Although the precise mechanism determiningthe GMR properties is still under investigation, the magnetic properties must berelated to the structural evolution in the film. According to the above results, thestructural development of the Ag/Co granular thin films, in particular of the Coparticles, can be summarized as follows:

• With increasing temperature the volume ratio of hcp Co will gradually de-crease. At about 500 C only fcc Co remains.

• Annealing the films above 400 C, changes the microstructure dramatically.Both Ag and Co clusters will grow as separated phases. Co particles accu-mulate at the Ag grain tri-junctions and the grain boundaries change fromheavily strained with a lot of defects to sharp interfaces upon annealing.

Since the GMR properties are strongly size-dependent; the ferromagnetic (Co)and nonferromagnetic (Ag) particles should be less than a few nm in size, i.e.

158 8.5. Conclusion

less than mean-free path for inelastic scattering of the conduction electrons [3].According to the chemical element map for the 300 C sample, the Co grains havea size between 3 and 5 nm and HRTEM results point out that the grain boundariesare under strain and show different types of imperfections.

Annealing the samples at 400C and 500C releases this strain and removesdefects in the film. Incoherent phase or grain boundaries are finally formed.

However, a phenomenological model shows, that the spin-dependent scatter-ing at the interface dominates the GMR properties and that interfacial roughnessenhances GMR [4].

In this respect, there is a critical annealing temperature. Below this temper-ature, the ferromagnetic Co grains grow with increasing annealing temperaturewhile keeping their high interfacial roughness. Above this critical temperature,the grains grow even larger and form incoherent sharp interfaces that have a neg-ative influence on the GMR properties.

The structural development due to annealing is obviously controlled and de-termined by the movement of defects (dislocations, stacking faults etc.) in thefilms. The critical annealing treatment should be determined by the “soft” com-ponent, Ag in this case. Considering the melting temperature of Ag Tm=1230K(i.e. 960 C), the 400 C (or 670 K > 0.5Tm(K)) annealing temperature is close tothe so-called “recovery” temperature for Ag. Annealing the film at a temperaturehigher than this “recovery” temperature or long time, will move the defects in thefilm and the strain at the boundary will be released.

To optimise the GMR properties, a critical annealing temperature is thereforeessential.

8.5 Conclusion

Transmission electron microscopy was performed to investigate the film mi-crostructure of Co-Ag granular films prepared by coevaporation. The film mi-crostructure was studied for different annealing treatments at 300 C, 400 C and500 C.

The as-grown films contain fine Co and Ag clusters. Most of Ag clusters aretwinned and the film contains dislocation and planar defects. The grain boundariesare under strain. Both fcc and hcp Co clusters are present.

Annealing the film at 300 C will make the Co clusters grow larger to diam-eters of about 3 nm. The film still contains a lot of defects and the interfaces arerough.

Annealing at 400 C will make the fcc Co clusters grow up to a size between6 and 10 nm. The Co clusters are located at tri-junction boundaries in the Agmatrix. Sharp and incoherent interfaces are formed.


Since the GMR properties are linked to grain structure, size and interfacialstructure, a critical annealing treatment is essential to optimize these properties.

Bibliography

[1] J. Q. Xiao, J. S. Jiang, and C. L. Chien. Giant Magnetoresistance in Non-multilayer Magnetic Systems. Physical Review Letters, 68(25):3749–3752,1992.

[2] A. E. Berkowitz, J. R. Mitchell, M. J. Carey, A. P. Young, S. Zhang, F. E.Spada, F. T. Parker, A. Hutten, and G. Thomas. Giant Magnetoresistance inHeterogeneous Cu-Co Alloys. Physical Review Letters, 68(25):3745–3748,1992.

[3] R. E. Camley and J. Barnas. Theory of Giant Magnetoresistance Effects inMagnetic Layered Structures With Antiferromagnetic Coupling. PhysicalReview Letters, 63(6):664–667, 1989.

[4] E. E. Fullerton, D. M. Kelly, J. Guimpel, I. K. Schuller, and Y. Bruynseraede.Roughness and Giant Magnetoresistance in Fe/Cr Superlattices. PhysicalReview Letters, 68(6):859–862, 1992.

[5] B. J. Kooi, T. Vystavel, and J. T. M. De Hosson. Microstructure and prop-erties of giant magneto-resistant Au80Co20, Au80Co10Fe10, Cu70Ni25Fe4Mnand Cu53Ni31Fe15Mn. Scripta Materialia, 44(8-9):1461–1464, 2001.

[6] H. Vrenken, B. J. Kooi, and J. T. M. De Hosson. Microstructure and proper-ties of giant magnetoresistive granular Au80Co20 alloys. Journal of AppliedPhysics, 89(6):3381–3387, 2001.

[7] J. H. Du, W. J. Liu, Q. Li, H. Sang, S. Y. Zhang, Y. W. Du, and D. Feng. Mi-crostructural characterization of CoAg granular films. Journal of Magnetismand Magnetic Materials, 191(1-2):17–24, 1999.

[8] C.H. Lei, A.G. Li, J. Verbeeck, G. Van Tendeloo, and H. Pattyn. Structuralinvestigation of Ag-Co granular films prepared by co-evaporation. in prepa-ration for Journal of Magnetism and Magnetic Materials, 2002.


[10] R.W.G. Wyckoff. Crystal structures. Interscience Publishers, London, 1965.


[11] M. Hou, M. El Azzaoui, H. Pattyn, J. Verheyden, G. Koops, and G. L. Zhang.Growth and lattice dynamics of Co nanoparticles embedded in Ag: A com-bined molecular-dynamics simulation and Mossbauer study. Physical Re-view B, 62(8):5117–5128, 2000.

Chapter 9

Running projects, future

To conclude the experimental part of this thesis, a short overview of otherexperiments conducted during this thesis will be presented. The experiments listedhere, are either not completely finished or where not selected for representation.The experiments should give a better view of the wide spectrum of samples thatwere studied.

9.1 Plasmon delocalisation

In cooperation with D. van Dyck (EMAT) and P. Kruyt from the TU delft (NL),experiments were performed to measure the delocalisation of plasmon excitationsin aluminum. Energy filtered images of the zero-loss peak and the plasmon peakare compared for a large set of different focus values in a two-beam condition.The focal series can be used to measure the coherence length from the inelastic(zero loss) and plasmon images. Comparison of both, enables the experimentaldetermination of the coherence length of the primary electron beam as well as thecoherence length of the plasmon.

9.2 Ferrite thin films

In cooperation with M. Takano from the university of Kyoto (Japan), thinfilm samples of SrFeO3−δ on a substrate of (SrAl0.5Ta0.5O3)0.3(LaAlO3)0.7(100)(LSAT) prepared by pulsed laser deposition were studied. Samples were cooleddown to room temperature after deposition under different oxygen environments:0.2 Torr for the sample labelled as (1T); 150 Torr for (2T) ; blowing O3/O2 for(3T) and non oxidized for the sample labelled as (NO). The oxygen treatmentwas done, in order to try to create a stoichiometric SrFeO3 thin film. Combining

161

162 9.3. LSMO on STO(110)

HRTEM, ED and local EELS enabled us to identify the phases present in the dif-ferent samples: The non-oxidized sample was found to be SrFeO2.5 with oxygenrich planar defects. The (1T) and (2T) sample are found to be SrFeO2.75 and the(3T) sample is a mixture of SrFeO2.75 and SrFeO2.87

9.3 LSMO on STO(110)

In cooperation with F. Ravazi of the Brock university (Canada) and H. -U.Habermeier from the Max-Planck-Intitut fur festkorperforschung in Stuttgart (Ger-many), thin films of La1−xSrxMnO3 (x ≈ 0.16) grown on a SrTiO3 (110) substratewere studied. Within the film, close to the interface, inclusions where found.These inclusions where studied with quantitative EELS and found to be La rich.This study resulted in a publication.

9.4 Manganite layered samples

In cooperation with B. Mercey of the university of Caen (F), complex layeredmanganite samples are studied. The samples are represented as:

(PMO)10(CMO)9(P25C75MO)35(P5C5MO)35(P75C25MO)35(PMO)36(PMO)10(SMO)30(P25S75MO)35(P5S5MO)35(P75S25MO)35(PMO)36(LMO)10(SMO)30(L25S75MO)35(L5S5MO)35(L75S25MO)35(LMO)36

with PMO for PrMnO3, LMO for LaMnO3, SMO for SrMnO3 and CMO forCaMnO3. The substrate is SrTiO3 (100). EFTEM studies showed the chemicalmodulation of the layers. The EELS fine structure of the layers is studied by scan-ning a fine probe perpendicular to the layers and by making use of the imagingspectroscopy technique. Both techniques show distinct changes in the O K-edgeand the Mn L2,3-edge which need to be compared with electronic structure calcu-lations. These experiments can give a better insight in the influence of the dopingon the Mn valency in the manganites as well as providing information on the lo-calisation of the charge around manganese.

Appendix A

Dipole transition rules

The general matrix element between two atomic eigenstates described in aspherical basis (in an APW method, we have the final states in a spherical basisaround the atom, in other cases, a projection can be made) can be calculated inthe dipole approximation replacing eiq·r by 1 + q · r for small q. Because of theorthogonality of the eigenfunctions in the chosen basis, only the matrix elementwith q · r remains:

〈Ψn′l′m′ |q · r|Ψnlm〉 (A.1)

The basis functions are independent of q so we only need the matrix elementaround the r-vector.

〈Ψn′l′m′ |r|Ψnlm〉 (A.2)

This can be split in three components of r.

rz = rcosθ (A.3)

rx =r+ + r−

2(A.4)

ry =r+− r−

2i(A.5)

with

r+ = rsinθeiφ (A.6)

r− = rsinθe−iφ (A.7)

The eigenstates in an (r,θ ,φ) basis are given by:

Ψnlm = Rnl(r)Pml (cosθ)eimφ (A.8)

With Rnl(r) an orthogonal radial part including the normalisation factor and Pml

the associated Legendre function of the first kind, for definition and properties seeref. [1] p.331.

A-1

A-2 A.1. rz component

A.1 rz component

We write the matrix element in r-space as:

〈Ψn′l′m′ |rz|Ψnlm〉 =∫

Ψ∗n′l′m′rzΨnlmd3r (A.9)

Writing this in (r,θ ,φ) basis and substituting µ = cosθ :

〈Ψn′l′m′ |rz|Ψnlm〉 =[∫ ∞

0Rn′l′(r)Rnl(r)r

3dr][∫ 1

−1Pm′

l′ (µ)µPml (µ)dµ

]×[∫ 2π

0ei(m−m′)φ dφ

](A.10)

The φ integration leads to m = m′, which makes the µ integral:[∫ 1

−1Pm

l′ (µ)µPml (µ)dµ

](A.11)

Making use of the following recurrence relation of the associated Legendre func-tions [1]:

µPml (µ) =

12l +1

[(l −m+1)Pml+1(µ)+(l +m)Pm

l−1(µ)] (A.12)

And the orthogonality of the associated Legendre polynomials [1]:∫ 1

−1Pm

l (µ)Pml′ (µ)dµ =

22l +1

(l +m)!(l −m)!

δll′ (A.13)

The µ integral can be non-zero only if l′ = l ±1. So the selection rules for rz are∆m = 0 and ∆l = ±1.

A.2 r+ component

〈Ψn′l′m′ |r+|Ψnlm〉 =[∫ ∞


3dr][∫ 1

−1Pm′

l′ (µ)√

1−µ2Pml (µ)dµ

]×[∫ 2π

0ei(m−m′+1)φ dφ

](A.14)

The φ integration leads to m′ = m+1, which makes the µ integral:[∫ 1

−1Pm+1

l′ (µ)√

1+ µ2Pml (µ)dµ

](A.15)

Chapter A. Dipole transition rules A-3

Making use of the following recurrence relation of the associated Legendre func-tions: √

1−µ2Pml (µ) =

i2l +1

[Pm+1l+1 (µ)−Pm+1

l−1 (µ)] (A.16)

The µ integral can be non-zero only if l′ = l ±1. So the selection rules for r+ are∆m = 1 and ∆l = ±1.

A.3 r− component

〈Ψn′l′m′ |r−|Ψnlm〉 =[∫ ∞


3dr][∫ 1

−1Pm′

l′ (µ)√

1−µ2Pml (µ)dµ

]×[∫ 2π

0ei(m−m′−1)φ dφ

](A.17)

The φ integration leads to m′ = m−1, which makes the µ integral:[∫ 1

−1Pm−1

l′ (µ)√

1−µ2Pml (µ)dµ

](A.18)

Making use of the following recurrence relation of the associated Legendre func-tions: √

1−µ2Pml (µ) =

i2l +1

[Pm+1l+1 (µ)−Pm+1

l−1 (µ)] (A.19)

The µ integral can be non-zero only if l′ = l ±1. So the selection rules for r− are∆m = −1 and ∆l = ±1.

A.4 Conclusion

The matrix element 〈Ψn′l′m′ |r|Ψnlm〉 is non-zero only if ∆l = ±1.

Bibliography


A-4 A.4. Bibliography

Appendix B

Derivation of the cross section forthe hydrogen-like atom

B.1 Introduction

The cross section for inelastic scattering by a hydrogen or hydrogen-like atomcan be derived analytically. In Egerton [1] only the results are given. Here, themethod which was briefly outlined by Bethe [2] and Landau and Lifshitz [3] isworked out for the interested reader. The main goal is to indicate where the ex-pression for the GOS in chapter 1 comes from and how the derivation is done.

The final expression is used to make remarks on the angular distribution ofthe scattered electrons in chapter 1 and is also used in the SigmaK program byEgerton [1] to compute values for the cross section of an arbitrary atom to use inquantification of an experimental spectrum.

The derivation consists of two parts. One part calculates the cross section forexciting the 1s core state to another discrete state, while the second part calculatesionization excitations, where the core electron is ejected from the atom to a con-tinuum state (i.e. it is no longer bound to the nucleus). A schematic overview ofthese two energy regions is given in fig. B.1, which also contains the definitionof the energy axis E (the energy loss) to be zero at the 1s state and R (Rydbergenergy) at the ionization threshold. The final section makes a generalisation of theresult for hydrogen to a hydrogen-like atom, which is useful for the (approximate)calculation of the cross section for K-edges of other atoms than hydrogen.

B-5

B-6 B.2. Parabolic coordinates

Figure B.1: Schematic overview of the discrete and continuum states in hydrogen. Thedefinition of E (the energy loss) is taken to be zero at the 1s state and R at the ionisationthreshold.

B.2 Parabolic coordinates

It is advantageous to use parabolic coordinates (ξ ,η ,φ) in this section. Theyare linked to the conventional spherical coordinates (r,θ ,φ) as:

η = r(1+ cosθ) (B.1)

ξ = r(1− cosθ) (B.2)

φ = φ (B.3)

the volume element dV in parabolic coordinates is:

dV =14(ξ +η)dξ dηdφ (B.4)

B.3 Excitation of H to discrete states

The normalized hydrogen 1s state Ψ0 and the discrete states Ψn are given inparabolic coordinates by Landau and Lifshitz [3]:

〈η ,ξ ,φ |Ψ0〉 =α 3

2√π

e−α2 (ξ+η) (B.5)

〈η ,ξ ,φ |Ψn〉 =

√1

πn

(αn

) 32

e−α2n (ξ+η)Ln1

(ξ αn

)Ln2(ηαn

)eimφ (B.6)

with α the fine-structure constant. n1 and n2 are two new quantumnumbers inparabolic coordinates replacing the conventional quantum numbers n and l in

Chapter B. Derivation of the cross section for the hydrogen-like atom B-7

spherical coordinates. They are linked by n = n1 + n2 + |m|+ 1 which gives npossibilities for m = 0, just as there where n possible values for the quantum num-ber l in spherical coordinates. We have to calculate the matrix element M:

M = 〈Ψn|eiq·r|Ψ0〉 (B.7)

with q the momentum transfer k−k′. Writing this in position space and paraboliccoordinates and performing the φ integration gives:

M =α 3

2√π

√1

πn

(αn

) 32∫ 2π

0

∫ ∞

0

∫ ∞

0e−

α2 (ξ+η)e−

α2n (ξ+η)×

Ln1(ξ αn

)Ln2(ηαn

)eiq ξ−η2

14(ξ +η)dφdξ dη (B.8)

M = 2πα 3

2√π

√1

πn

(αn

) 32 1

4

∫ ∞

0

∫ ∞

0e−

α2 (ξ+η)e−

α2n (ξ+η)×

Ln1(ξ αn

)Ln2(ηαn

)eiq ξ−η2 (ξ +η)dξ dη (B.9)

M =α3

21n2 I (B.10)

with:

I =∫ ∞

0

∫ ∞

0e−

α2 (ξ+η)e−

α2n (ξ+η)Ln1

(ξ αn

)Ln2(ηαn

)eiq ξ−η2 (ξ +η)dξ dη (B.11)

This integral can be split in two parts:

I =∫ ∞

0

∫ ∞

0e−

α2 (ξ+η)e−

α2n (ξ+η)Ln1

(ξ αn

)Ln2(ηαn

)eiq ξ−η2 ξ dξ dη

+∫ ∞

0

∫ ∞

0e−

α2 (ξ+η)e−

α2n (ξ+η)Ln1

(ξ αn

)Ln2(ηαn

)eiq ξ−η2 ηdξ dη (B.12)

I = I1 + I2 (B.13)

I1 =∫ ∞

0

∫ ∞

0e−

α2 (ξ+η)e−

α2n (ξ+η)Ln1

(ξ αn

)Ln2(ηαn

)eiq ξ−η2 ξ dξ dη (B.14)

I2 =∫ ∞

0

∫ ∞

0e−

α2 (ξ+η)e−

α2n (ξ+η)Ln1

(ξ αn

)Ln2(ηαn

)eiq ξ−η2 ηdξ dη (B.15)

These can be split further in two factors:

I1 =∫ ∞

0e−

α2 ηe−

α2n ηe−iq η

2 Ln2(ηαn

)dη

×∫ ∞

0e−

α2 ξ e−

α2n ξ Ln1

(ξ αn

)eiq ξ2 ξ dξ (B.16)

I1 = I11I12 (B.17)

B-8 B.3. Excitation of H to discrete states

with:

I11 =∫ ∞

0e−

α2 ηe−

α2n ηe−iq η

2 Ln2(ηαn

)dη (B.18)

=∫ ∞

0e−

αηn ( n

2 + 12 + iqn

2α )Ln2(ηαn

)dη (B.19)

=∫ ∞

0e−

αηn ALn2

(ηαn

)dη (B.20)

I12 =∫ ∞

0e−

α2 ξ e−

α2n ξ Ln1

(ξ αn

)eiq ξ2 ξ dξ (B.21)

=∫ ∞

0e−

αξn ( n

2 + 12− iqn

2α )Ln1(ξ αn

)ξ dξ (B.22)

=∫ ∞

0e−

αξn BLn1

(ξ αn

)ξ dξ (B.23)

with:

A =n2

+12

+iqn2α

(B.24)

B =n2

+12− iqn

2α(B.25)

(B.26)

Substituting

x =ηαn

(B.27)

y =ξ αn

(B.28)

gives:

I11 =∫ ∞

0e−

αηn ALn2

(ηαn

)dη (B.29)

=nα

∫ ∞

0e−xALn2

(x)dx (B.30)

I12 =∫ ∞

0e−

αξn BLn1

(ξ αn

)ξ dξ (B.31)

= (nα

)2∫ ∞

0e−yBLn1

(y)ydy (B.32)

For I2 similar:

I2 =∫ ∞

0e−

α2 ηe−

α2n ηe−iq η

2 Ln2(ηαn

)ηdη ×


∫ ∞

0e−

α2 ξ e−

α2n ξ Ln1

(ξ αn

)eiq ξ2 dξ (B.33)

I2 = I21I22 (B.34)

I21 =∫ ∞

0e−

αηn ALn2

(ηαn

)ηdη (B.35)

= (nα

)2∫ ∞

0e−xALn2

(x)xdx (B.36)

I22 =∫ ∞

0e−

αξn BLn1

(ξ αn

)dξ (B.37)

=nα

∫ ∞

0e−yBLn1

(y)dy (B.38)

We have two types of integrals now:

T1 =∫ ∞

0e−xALn0

(x)dx (B.39)

T2 =∫ ∞

0e−xALn0

(x)xdx (B.40)

The first type can be solved by writing the generating function of the Laguerrepolynomials: [4] p.784.

∞

∑n=0

Ln(x)zn =1

1− ze

xzz−1 for |z| < 1 (B.41)

We multiply both sides with e−xA and integrate over x:

∞

∑n=0

∫e−xALn(x)zndx =

∫ ∞

0e−xA 1

1− ze

xzz−1 dx =

−1−z+Az−A

(B.42)

Expanding the right side in z:

−1−z+Az−A

=1A

+1

A2 (A−1)z+1

A3 (A−1)2z2 +1

A4 (A−1)3z3

+1

A5 (A−1)4z4 +O(z5) (B.43)

The n0 term is:1

An0+1 (A−1)n0zn0 (B.44)

Putting the terms in zn0 on both sides of the equality gives:∫e−xALn0

(x)zn0dx =1

An0+1 (A−1)n0zn0 (B.45)


and dividing z out gives the result for the T1 integral:

T1 =∫

e−xALn0(x)dx = 1

An0+1 (A−1)n0 (B.46)

The procedure is identical for the second type integral T2. Making use of thegenerating function we get:

∞

∑n=0

∫e−xALn(x)znxdx =

∫ ∞

0e−xA 1

1− ze

xzz−1 xdx (B.47)

=1

1− z

∫ ∞

0ex( z

z−1−A)xdx (B.48)

=1

(1− z)(A− zz−1)2

∫ ∞

0e−ttdt (B.49)

=Γ(2)

(1− z)(A− zz−1)2 (B.50)

=1

(1− z)(A− zz−1)2 (B.51)

Where we made use of the definition of the Gamma function [4], p.255. and ofthe fact that Γ(2) = 1. Expanding the right side in z gives for the zn0 term:

[− n0

An0+1 (A−1)n0−1 +n0 +1

An0+2 (A−1)n0 ]zn0 (B.52)

Setting the terms in zn0 equal gives the result for the T2 integral:

T2 =∫

e−xALn0(x)xdx = (− n0

An0+1 (A−1)n0−1 + n0+1

An0+2 (A−1)n0) (B.53)

Using these results to express I11, I12, I21, I22 we get:

I11 =nα

1An2+1 (A−1)n2 (B.54)

=nα

2(n−1+ i qn

α )n2

(n+1+ i qnα )n2+1 (B.55)

I12 = 2(nα

)2(− n1

Bn1+1 (B−1)n1−1 +n1 +1

Bn1+2 (B−1)n1) (B.56)

= (nα

)2(−4n1(n−1− i qnα )n1−1

(n+1− i qnα )n1+1 +

4(n1 +1)(n−1− i qnα )n1

(n+1− i qnα )n1+2 ) (B.57)

I21 = 2(nα

)2(− n2

An2+1 (A−1)n2−1 +n2 +1

An2+2 (A−1)n2) (B.58)

= (nα

)2

(−4n2

(n+ iqnα −1)n2−1

(n+1+ iqnα )n2+1

+4(n2 +1)(n+ iqn

α −1)n2

(n+1+ iqnα )n2+2

)(B.59)


I22 =nα

1Bn1+1 (B−1)n1 (B.60)

=nα

1

(n2 + 1

2 − iqn2α )n1+1

(n2

+12− iqn

2α−1

)n1

(B.61)

=2nα

(n−1− iqnα )n1

(n+1− iqnα )n1+1

(B.62)

Putting everything together we get:

I = I11I12 + I21I22 (B.63)

I = 8(nα

)3

(n−1+ iqn

α

)n2(

n− iqnα −1

)n1(n+1+ iqn

α

)n2+1(n+1− iqn

α

)n1+1 ×

− n1(n− iqn

α −1) +

n1 +1(n+1− iqn

α

) −n2(

n+ iqnα −1

) +n2 +1(

n+1+ iqnα

)

(B.64)

The total matrix element M then becomes:

M =α3

21n2 I (B.65)

M = 4n

(n−1+ iqn

α

)n2(

n− iqnα −1

)n1(n+1+ iqn

α

)n2+1(n+1− iqn

α )n1+1×

− n1(n− iqn

α −1) +

n1 +1(n+1− iqn

α

) −n2(

n+ iqnα −1

) +n2 +1(

n+1+ iqnα

)

(B.66)

In agreement with [3] and [2]. Putting everything on the same denominator andmaking use of n1 +n2 +1 = n we get:

M = 24n2

(n−1+ iqn

α

)n2−1(n− iqn

α −1)n1−1

(n+1+ iqn

α

)n2+2(n+1− iqn

α

)n1+2

qnα

[(qnα

)− i(n1 −n2)

](B.67)

And taking the modulus squared:

∣∣∣Mn1,n2

∣∣∣2 = 28( q

α

)2n6

((n−1)2 +

(qnα)2)n−3

((n+1)2 +

(qnα)2)n+3

[(qnα

)2+(n1 −n2)

2]

(B.68)


Now we have to sum over all n possible n1 and n2 values for a given n. The term(n1 −n2) runs from −n+1,−n+3, . . . ,n−3,n−1. The general term is:

(n−2p+1)2 (B.69)

with p=1 to n. The sum then becomes

n

∑1

(n−2p+1)2 =13

n3 − 13

n (B.70)

The(qn

α)2

term also appears n times, so we get for the total matrix element for agiven n:

|Mn|2 = ∑n1+n2+1=n

∣∣∣Mn1,n2

∣∣∣2 (B.71)

= 28( q

α

)2n7

((n−1)2 +

(qnα)2)n−3

((n+1)2 +

(qnα)2)n+3

[(qnα

)2+

13(n2 −1)

](B.72)

In agreement with [3] and [2]. The differential cross section for exciting a statewith quantum number n becomes:

dσn

dΩ=

4(me2

)2

h4q4

k′

k|Mn|2 (B.73)

The total differential cross section for exciting to any discrete state is:

dσdΩ

=n=∞

∑n=2

4(me2

)2

h4q4

k′

k|Mn|2 (B.74)

Replacing this sum by an integral and making the n quantum number a continuousvariable we get:

dσdΩ

=∫ ∞

2

4(me2

)2

h4q4

k′

k|Mn|2 dn (B.75)

We can define the double differential cross section as:

dσdndΩ

=4(me2

)2

h4q4

k′

k|Mn|2 (B.76)

The differential cross section consists theoretically of delta functions as a functionof n and this is replaced by a continuous function in n. Finally the cross section


as a function of energy is needed because that is what is recorded in an EELSspectrum. The transformation is made consistent with the energy axis defined inthe introduction:

E = R(1− 1n2 ) = R(

n2 −1n2 ) (B.77)

n2 = −RE

1

(1− RE )

= −R1

(E −R)(B.78)

dn =12

√−E −R

RR

(E −R)2 dE (B.79)

With two new variables:

k2H =

ER−1 =

E −RR

(B.80)

Q =q2

α2 (B.81)

and their relation to the n:

dn = =12

1R

(√1(−k2

H

))3

dE (B.82)

n =

√− 1

k2H

(B.83)

we can write the matrix element |Mn|2 as a function of energy:

|ME |2 = 28Q

(√− 1

k2H

)7

((√− 1

k2H−1)2 +

(√− 1

k2H

Q

)2)√

− 1k2H−3

((√− 1

k2H

+1)2 +(√

− 1k2

HQ

)2)√

− 1k2H

+3×

(√− 1k2

H

Q

)2

+13(− 1

k2H

−1)

(B.84)

In chapter 1 an expression for the generalized oscillator strength was given:

d fdE

=12

ER2Q

(√1(−k2

H

))3

|ME |2 (B.85)

B-14 B.4. Excitation of H to continuum states

Filling in the matrix element and rewrite it to a form resembling the expressionfor the continuum states (see next section) gives:

d fdE

= 27 ER2

(√− 1

k2H

)10

(√− 1

k2H

)2 [Q+ 1

3(1+ k2H)]

(√− 1

k2H

)12((1−

√−k2

H)2 +Q)3(

(1+√

−k2H)2 +Q

)3×

(1−√

−k2H)2 +Q

(1+√

−k2H)2 +Q

√− 1

k2H

(B.86)

= 27 ER2

[Q+ 1

3 + k2H3

][(

(1−√

−k2H)2 +Q

)((1+

√−k2

H)2 +Q)]3 ×

(1+√

−k2H)2 +Q

(1−√

−k2H)2 +Q

−√− 1

k2H

(B.87)

= 27 ER2

[Q+ 1

3 + k2H3

]((

1− k2H +Q

)2 +4k2H

)3 e−√− 1

k2H

ln

[(1+√

−k2H )2+Q

(1−√

−k2H )2+Q

](B.88)

(B.89)

Which is of the form given by Egerton et al. [1].

B.4 Excitation of H to continuum states

For energy losses higher than the ionisation energy R, the ground state is ex-cited to a continuum state Ψκ− given by Landau and Lifshitz [3]. The continuumstate is a plane wave for distances far away from the scattering center. The direc-tion and momentum of the plane wave are denoted by κ and the state is normalizedper dκ . Both initial 1s state and final continuum state are given in atomic unitsand in cartesian coordinates:

〈r|Ψ0〉 =1√π

e−r (B.90)

〈r|Ψκ−〉 =1

(2π)32

eπ

2κ Γ(1+iκ

)eiκ·rF(− iκ

,1,−iκr− iκ · r) (B.91)


with F the confluent hypergeometric function, for a definition and properties seeref. [4] chapter 13. Using this in the matrix element M:

M = 〈Ψ0|e−iq·r|Ψκ−〉 (B.92)

=∫

Ψ∗κ−e−iq·rΨ0dV (B.93)

=Γ(1− i

κ )eπ

2κ

232 π2

∫e−iq·r−iκ.r−rF(

iκ

,1,+iκr + iκ · r)dV (B.94)

=Γ(1− i

κ )eπ

2κ

232 π2

[− ∂

∂λ

∫e−iq.r−iκ·r−λ rF(

iκ

,1,+iκr + iκ · r)dVr

]λ=1

(B.95)

=Γ(1− i

k)eπ

2κ

232 π2

I (B.96)

with:

I =[− ∂

∂λ

∫e−iq·r−iκ·r−λ rF(

iκ

,1,+iκr + iκ · r)dVr

]λ=1

(B.97)

This integral can be solved in parabolic coordinates. We can choose the r-spacecoordinate system freely, since we integrate over the whole space. We choose thecartesian z-axis to be parallel to κ the direction of the secondary electron that isejected from the atom. We choose q to have an arbitrary direction making an angleγ with κ and an angle φ with the plane containing q and k, the primary electronmomentum. The projection of q on r then contains two parts: qr cosθ cosγ pro-jected along the z-axis and

√r2 − r2

z cosφ qsinγ projected on the x-y plane. Theintegral then becomes in parabolic coordinates:

I =[− 1

2∂

∂λ

∫ ∞

0

∫ ∞

0

∫ 2π

0e−

12 iq(ξ−η)cosγ−iq

√ξ η cosφ sinγ− 1

2 iκ(ξ−η)− 12 λ (ξ+η)×

F(iκ

,1, iκξ )dξ dηdφ]

λ=1(B.98)

=[− 1

2∂

∂λ

∫ ∞

0

∫ ∞

0e−

12 iq(ξ−η)cosγ− 1

2 iκ(ξ−η)− 12 λ (ξ+η)×

F(iκ

,1, iκξ )[∫ 2π

0e+iq

√ξ η cosφ sinγdφ

]dξ dη

]λ=1

(B.99)

The φ integral can be solved by making use of ref. [4] p.360.∫ 2π

0eixcosφ dφ =

∫ π

0eixcosφ dφ +

∫ 2π

πeixcosφ dφ (B.100)

=∫ π

0eixcosφ + e−ixcosφ dφ (B.101)

= 2∫ π

0cos(xcosφ)dφ = 2πJ0(x) (B.102)


with J0 the Bessel function of the first kind of zeroth order. The total integral thensimplifies to:

I =[− 1

2∂

∂λ

∫ ∞

0

∫ ∞

0e−

12 iq(ξ−η)cosγ− 1

2 iκ(ξ−η)− 12 λ (ξ+η)F(

iκ

,1, iκξ )×

2πJ0(q√

ξ η sinγ)dξ dη]

λ=1(B.103)

=[−π

∂∂λ

∫ ∞

0e−

12 iq(ξ )cosγ− 1

2 ik(ξ )− 12 λ (ξ )F(

ik,1, ikξ )×[∫ ∞

0e

12 iqη cosγ+ 1

2 ikη− 12 λη

J0(q√

ξ η sinγ)dη]

dξ]

λ=1(B.104)

The η integration can now be performed making use of the following expressionfrom ref. [4]p.486. ∫ ∞

0eAηJ0(B

√η)dη =

−eB24A

A(B.105)

This gives for the η integral:∫ ∞

0e

12 iqη cosγ+ 1

2 iκη− 12 λη

J0(q√

ξ η sinγ)dη = − 2i(qcosγ +κ)−λ

eq2ξ sin2 γ

2[i(qcosγ+κ)−λ ]

(B.106)Rewriting the total integral:

I =[π

∂∂λ

∫ ∞

0e−

12 ξ iqcosγ− 1

2 ξ iκ− 12 ξ λ F(

iκ

,1, iκξ )×2

i(qcosγ +κ)−λe

q2ξ sin2 γ2[i(qcosγ+κ)−λ ] dξ

]λ=1

(B.107)

= 2π∂

∂λ

[ 1i(qcosγ +κ)−λ

∫ ∞

0e− 1

2 ξ[−κ2−2κqcosγ−q2−λ2

i(qcosγ+κ)−λ

]×

F(iκ

,1, iκξ )dξ]

λ=1(B.108)

Finally, the ξ integral can be solved by using:∫ ∞

0e−ytF(z,1,xt)dt = yz−1(y− x)−z (B.109)

from ref. [3] appendix F. The total expression for I then becomes:

I = −2π∂

∂λ

[ 1i(qcosγ +κ)−λ

(−1

2κ2 +2κqcosγ +q2 +λ 2

i(qcosγ +κ)−λ

) iκ −1

×(−1

2κ2 +2κqcosγ +q2 +λ 2

i(qcosγ +κ)−λ− iκ

)− iκ ]

λ=1(B.110)


which can be simplified to:

I = −4π∂

∂λ

[(κ2 +2κqcosγ +q2 +λ 2) i

κ −1(−κ2 +q2 +λ 2 − i2κλ )−

iκ

]λ=1

(B.111)Taking the derivative and setting λ = 1 gives:

I = −8π(k2 +2kqcosγ +q2 +1

) ik−2

(−k2 +q2 +1− i2k)−ik−1 ×[(

ik−1

)[−k2 +q2 +1− i2k]−(

1+ik

)[k2 +2kqcosγ +q2 +1

]]= 16πq

(κ2 +2κqcosγ +q2 +1

) iκ −2 (−κ2 +q2 +1− i2κ

)− iκ −1 ×

(q+(κ + i)cosγ) (B.112)

Putting this in the expression for the matrix element M, we get:

M =Γ(1− i

κ )eπ

2κ

232 π2

I (B.113)

M = −Γ(1− iκ )e

π2κ

232 π

16q(κ2 +2κqcosγ +q2 +1

) iκ −2

(q2 −κ2 +1− i2κ)−iκ −1 ×

(q+(i+κ)cosγ) (B.114)

And for the squared modulus:

|M|2 =25

π2 Γ(1− iκ

)Γ(1+iκ

)eπκ q2 ×(

κ2 +2κqcosγ +q2 +1)−4 ×(

(q+κ cosγ)2 + cos2 γ)×∣∣∣(q2 −κ2 +1− i2κ))−

iκ −1

∣∣∣2 (B.115)

The last factor is of the type: ∣∣∣(a− i2k)−ik−1

∣∣∣2 (B.116)

and can be solved by rewriting as an exponential and noting that only the real partsin the exponential will make the modulus different from 1:∣∣∣(a− i2κ)−

iκ −1

∣∣∣2 =∣∣∣∣exp

(−(

iκ

+1

)ln(a− i2κ)

)∣∣∣∣2 (B.117)

ln(a− i2κ) = ln(a2 +4κ2)+ iarctan(−2κ

a) (B.118)∣∣∣(a− i2κ)−

iκ −1

∣∣∣2 =1

a2 +4κ2 exp(2κ

arctan(−2κ

a)) (B.119)


Using this to solve the last term in eq. B.115 gives:∣∣∣(q2 −κ2 +1− i2κ))−iκ −1

∣∣∣2 =1

(q2 +1−κ2)2 +4κ2 ×

exp

(− 2

κarctan(

2κq2 −κ2 +1

)(B.120)

The total matrix element M can be written taking into account the following prop-erty of the Gamma function from ref. [4] p.256:

Γ(1− iκ

)Γ(1+iκ

) =π

κ sinh(πκ )

=πκ

2

eπκ − e− π

κ(B.121)

The matrix element then becomes:

|M|2 = 26 1κ

1

1− e−2 πκ

1π

q2

((q+κ cosγ)2 + cos2 γ

)(k2 +2κqcosγ +q2 +1)4

1(q2 +1−κ2)2 +4κ2 ×

exp

(− 2

κarctan(

2κq2 −κ2 +1

))

(B.122)

In agreement with [3] and [2]. Now, filling this in the expression of the differen-tial cross section for exciting the atom to eject a secondary electron in the solidangle dΘ and with momentum κ → κ +dκ and finding the inelastically scatteredprimary electron in a solid angle dΩ.

dσκdΩ

=4q4

k′

k

∣∣Mk

∣∣2 k2dkdΘ (B.123)

in atomic coordinates and with κ2dκdΘ the volume element in the space of thesecondary particle.

dσn

dΩdκ=

1q2

(k′

k

)28 1

1− e−2 πκ

1π


)(κ2 +2κqcosγ +q2 +1)4

1(q2 +1−κ2)2 +4κ2 ×

exp

(− 2

κarctan(

2κq2 −κ2 +1

))

κdΘ (B.124)

The solid angle dΘ is determined by the angle γ as dΘ = 2π sinγdγ . Now westill have to integrate over all possible angles γ since we are not interested in thedirection of the secondary electron. We only want the cross section in a solidangle around the primary electron. Performing the γ integration gives:

dσn

dΩdκ=

1q2

(k′

k

)29 1

1− e−2 πκ

κ(q2 +1−κ2)2 +4κ2 exp(− 2

κarctan(

2κq2 −κ2 +1

))×

∫ π

0


)(κ2 +2κqcosγ +q2 +1)4 sinγdγ (B.125)


Substituting t = cosγ we get for the integral:

∫ π

0


)(κ2 +2κqcosγ +q2 +1)4 sinγdγ (B.126)

= −∫ −1

1

((q+κt)2 + t2

)(κ2 +2κqt +q2 +1)4 dt (B.127)

=∫ 1

−1

((q+κt)2 + t2

)(κ2 +2κqt +q2 +1)4 dt (B.128)

=∫ 1

−1

((q+κt)2 + t2

)(κ2 +2κqt +q2 +1)4 dt (B.129)

=23

1+κ2 +3q2

(κ2 +2κq+q2 +1)2 (κ2 −2κq+q2 +1)2 (B.130)

The differential cross section then becomes:

dσdΩdκ

=1q2

(k′

k

)29 1

1− e−2 πκ

κ(q2 +1−κ2)2 +4κ2 exp(− 2

κarctan(

2κq2 −κ2 +1

))×

23

1+κ2 +3q2

(κ2 +2κq+q2 +1)2 (κ2 −2κq+q2 +1)2 (B.131)

which can be rewritten as:

dσdΩdκ

=1q2

(k′

k

)210 κ

1− e−2 πκ

(13 + κ2

3 +q2)

((q2 +1−κ2)2 +4κ2)3 ×

exp

(− 2

κarctan(

2κq2 −κ2 +1

))

(B.132)

In agreement with [3] and [2]. Converting this formula now to energy instead ofmomentum with the energy loss of the primary electron:

E = Ek +R =k2 +1

2(B.133)

dE = kdk (B.134)

where we used the energy scale defined in the introduction to be 1 Rydbergto ionise the hydrogen atom. In atomic coordinates the energy is expressed in

B-20 B.5. Combined result and hydrogenic corrections

Hartrees and the ionisation energy is 12 . The cross section with respect to energy

then becomes:

dσdΩdE

=1q2

(k′

k

)210 1

1− e−2 πκ

(13 + κ2

3 +q2)

((q2 +1−κ2)2 +4κ2)3 ×

exp

(− 2

κarctan(

2κq2 −κ2 +1

))

(B.135)

Which can be converted now to SI units by introducing new variables:

E ′ = 2ER (B.136)dE ′

2R= dE (B.137)

a0qm = q (B.138)

a0κm = κ (B.139)

with E ′ the energy loss in Joule and qm and κm in the momentum transfer and themomentum of the secondary particle in [1/m]. The total differential cross sectionfor excitations to continuum states then becomes:

dσn

dΩdE ′ = a20

1R

1q2

ma20

(κ ′

m

κm

)29 1

1− e−2 π

a0κm

(13 + a2

0κ2m

3 +a20q2

m

)((a2

0q2m +1−a2

0κ2m)2 +4a2

0κ2m

)3 ×

exp

(− 2

a0κmarctan(

2a0κm

a20q2

m −a20κ2

m +1))

(B.140)

Converting this to a generalized oscillator strength we get:

d fdE

=dσn

dΩdEkk′

Eq2

4R(B.141)

=ER2 27 1

1− e−2 π

a0km

(13 + a2

0k2m

3 +a20q2

m

)((a2

0q2m +1−a2

0k2m)2 +4a2

0k2m

)3 ×

exp

(− 2

a0kmarctan

(2a0km

a20q2

m −a20k2

m +1

))(B.142)

B.5 Combined result and hydrogenic corrections

The main difference with the result for hydrogen compared to other atoms isthe fact that all other atoms contain 2 (instead of 1) electrons in their 1s core state.


This means that it is twice as probable to make a certain excitation and thereforethe cross section has to be multiplied by two.

Another correction has to be made to take into account the different numberof protons in the nucleus. This can be done by replacing a0 by a0/Z, with Z theatom number and the ionization energy R by Z2R. Egerton et al. [5] found bycomparison with experimental spectra that a small screening correction makes thefit with experiment better. For K-edges he proposes a correction of

Ze f f = Z −0.3 (B.143)

The total expression for the cross section then becomes:

d fdE

= 28 EZ4

e f f R2

[Qs + 1

3 + k2s3

]((1− k2

s +Q)2 +4k2s

)3 ×

exp

(−√− 1

k2s

ln

[(1+

√−k2

s )2 +Qs

(1−√

−k2s )2 +Qs

])for Ek < E < Z2

e f f R (B.144)

d fdE

=E

Z4e f f R2 28 1

1− e−2 πks

(13 + k2

s3 +Qs

)((Qs +1− k2

s )2 +4k2s )

3 ×

exp

(− 2

ksarctan

(2ks

Qs − k2s +1

))for E > Z2

e f f R (B.145)

with two new variables:

Qs =q2a2

0

Z2e f f

(B.146)

k2s =

k2a20

Z2e f f

=E

Z2e f f R

−1 (B.147)

where we made use of a0 = h2/me2 and R = me4/2h2. And Ek the energy of theedge onset. It is taken from a list of experimental values in the Sigmak program[1].

Bibliography


B-22 B.5. Bibliography

[2] H. Bethe. Zur Theorie des Durchgangs schneller Korpuskularstrahlen durchMaterie. Annalen der Physik, 5:325–400, 1930.

[3] L.D. Landau and E.M. Lifshitz. Quantum Mechanics-Non relativistic theorycourse of theoretical physics, volume 3. 2nd edition, 1965.


[5] R. F. Egerton. K-Shell Ionization Cross-Sections For Use in Microanalysis.Ultramicroscopy, 4(2):169–179, 1979.

Appendix C

Guidelines for experimental work

C-23

Experimental guidelines for doing EELS with

CM30 microscope

•E0 300kV (297kV when GIF is on)

•energy resolution ∆E=0.8eV

•spherical aberation Cs=0.65mm

•chromatic aberation Cc=1.42mm

CM30 parameters GIF parameters•CCD 1024x1024

•PSF CCD 2.2 pixels

•min exposure time:

•standard GIF shutter 0.08s

•alternate shutter 0.01s

•Saturation 12000 counts

•Dark current +-1000 counts at -30°C

•Minimum slit size 1eV

EELS in diffraction mode EFTEM mode

EFTEM

none: >40 mrad

1st: 19 mrad

2nd: 12 mrad

3rd: 6 mrad

avoid zone axis conditions: unless interfaces are studied; choose zone axis in one direction in that

case

magnification: pixels size ~ 1/3 minimum detail needed

consider reducing field of view by taking 8X binning instead of 4X.

collection angle: look in resolution graph, take as large as possible, center around 000 beam

convergence angle: determined by beam size and cond. aperture: choose largest cond. aperture

specimen thickness: look for optimal thickness around t/λ ~0.3

specific alignment:

•create an evenly illuminated spot slightly larger than CCD area

•focus the image on the TV screen at 100eV with the slit width used for mapping

•center the beam at 100eV in the center of the TV screen

•test the elemental mapping for the elements under study and determine the optimum

exposure time (target intensity 10.000 counts, no saturation)

•Choose the energy selecting slits to fit the resolution needs (see graph)

•Main goal: keep exposure times low, get as much counts as possible

•check zero loss position

•don’t use alternate shutter

•if exposure times are low, consider averaging more readouts to improve signal to noise ratio

obj. apertureresolution graph

Quantitative EELS

•collect as much count as possible

•Use 0.3eV energy dispersion

•Collection angle β is determined by camera

length L and GIF entrance aperture

•Choose β~10 θE (larger only increases

background)

• θE~0.17mrad per 100eV energy loss (θE=E/2E0)

•convergence angle is determined by condenser

aperture

•if beam is focused, choose as large as possible

for increased beam current, unless a small probe

is required.

•choose thin region to avoid multiple scattering as

much as possible

•avoid zone axis orientation

•center diffraction pattern on TV screen

•Collect zero loss spectrum before and after core

loss and look for energy drift and beam damage

(use automated script to minimize exposure time).

entrance ap. 3mm 2mm 0.6mm

ind. cam. length [mrad] [mrad] [mrad]

92 mm 15.57 10.38 3.11

115 mm 11.96 7.98 2.39

155 mm 9.21 6.14 1.84

195 mm 5.02 3.35 1

240 mm 4.05 2.7 0.81

320 mm 3.06 2.04 0.61

440 mm 2.18 1.45 0.44

570 mm 1.69 1.13 0.34

780 mm 1.26 0.84 0.25

900 mm 0.95 0.63 0.19

1.3m 0.71 0.47 0.14

175m 0.53 0.35 0.11

2.4m 0.4 0.27 0.08

choose convergence angle to avoid overlap of

CBED discs α+θE< θ/2 with θ the smallest

Bragg angle

•choose collection angle to contain only 000

beam

•choose entrance aperture of GIF smaller for

best energy resolution

•choose energy dispersion 0.3 or 0.1 eV

•keep exposure times low to avoid energy drift

smearing (10s is acceptable)

•select crystal orientation as in theoretical

calculations

•focus probe to a small region with constant

thickness

•avoid surface contamination and drift

•keep metal objects (like chairs) away from

the spectrometer during alignment and

recording

•reduce extraction voltage and increase gun

lens if energy resolution is important

•know α and β for comparison with theory

ELNES specificOptimizing precision

Appendix D

Published results and contributions

D.1 Published results

J. Verbeeck, O. I. Lebedev, G. Van Tendeloo, J. Silcox, B. Mercey, M. Hervieu,and A. M. Haghiri-Gosnet. Electron energy-loss spectroscopy study of a(LaMnO3)8(SrMnO3)4 heterostructure. Appl. Phys. Lett. 79(13):2037-2039,2001.

O. I. Lebedev, J. Verbeeck, G. Van Tendeloo, S. Amelinckx, F. S. Razavi and H.U. Habermeier, Structure and microstructure of La1−xSrxMnO3 (x ≈ 0.16) filmsgrown on a SrTiO3 (110) substrate, Philos. Mag. A 81(12):2865-2884, 2001.

P. L. Potapov, S. E. Kulkova, D. Schryvers and J. Verbeeck. Structural and chem-ical effects on EELS L3,2 ionization edges in Ni-based intermetallic compounds,Phys. Rev. B 64:184110-1, 2001.

O. I Lebedev, J. Verbeeck, G. Van Tendeloo, O. Shapoval, A. Belenchuk, V. Mosh-nyaga, B. Damaschke and K. Samwer. Structural phase transitions and stressaccomodation in (La0.67Ca0.33MnO3)1−x:(MgO)x composite films. Submitted toPhys. Rev. B, 2002.

J. Verbeeck, O. I. Lebedev, G. Van Tendeloo, B. Mercey.SrTiO3(100)/(LaMnO3)m(SrMnO3)n layered heterostructures: A combined EELSand TEM study. Submitted to Phys Rev. B, 2002.

C. H. Lei, A. G. Li, J. Verbeeck, G. Van Tendeloo and H. Pattyn. Structuralinvestigation of Ag-Co granular films prepared by co-evaporation. In preparationfor Journal of Magnetism and Magnetic Materials, 2002.

D-27

D-28 D.2. Oral presentations

D.2 Oral presentations

Electron energy-loss spectroscopy study of a (LaMnO3)8(SrMnO3)4 heterostruc-ture, Dreilandertagung fur elektronenmicroscopie, Innsbruck Austria, sept. 9-14,2001

EELS nanoscale analysis: some examples, Annual BSM meeting Probing themolecular level, Rixensart Belgium, dec. 1, 2001

Electron microscopy in materials science: EELS, Ecole de doctorats de la Facultedes Sciences, Facultes Universitaires Notre-Dame de la Paix, Namur Belgium,feb. 25, 2002

EELS study of manganite heterostructures, INTAS meeting, EMAT AntwerpenBelgium, may 24, 2002

Appendix E

List of abbreviations

EELS Electron energy loss spectroscopyAES Auger energy spectroscopyXAS X-ray absorption spectroscopyPL Photo luminescenceEDS Energy dispersive spectroscopyUPS Ultraviolet photon spectroscopyXPS X-ray photon spectroscopyINS Inelastic neutron scatteringEXEFS Extended energy fine structureELNES Energy loss near edge structureXANES X-ray absorption near edge structureGIF Gatan imaging filterTEM Transmission electron microscopyHRTEM High resolution TEMFEG Field emission gunED Electron diffractionDOS Density of statesGOS Generalized oscillator strengthCMR Colossal magneto resistanceAMR Anisotropic magneto resistanceGMR Giant magneto resistanceFM Ferro magneticAFM Anti ferro magneticPM Para magneticPC Poly carbonateHT High tension

E-29

Index

EDX, Energy dispersive x-ray spec-troscopy, 26

AMR, anisotropic magnetoresistance,133

Bethe-ridge, 15

Characterisitc scattering angle, 13CMR, Colossal Magneto Resistance,

84Collection angle, 31Colour coded maps, 62contrast transfer function, EFTEM, 65Convergence angle, 31Cross section, 7

density of states, 19dipole approximation, 65Double differential cross section, 12Double exchange, 84Drift tube, 29

ELNES, 8Energy selecting slit, 30EXELFS, 8

First order Born approximation, 9Fischer information matrix, 51focal spread, EFTEM, 68Fourier-log deconvolution, 42Fourier-ratio deconvolution, 43

Gatan Imaging Filter (GIF), 29Generalised oscillator strength, 11GMR, Giant Magnetoresistance, 134

impulse response function, EFTEM,65

Inelastic cross section, 7Inelastic form factor, 11

Jump-ratio method, 61

k-factor, 45

local density of states, 20

Momentum transfer vector, 10

Optimal focus, EFTEM, 68

Plasmon excitations, 7Pulsed Liquid Injection MOCVD, 107

r-map smoothing, 60radial distribution function, 67resolution, definition, 69

Scherzer defocus, EFTEM, 68Signal to noise ratio, 73symmetry projected DOS, 20

template electrodeposition, 134Three-window technique, 60

Valence band excitations, 7

White lines, 87

Zero-loss peak, 6

Dankwoord

Dit werk is tot stand gekomen dankzij de enthousiaste hulp van vele mensendie ik hier wil bedanken.

Eerst en vooral wil ik mijn promotor, Gustaaf van Tendeloo, bedanken voorhet geloof dat hij vanaf de eerste kennismaking in mij had. En natuurlijk voor dekans om dit werk te mogen starten. Mijn andere promotor, Dirk van Dyck, wil ikbedanken voor steeds nieuwe ideeen aan de rand van het gekende. Een gesprekmet hem leverde steevast nieuwe inzichten en nieuwe impulsen op.

Ich mochte Andreas Rosenauer danken, fur die Grundlichheit, im Lesen undim Verbessern dieses Manuskriptes und fur die vielen faszinierende Diskussionen.

Bernard Mercey et Maryvonne Hervieu pour leur interessante cooperation etpour nos discussions captivantes.

Special thanks to John Silcox who was so kind to give me the opportunityto visit his lab for three months. And especially for his inspiring doughnut-timescientific discussions on EELS. Many thanks to K. Andre Mkhoyan for scientificdiscussions and for guiding me around and making my stay in the US the niceexperience it was.

Ik was blij om samen te mogen werken met Sandra van Aert die me intro-duceerde in de wereld van precisie en nauwkeurigheid en me de geheimen vanCramer Rao bijbracht. Philippe Geuens dank ik voor de vele gesprekken overelektronen verstrooing en computerproblemen, en natuurlijk om mij te laten ziendat communicatie in de wetenschap erg belangrijk is en heel motiverend kan wer-ken. Herman Lemmens wil ik bedanken voor zijn relativerende commentaar overhet doctoraatsgebeuren en het leven in het algemeen voor zover beiden niet over-lappen. Dirk Lamoen voor de vele discussies over DFT, computers en fysica. Olegvoor de goede samenwerking en het nemen van de vele hoge resolutie fotos in ditwerk. De bijhorende discussies waren niet altijd even gemakkelijk te volgen maaruiteindelijk begreep ik het wel. Sara voor het verlichten van de laatste loodjes enom mij te verdragen in een buro. Steven voor het uitwerken van de QES theorieen voor de vrolijke noot.

Verder wil ik alle professoren en EMAT-mensen bedanken voor hun openheidom mijn poging te doctoreren als industrieel ingenieur een eerlijke kans te geven.

Bedankt ook aan alle mensen van de ondersteunende functies binnen EMAT: demensen van het fotolabo, de preparaat bereiding, de microscoop technici, secreta-riaat en onderhoud.

Mijn Vader voor zijn vraag aan het begin van dit doctoraat:”wat zal dan hetvolgende zijn wat je zal nastreven?”. En inderdaad, ik weet het nu nog niet, maarvoor hem en voor diegenen die zich herkennen, een gedicht aan het einde methet antwoord op deze vraag. Kristel voor zeer veel geduld en de bereidheid ommet mijn drakengevecht te leven, en haar parallele drakengevecht te voeren. Ennatuurlijk voor haar uitstekende kookkunst en om me af en toe weg te sleuren vande computer; naar buiten om te lopen of te wandelen. Tot slot wil ik ieder die lichtprobeerde te werpen op mijn pad bedanken. Zij zorgden voor de nodige moed enperspectief op momenten dat ik m‘n ogen durfde te openen.

ELDORADOE.A. Poe (1849)

Gaily bedight,A gallant knight,

In sunshine and in shadow,Had journeyed long,

Singing a song,In search of Eldorado.

But he grew old-This knight so bold-

And o’er his heart a shadowFell as he found

No spot of groundThat looked like Eldorado.

And, as his strengthFailed him at length,

He met a pilgrim shadow-”Shadow,”said he,”Where can it be-

This land of Eldorado?”

”Over the MountainsOf the Moon,

Down the Valley of the Shadow,Ride, boldly ride,”The shade replied-

”If you seek for Eldorado!”

Electron energy loss spectroscopy of nanoscale materials

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