Electronic Structure of the 3d Metals: An Investigation by ... · phase atom. Both laser...

Electronic Structure of the 3d Metals:An Investigation by L-Shell-Photoionisation

vorgelegt vonDiplom-Physiker Tobias Stefan Richter

aus Heidelberg

Von der Fakultt II Mathematik undNaturwissenschaften

der Technischen Universitt Berlinzur Erlangung des akademischen Grades

Doktor der Naturwissenschaften doctor rerum naturalium

genehmigte Dissertation

Promotionsausschuss:Vorsitzender: Prof. Dr. Erwin SedlmayrBerichter: Prof. Dr. Peter Zimmermann

Prof. Dr. Thomas Mller

Tag der wissenschaftlichen Aussprache: 3. Dezember 2007

Berlin 2007D 83

English Abstract The 3d transition metal elements from Sc to Cu have been inves-tigated by both photo electron emission and photo absorption. Experimental spectrain the 2p energy range are discussed based on atomic multiplet models and Hartree-Fock calculations. The samples have been evaporated from an electron bombardmentcrucible and excited/ionized by monochromatized synchrotron radiation. Funda-mental effects and the main interactions which govern the electronic structure of the3d metal atoms are covered. Common spectral features and trends in the series arediscussed as well as the importance of many body electron correlation effects.

Deutsche Zusammenfassung Die 3d bergangsmetalle von Sc bis Cu wurden mit-tels Photoelektronenspektroskopie und Photoabsorption untersucht. ExperimentelleSpektren im Bereich der 2p-Schwellen werden auf der Basis atomarer Multiplettmod-elle und Hartree-Fock-Rechnungen analysiert. Die Elemente wurden in einem Tiegelmittels Elektronenstossheizung verdampft und durch monochromatisierte Synchro-tronstrahlung angeregt/ionisiert. Fundamentale Effekte und die wichtigsten Wech-selwirkungen, die die elektronische Struktur der 3d-Metallatome bestimmen werdenbehandelt. Dabei werden gemeinsame Charakteristiken und Trends in den Spek-tren der Serie und die jeweilige Bedeutung von Vielteilchenelektronenkorrelationendiskutiert.

Contents

1 Introduction 1

2 Atomic Photoionisation 42.1 Photoionisation Processes . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Calculation of Atomic Structure . . . . . . . . . . . . . . . . . . . . . . . 8

3 Instrumentation and Experiments 163.1 Photon Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.2 Atomic Vapour Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.3 Time of Flight Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . 213.4 Electron Analyser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.5 Data Aquisition Software . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.5.1 Electron Analyser . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.5.2 Time of Flight Spectrometer . . . . . . . . . . . . . . . . . . . . . 34

4 Results and Discussion 374.1 Copper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.2 Nickel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.3 Cobalt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.4 Iron and Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514.5 Manganese and Chromium . . . . . . . . . . . . . . . . . . . . . . . . . 574.6 Vanadium and Titanium . . . . . . . . . . . . . . . . . . . . . . . . . . . 644.7 Scandium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

5 Summary 725.1 Photo Absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725.2 Photo Electron Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . 755.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

A MCP Procedure 81

Bibliography 82

Acknowledgements 93

i

List of Figures

2.1 A few inner shell processes . . . . . . . . . . . . . . . . . . . . . . . . . 5

3.1 A series of Mn photo electron spectra in 2 dimensions . . . . . . . . . . 323.2 Manganese (and rest gas) time of flight spectrum vs. photon energy . . 353.3 Partial ion yield spectra in the Mn 3p 3d resonance . . . . . . . . . . 36

4.1 Experimental 2p photo electron spectra of copper . . . . . . . . . . . . 384.2 FISCI vs. first order 2p photo electron calculation for copper . . . . . . 394.3 2p photo absorption spectra of nickel . . . . . . . . . . . . . . . . . . . . 414.4 2p photo electron spectrum of nickel and SCA and CI calculations . . . 444.5 Experimental and theoretical 2p photo absorption spectrum of cobalt . 474.6 Ion charge resolved experimental 2p photo absorption spectrum of cobalt 484.7 Different calculations for the 2p photo electron spectra of cobalt . . . . 504.8 Total ion yield spectra from Fe and FeCl2, calculated spectrum for Fe . 524.9 Experimental 2p photo electron spectra of Fe and FeCl2 . . . . . . . . . 534.10 Iron 2p photo electron spectrum and calculation . . . . . . . . . . . . . 544.11 Experimental and modelled molecular FeCl2 2p spectrum . . . . . . . . 554.12 2p photo electron spectrum of manganese . . . . . . . . . . . . . . . . . 594.13 2p photo electron spectrum of chromium . . . . . . . . . . . . . . . . . 604.14 2p photo absorption spectrum of vanadium . . . . . . . . . . . . . . . . 654.15 2p photo absorption spectrum of titanium . . . . . . . . . . . . . . . . . 664.16 2p photo electron spectrum of vanadium . . . . . . . . . . . . . . . . . 674.17 2p photo electron spectrum of titanium . . . . . . . . . . . . . . . . . . 684.18 2p partial ion yield spectrum of scandium . . . . . . . . . . . . . . . . . 694.19 2p photo electron spectrum of scandium . . . . . . . . . . . . . . . . . . 70

5.1 Overview of the experimental 2p absorption spectra . . . . . . . . . . . 735.2 Overview of the calculated 2p absorption spectra . . . . . . . . . . . . . 745.3 Overview of the experimental 2p photo electron spectra . . . . . . . . . 765.4 Overview of the calculated 2p photo electron spectra . . . . . . . . . . 77

ii

1 Introduction

Currently a vast number of experiments focusses on the electronic and magneticproperties of the 3d transition metals and metal compounds because of their majortechnological relevance for a large variety of applications. The Encyclopdia Bri-tannica says iron is the cheapest and most abundant, useful, and important of allmetals. Titanium, vanadium, chromium, manganese, cobalt and nickel are used inengineering applications and for forming alloys and steels, some of their compoundsare widely used as paint pigments. Scandium is used e.g. as an additive in mercuryvapor lamps, but is the most expensive and least abundant of them all. Besides theseeveryday uses, a major share of todays focus is on the deployment of these metalsin integrated circuits and as magnetic material, for data storage and data processing.This is where the more accurate electronic and magnetic properties gain interest.

Spectroscopy with monochromatized radiation available from the novel brilliantsynchrotron light sources in a tunable wide energy range has evolved into a stan-dard tool to gain insight into these properties. The spectra of L shells are often saidto be element specific, meaning that they exhibit lines which do not overlap withlines from neighboring elements. This is not the case for M shell spectra of the 3delements, where the energetic distance of spectral features from different elementsis in the same order of magnitude as the energy spread of one atoms multiplet. Asan additional obstacle in M shell photo electron spectra, one has to cope with stronglifetime effects obscuring parts of the spectrum [Tiedtke01] at least in the atomic case.So the overall assumption would be that 2p shell ionization/excitation is generallyeasier to understand than the 3p case. The 2p core level spectra of the 3d transitionmetal compounds have consequently been studied extensively in the solid phase toobtain information on their electronic structure. As a 2p core hole strongly perturbsthe electronic states of the outer electrons it can be used as a test charge to investi-gate the response of the valence electrons. This allows to derive information on thechemical environment and local bonding with the neighbouring ligands.

While in application mostly bulk material is used, atomic species are of great inter-est for research, too, as in bulk material most measured quantities not only dependon effects specific to the material investigated but are also influenced by a strong con-tribution of collective solid state interactions. To gain a simple picture and to dissectpure atomic, molecular or bulk properties data on single atoms is valueable. Anotheradvantage of studying atoms in the gas phase that comes with the absence of com-plicated solid state effects is the higher resolution achievable. This generally allows a

1

1 Introduction 2

more detailed and unambiguous interpretation of the spectral features observed anda more accurate look on the specific electronic structure of the specimen.

Also the sample sizes that are of technological relevance approach the atomic limitswith structure sizes in semiconductors becoming smaller and smaller. For exampleIBM researchers recently investigated a chain of two to ten manganese atoms on anelectrically insulating surface [Hirjibehedin06]. The atoms were placed in a distance50% larger than in bulk material, but were nevertheless able to exchange spin in-formation or in other words magnetization. Seemingly the industry is interested inprobing the atomic limit, in particular because the collective bulk effects like mag-netism to not scale linearly with the number of atoms in the sample [Lau02].

The solid state magnetism is investigated at synchrotrons by routine using X-raymagnetic circular dicroism (XMCD) techniques, e.g. [Wende04]. Atomic data is thereuseful to compare and verify the sum rules applied. However, in contrast to bulkmaterial it is not as easy to prepare different orientations of magnetization for a gasphase atom. Both laser polarization, as used in [Borne97], and the use of magnetichexapole guides, favored by another group [Plotzke96], would add complexety toexperiments where not even data from raw atoms existed prior to this work. But alot information for the distribution of states can be gathered already from the com-parison of theoretical data and atomic experimental results. An additional approachtaken is the measurement of the angular distribution parameter, that closely linkswith magnetic properties, but also gives insight into correlation effects.

The interpretation of the experimental spectra for the evaluation of electrical prop-erties or local magnetic moments due to the mostly unpaired 3d electron spins relieson the interplay of intraatomic and interatomic interactions. The satellite structureof the 2p photo electron spectra of the 3d transition metal oxides, sulfides or halides,for example, is thoroughly investigated experimentally, but controversially discussedusing either intraatomic effects of multiplet splitting and 2p hole interaction or inter-atomic charge transfer from the neighboring ligand valence orbitals to the 3d statesof the transition metal [Bagus00, Taguchi01, Bagus01]. In cluster model calculationsthe 2p photo electron spectra are described in terms of a few parameters such as thecharge transfer energy, the ligand p and metal d hybridization and the on-site d dCoulomb repulsion energy. These parameters are usually adjusted to reproduce theexperimental spectra. To obtain such parameters by ab-initio methods would there-fore be a substantial progress [Groot94]. One step for such a program is the care-ful study of corresponding spectra both for metals and metal compounds in the gasphase.

From a theoretical point of view, atoms with more than 20 electrons pose a strongtest on the numerical approximations introduced to cope with such a many bodyproblem. While some experiments, for example optical transistions or spectroscopyof noble gases, can be simplified in theory and treated quite satisfactory, the situa-tion for open shell metal atoms undergoing core level excitation is considerably morecomplex. Main factors governing the spectra are core valence interaction 2p spin-orbit interaction and 3p 3d Coulomb interaction. So obviously a large number of

1 Introduction 3

electrons contributes to the final result. Thus the comparison of theory and exper-iment will give a unique possibilty to verify the quality of the numerical approachtaken. And in combination the relative importance of the different interactions con-tribution can be determined.

In conclusion 2p photoionization studies of 3d metals in the gas phase are deemedvery fruitful, yet challenging both to the experiment and theory. The experimentalside is confronted with problems of the high evaporation temperatures, resulting incomparatively low target density, and the aggressiveness of the molten material. Thetheoretical side has to deal with the coupling properties of the non-filled 3d-subshelland the near degeneracy of the 3d and the 4s orbitals.

2 Atomic Photoionisation

This chapter is aimed to briefly introduce the reader into the background theory.At first photoionisation effects and related decay processes will be discussed on aphaenomenological level combined with some notes on possible experiments. Thena section on the origin and calculation of energy levels and other atomic propertieswill follow. In both cases treatment will be narrowed down to focus on topics impor-tant in dealing with inner shell photoionisation of light metal atoms.

For the interpretation of atomic (and solid state) spectra an abundance of differ-ent expressions is used to describe the most important effects. They include termslike spin-orbit interaction, relativistic perturbations, multiplet effects, many body ef-fects, correlation, configuration interaction, interchannel coupling. Some light is shedon these to help distinguishing what effect is referenced by which name, as even inhighly specialized fields the hardest task is often to agree on a common naming con-vention first.

2.1 Photoionisation Processes

This sections will focus on basic atomic processes induced by photons, the readershould be (made) familiar with. Those processes to occur very likely in light metalatoms (like the 3d metals) induced by soft X-rays or VUV photons (as provided in thebeamlines used: 100 1000 eV) are specially emphasised. Four of those are displayedin figure 2.1. Each of them is illustrated by a simplified set of three discrete atomiclevels, one at the bottom (core level) and two on the top (outer shells/valence). Theionisation threshold is shown above the top levels.

A very simple case is the direct photoionisation (top feature in the figure) where anelectron is lifted into the continuum by the energy gained from the photon. The out-going electrons kinetic energy Ekin is given from the photon energy h and the ioni-sation (binding) energy via the Nobel prize winning Einstein equation [Einstein05]:

Ekin = h

With photon energies high enough, different electronic states can be ionized, turninga monochromatic radiation source and an electron spectrometer into a useful coupleto investigate electronic binding energies, the most prominent property of electronsbound to an atom. Constants of motion, like parity and angular momentum, lead to

4

2.1 Photoionisation Processes 5

a set of selection rules for the final states the are reachable from a well defined initialstate. These will be discussed later in this section.

sh

ake

up

Au

ger d

ecay

ph

oto

excita

tion

dire

ct p

ho

toio

niz

atio

n

Figure 2.1: A fewinner shell processes

The process of excitation (second feature in figure 2.1) con-nects two discrete atomic states. An electron is lifted to a lesstightly bound unoccupied orbital. Thus the incident pho-ton must have the correct difference energy for the processto happen. An experiment making use of discrete excitationwill usually explore photon energies matching a transitionand the corresponding transition probabilities. It will deliverinformation on the properties of both states involved, limitedagain by the dipole transition rules.

It is quite obvious that both processes (excitation and pho-toionisation) annihilate the photon that provides the neces-sary energy, this general behaviour we refer to as absorption.The absorption strength is a property that is well accessi-ble by experiments, either in transmission or yield measure-ments (see below). In contrast a much more complex setup isneeded to detect the state of excitation of an atom. So in orderto derive an excitation spectrum an experiment will look outfor energies where absorption is high. A local maximum at aphoton energy matching a transition is called a resonance. Asthe term resonance suggests the cross section there is biggerthan the cross section of direct photoionization, by orders ofmagnitude. But in the absorption data you still can expect tofind a fraction of signal due to direct ionization.

The so-called shake-up (third row in 2.1) is an important sec-ondary process of photoionization. In this process a secondelectron is excited, the discrete excitation energy will be miss-ing from the ejected electrons kinetic energy. The effect canbe understood and calculated from the difference betweenthe atomic (initial) and ionic (final) orbitals. The orbitalsshrink upon the removal of an electrons charge, resulting insome overlap between the initial and an excited ionic state.The discrete energy consumed by the secondary excitation ismissing in the kinetic energy of the outgoing electron. So thefeatures to be expected in an electron spectrum from a shake-up process are peaks at apprearently higher binding energypositions. No direct evidence of this effect can be expected inabsorption data. The two similar effects of shake-down andshake-off are not relevant here. Shake-down needs an excitedatom as inital state and we only have some thermal excitation. Shake-off is beyondscope, too, as it will manifest itself in form of a continuos background feature in theelectron spectrum only.


Subsequent to an excitation, the energy stored in the atom can be set free againin a fluorescence decay or an autoionisation process. With fluorescence a photon isemitted, carrying away the deexcitation energy of the atom. As there is no need forthe same electron to jump back, there is no need for the atom to reach its originalinital state. With core-excited 3d elements, the dominating decay process howeveris autoionisation, i.e. the inner shell vacancy is filled by an electron and another oneis emitted with Ekin being equal to the energy difference between the vacancy andthe filling electrons levels minus its own binding energy. This leads to cases, wherewe reach the same final state from the same initial state by two or more competingprocesses. Either we can have a direct ionization of one level or excite an electron froma more tightly bound level and subsequently remove an electron in an autoionizationdecay. The quantum mechanical interference can lead to asymmetric line shapes inresulting experimental spectra.

Core holes created by photoionisation decay in a similar fashion, via fluorescenceor electron emission, only that the latter process is called Auger decay [Auger25] then,instead of autoionisation. In contrast to autoionisation the Auger electrons kineticenergy solely depends on the energies of atomic levels and has no relation to the pho-ton energy. This is the reason there are two names for the two processes, because apartfrom this difference both decays are fueled by the Coulomb interaction, resulting in asimilar calculation.

Now that we concluded the short introduction in the processes in figure 2.1, weturn towards the selection rules as already promised. Every atomic state has a set ofcorresponding quantum number that characterizes it. The total angular momentumhas to be conserved, thus J = 1, 0, 1. The same is true for the magnetic quantumnumber: MJ = 1, 0, 1. Further prohibited is L = 0 for states without an totalangular momentum (J : 0 6 0). Additionally the parity of the state must change inthe transition. These rules reduce the set of possible state transitions, in some casesto be commendably concise.

The two major types of experiments proposed above, photo absorption and elec-tron emission, probe distinct atomic properties. Some of the experimental equipmentis the same, the target and its inital state are the same, but the final states make thedifference. In a first approximation absorption investigates the dipole selected den-sity of unoccupied valence orbitals, while the shape of the photo emission spectrumis determined by the reaction of the system on the core hole. Dipole transitions aregenerally dominant in both cases. As there is no electron emitted into the contiuumin resonance excitation the number of final states that can be reached in absorptionspectroscopy is apparently more limited by selection rules, than in electron emission,where the outgoing electron provides an additional degree of freedom for spin andangular momentum. Additionally the large perturbation of the complete removal ofan inner electron gives rise to secondary transitions in the outer orbitals. Thereforeboth techniques can be regarded as complementary in a way.

The two different setups mentioned above to measure the absorption strength,transmission and yield mode, work in the following way: The transmission mode


detects the real attenuation of the photon flux sent through a sample, in our case anatomic vapour, quite similar to the well-known Lambert-Beer law:

I1I0

= e(h)lc

In this general case the incoming and outgoing photon flux I0 and I1 are recorded,passing through an absorption cell of length l with sample concentration c. There areseveral problems in this scheme, when applied to the targeted atomic vapour. Themain issue is the dilute sample producing a very low attenuation . Therefore thesignal to noise quality will be poor. Yield spectra, on the other hand, focus not onthe photon loss, but detect products of ionization or decay, for example fluorescence,electrons or ions. That way signal is only is generated when there is absorption, re-moving the background, thereby improving signal to noise ratio to allow workingwith small absorption rates. On the other hand, this scheme records decays, so notrue absorption data is aquired but an absorption-like signal. Depending on the typeof yield measured (ions, electrons or photons), this kind of experiment will neglectthose processes where the chosen type is not produced. For our case of light ele-ments the detection of ions is most useful, as ions can be detected with high efficiency(4 geometry) and the radiative decays that are not accounted for have a below 1%propability for the L edges. With this small deviation in mind, we will skip the -likeappendix in absorption-like from now on for brevity, but still remember it. Moreon this in the experimental section 3.3.

Due to lifetime and experimental effects the binding or resonance energy that willbe derived is not a single value, but follows a intensity distribution. A closer lookon the experimental resolution being observed as a broadening will follow in therespective sections. But some words on the natural line widths are necessary here.The basic equation for the energetic uncertainty perceived as increased line widthstems from the uncertainty principle:

E = h/t

In our case t is the life time of the excited or core hole state. In cases where this levelis short lived, we will observe energetically broad features. A 1 fs life time accountsfor 0.60 eV line width, for example. The lifetime of a state i is the inverse of the sumover the transition rates into all states it can decay into:

=1

n ain

Obviously if the indudivdual ain transition rates are of different magnitude, is gov-erned by the largest contribution. So usually in good approximation it is sufficient totake into account the main decay route only. For photonic transitions the transitionrate can be derived from the spacial overlap of the involved wave functions and thecube of the transition frequency. Auger and autoionisation probabilities on the other

2.2 Calculation of Atomic Structure 8

hand depend only on the spacial overlap due to the acting Coulomb operator. So forrelatively high fluorescence energies, radiative transitions revail. However, in the 3dtransition metals only K shell hole states have a significant probability for radiativedecays, all other vacancies are filled by Coulombic Auger processes, if energy per-mits. Lifetimes are therefore governed by ionic decays, mainly into 1+ and 2+ for the3p 3d resonances and up to 5+ for 2p 3d excitations. Coulombic decays particu-larly fast are the so-called Coster-Kronig (CK) or Super-Coster-Kronig (SCK) decays,where either two or three (read: all) of the levels involved share the same principalquantum number. This gives a huge spatial overlap and results in extremely shortlifetimes. For SCK decays, the most likely process for a 3p hole in a 3d metal (if at allpossible), line widths exceeding some eV are seen.

If lifetime effects dominate, a Lorentzian line shape is measured. Experimentaleffects, such as spectroscopic resolution or Doppler broadening, lead to a Gaussianprofile. With relatively short lifetimes and moderate resolution when compared tolaser experiments we are in no way limited by Doppler effects, even when high tem-perature are needed for evaportation of the sample elements. In the intermediateregion, where both types of broadening effects are in the same order of magnitude,a Voigt profile can be used as an appropriate description. All of these line shapesare symmetric. The respective contributions can be deduced from a numerical curvefitting routine.

2.2 Calculation of Atomic Structure

Quantum mechanics is the key to a precise description for atomic processes. In thestatic case there is only one simple equation atomic theory only has to evaluate togain information on atomic levels:

H = E

The eigenfunctions to the energy eigenvalues E completely describe the electronicstructure in the atom or ion defined by the Hamilton operator H. Yet for non-trivialcases H contains many-particle interactions, especially the Coulomb force betweenthe electrons. But as an exact analytical solution of many body problems is impossi-ble, approximations have to be introduced. Therefore simplifications are needed notonly for a handy explanation of spectra, but already to allow numerical calculations atall. The suitable choice of simplifications is important, as a too simple approach willyield poor agreement with the experiment, a more than adequate treatment on theother hand will waste CPU time in the calculation. But worse, a picture too detaileddoes not reveal the basic information to the observer. So it is equally important toidentify the necessay terms in an adequate theoretical description, as it is importantto name the terms that can be left out.


The simplified many-body operator H consists of (using atomic units for brevity,i.e. e = c = h = me = 1):

H = 12 i2i Z

i

1ri

+ i 6=j

1rij

+ i

(ri)li si

where ri is the distance from the nucleus to electron i, rij is the distance betweenelectron i and j. The first sum represents the kinetic energy of the electrons, the secondsum term describes the Coulomb interaction between electrons and nucleus followedby the term for the interelectronic Coulomb interaction. The last sum is the relativisticcorrection describing the spin-orbit interaction. It accounts for the potential arisingfrom the electrons spin magnetic moment moving in the perceived magnetic field ofthe nucleus. Further relativistic effects are neglected and are negligible here.

There exist numerical methods that are able to approximately solve this many-bodyequation. We will focus on the self consistent field Hartree-Fock method, used in thecode developed by R. D. Cowan [Cowan81]. (For the calculations presented here theCowan code as been amended to include the effects of overlapping resonances andto improve usability for spectroscopy purposes by Michael Martins [Martins01].) Wewill later see that these algorithms well describe most of the presented data.

The most annoying summand in the above equation is of couse the rij containingterm, as it describes the many body nature of the problem. To overcome this onecan use the independent particle approximation and model the Coulomb field expe-rienced by an individual electron via a a time-averaged, spherically symmetric fieldcaused by the nucleus and all N 1 other electrons. The spherical symmetry allowsthe separation wave functions into radial Rnl(r) and angular part Yml(, ) again.The solutions for the angular part are the same as for the hydrogen atom, while theradial wave functions do have a different central potential and are therefore different.This so-called central field approximation is evaluated iteratively for each subshell,starting from a set of trial functions.

As the electrons are treated independently the total wavefunction of the atom canbe constructed as the product of single-electron wavefunctions:

= 1(~r1)2(~r2)3(~r3)4(~r4) N(~rN)

To obey the Pauli principle the final wavefunction must be antisymmetric uponinterchange of two electrons. This antisymmetricity can be guaranteed from a lin-ear combination of products of single electron wavefunctions in form of a determi-nant, referred to as Slater determinant. This approach inherently yields antisymmet-ric wavefunctions upon interchange and the determinant vanishes when two electronwavefunctions are identical.

When the desired level of convergence is reached and all functions with given l aremutually orthogonal the radial wavefunctions can be used to calculate the configura-tion average energy, the radial Coulomb interaction parameters Fk (direct part) and


Gk (exchange part) as well as the spin-orbit parameters . The configuration aver-age energy or center of gravity energy is computed by averaging the central potentialover the entire basis set of functions. As Fk and Gk are calculated by integration overthe radial functions Pn`(r), they are mostly referred to as Coulomb Slater integrals[Slater29]:

Fk =e2

4e0

rk

Pniì(r1)2Pnj`j(r2)

2 dr1 dr2

Gk =e2

4e0

rk

Pniì(r1)Pniì(r2)Pnj`j(r1)

Pnj`j(r2) dr1 dr2.

Fk and Gk give the Coulomb interaction between different angular momenta l anddifferent multiplicities, respectively. Their corresponding angular parameter fk andgk account for the splitting in both cases. While the direct Coulomb interaction parthas an obvious origin in the electrons repelling each other, the exchange part mightneed some explanation. The exchange interaction is a spin dependent Coulomb in-teraction. Despite being spin dependent the interaction is connected to the spin onlybecause of the Pauli principle: Electrons with the same spin cannot occupy the sameorbital, therefore they are spatially separated and thus their Coulomb replusion islow. So the exchange interaction is spin dependent but does not act on the spin itself.Together the above properties and involved states form the so called atomic multipletstructure.

In the general case the set of basis functions needed to describe the total wavefunc-tion is infinite. This obviously poses a problem for numerical calculations. Fortu-nately it is often sufficient to limit to a number of basis functions that constitute oneconfiguration (single configuration approximation, SCA). The simplified SCA model ofcourse neglects deviations from the two approximations made: a central field withspherical symmetry as well as the independent motion of electrons.

When these approximations lead to false results, the set of basis functions has tobe extended by further configurations. This approach is referred to as configurationinteraction (CI). It allows for an admixture of neighbouring states of the same parityand accounts for deviations from the pure central potential model. The need for CIis often said to be a sign for so called electron correlations, although a large fractionof electron-electron interactions (rik), like the basic shielding of the nuclear charge bythe inner shells experienced by the valence electrons, can already be separated into aspherical contribution. In agreement with textbooks and reputable publications in thefield, e.g. [Cowan81, Schmidt97, Martins06], we use the term electron correlation in itsrather strict meaning, i.e. only cases where the assumption of a central potential fails.This definition leads to the perhaps confusing result, that two electron transitionsarising from a change of the spherical charge distribution, like shake-up processes,are here said to be calculated and described without including electron correlationsat all. While this may sound disturbing, a wider interpretation, including all effects


of the term rik would lead to problems in the opposite direction, on the other hand.Electron correlations would be ubiquitous, so the term would not have any distictiveeffect anymore. So we silently include the spherical rik contribution, as it cannot beneglected in majority of cases anyway.

The calculation of spectra involves two or three atomic states, depending if thereis an intermediate state (like a decaying resonance) in addition to the initial and thefinal state. CI can occur in each to all of these states. To distinguish between interme-diate and initial state configuration interaction in the abbreviation that latter is oftennamed ground state configuration interaction (GSCI), leaving ISCI for the mixing inthe intermediate state. This naming scheme has the disadvantage to taint the termground state being the lowest energetic state normally, but it is widely used never-theless, e.g. [Armen00]. Fortunately no intermediate state needs to be considered forthe spectra to be evaluated here anyway, because the effects of decay can be easilyattributed to a global lifetime broading. With no SCK possible there is no disctict dif-ference in lifetime of individual lines. Finally, if mixing occurs in the final state, onecould include the outgoing electron (final continuum state configuration interaction,FCSCI) in consideration or not (final ionic state configuration interaction, FISCI).

But in general, even calculations taking into account a fair number of explicit ad-ditional configurations tend not to give the correct energy spread of the multiplet.As has been shown by Rajnak and Wybourne [Rajnak63, Rajnak64] this failure of ex-plicit (so called strong) CI can by understood as a result of the cumulative effect of aninfinite number of high-lying configurations interfering with the investigated states.These configurations will have only very small individual mixing coefficients, theirinfluence is therefore often referred to as weak CI. A huge number of those high-lyingconfigurations will nevertheless cause a compression of the width of the multiplet bysqueezing the energy of upper configuration terms more than the lower ones. To ac-count for this, weak CI is modelled by scaling the Coulomb Slater integrals in thecalculation, which has the same effect on the energy levels. Typical values for atomsare reported as 70% to 80% of their ab-initio value by [Cowan81, Chapter 16-2]. Butfor the 2p ionization slightly higher values near 85 or 90% are more appropriate, aswe will see later. Of course one has to consider wether strong CI was applied before-hand and to which extent. In summary, the approach that is expected to yield themost accurate calculated spectra is the explicit inclusion of strong CI for a number ofselected configuration together with the implicit inclusion of weak CI via scaling fac-tors. Although well understood and widely accepted, one should keep in mind thatthis scaling is an empirical parameter in our calculation, it will be the only value usedthat is not derived by ab-initio methods. There is one more calculated value, however,that is not displayed verbatim: All spectra will be shifted by a tiny relative offset ofbinding energies to match experimental data. The shift is not negligible comparedto the spread of the multiplet usually, so applying it greatly eases the comparison ofexperiment and theory. But nevertheless, seen relative to the binding energy it is atiny computational offset. It is a matter of graphical representation that a 1% offsetin terms of binding energy is clearly visible, when only a 5% range is displayed. The


same relative error of 1% in relative intensity of one or more lines, will on the otherhand remain unnoticed without doubt.

An effect slightly related to CI is the so called interchannel coupling. It becomesapparent mostly in a weak ionization channel in the vicinity of another resonanceor similar feature. Usually the cross section will be amplified for the weak channel,but other properties like angular distribution can be affected as well. Interchannelcoupling is known to occur in a wide range of kinetic energies both for inner andouter shells [Hemmers01, Deshmukh04]. Many body perturbation theory models areusually applied to account for the interchannel coupling. However, there is no strictdistiction between the effects of configuration interaction and interchannel coupling.In principle both approaches should lead to the same results when applied to the fullextent. Being limited in computational power, nevertheless, it is wise to chose theright approximation for the process to model. Therefore the limited CI HF approachtaken as theoretical model here does not include what is usually referred to as inter-channel coupling to its full extent. As in the spectra taken here, at kinetic energiesbetween 50 and 100 eV for the 2p ionization, no strong competing channels exist,hence interchannel coupling can be mostly negletected. In other cases, the FCSCIapproach mentioned above can help to include these effects to some extent withinthe HF framework. Going further other computational codes like random phase ap-proximation (RPA) and relativistic descendents tend to give better results for moresevere interchannel coupling. For (near) closed shell atoms RPA calculations even ofhigher order effects can reach excellent agreement, see e.g. [Amusia97]. Open shellconfigurations are not handeled as well, therefore we stay with the HF methodology.

In spectroscopy it is desirable to identify groups of lines of similar origin to com-prehend spectra composed of a large number of features. Different configurations,states and angular momenta can be distinguished in atomic spectra. For the angularmomenta spin and orbital momenta of the electrons have to be coupled (neglegtingcore momenta). In principle any linear combination is possible, which means everycoupling scheme will yield the same total momenta. There exists several special cou-pling schemes nevertheless, as they allow for a grouping of lines and an estimate fortheir energetic ordering and distances. An optimal coupling scheme reflects the cor-rect order and splitting of lines in the experimental spectrum. Therefore groups areformed by dividing all lines into smaller and smaller groups, starting from large tosmall splitting energies. The (most) adequate scheme has to be chosen based on theactual dominance of interactions.

The common case for optical transitions is LS (Russel-Saunders) coupling. It isideal when in a first approximation states can be grouped by their orbital momenta(direct Coulomb repulsion), thereafter by their spin (exchange interaction), followedby a weak spin-orbit dependence. This is the assumption Hund based his rules upon,too. Russel-Saunders coupling is valid when the relativistic spin-orbit interactionis small compared to the electrostatic interactions between the electrons. Even forlighter elements (low Z) this is violated for inner shells. In this case it is adequateto couple the spin and orbital moments of the individual electrons first and calculate


the total momentum from the sum over all electrons. This procedure is called jj-coupling. For the coupling of inner and outer shell electrons pair coupling schemeslike jK coupling can be more adequate. These schemes take into account the fact thatthe (relative and absolute) magnitude of interactions is very different for electronspopulating different subshells.

An obvious splitting in spectroscopy can be used to derive measureable physicalproperties from an analysis. E.g. the (relative) intensites of 2p1/2 and 2p3/2 photoelectron lines should mirror the original occupation of the ionized levels (2 J1 + 1) :(2 J2 + 1) = 1 : 2. For magnetical investigations in solids there exist rules to de-rive spin and angular momenta (and therefore magnetical properties) from sums anddifferences of line intensites (sum rules), especially for the 2p 3d X-ray absorp-tion [Thole92, Carra93]. They are, however, hampered by the break down of theunderlying independent particle approximation, i.e. the presence of a more atomiccore-valence coupling [Schwitalla98].

In case that one finds interactions of similar strength, no scheme can be appliedpurely and a mixed intermediate coupling has to be used. Even more: in thevery general case, far from any pure coupling conditions, no more can be done thanlabelling the energetic levels by serial numbers or other means [Cowan81]. Still theLS notation is widely used as a means of arbitrary labelling, even in non-LS couplingconditions, to provide at least some information on the states.

From zero order calculations one can assume, that the electronic structure of the2p excited 3d transition metals has to be described in intermediate coupling, becausethe 2p spin-orbit parameter 2p, and the Slater integrals Fk(2p3d), Fk(3d3d), Gk(2p3d)are of similar magnitude (several eV). An energetic ordering can not be establishedunambiguously. Compared to 3p photoionisation the larger spin-orbit splitting of the2p core hole states spreads the lines over a larger energy range, leading to a decreasein configuration mixing or CI. So in general it should be easier to calculate 2p core holespectra as with the smaller amount of electron correlations an SCA can be sufficient.

The cross section for direct photoionisation with a continuum wavefunction as finalstate, usually is maximal right at threshold and then exponentially drops. Abovethe first threshold energy of an atom, in the order of some eV, direct ionisation ispossible with every photon, so there is a direct ionization contribution even in everyhigher resonance. As noted earlier it is in some cases possible to reach the same finalstate both via direct ionisation into the continuum and via a discrete intermediatestate plus a subsequent (autoionisation) decay. This results in quantum mechanicalinterference, yielding a, possibly asymmetric, Fano-Beutler profile in the spectrum[Fano61, Fano65].

The assumption that electric dipole interactions are the most dominant contribu-tion is usually well justified. Within this dipole approximation (DA) the photoioni-sation or excitation cross section can be conveniently calculated by Fermis goldenrule. For the atomic case this boils down to the matrix element of the perturbationHamiltonian, the dipole operator D between final and initial state ( f and i):


f |D |i 2

So the cross section is large when the D modified overlap integral for the wave-functions for state i and f is large. For ionization this is usually the case right above(at) threshold. With no ionization before that and an exponential drop afterwards,one usually speaks of an absorption edge in solid state experiments. For the atomswe will find spectra dominated by a resonance multiplet structure and therefore notuse this term.

The dipole nature of the radiation will also result in a special angular distributionpattern of the emitted photo electrons. This will be introduced briefly now. For pho-toionisation of an unpolarised (unoriented) target by linearly polarised radiation andwithin the dipole approximation, the differential cross section is defined by Yangs[Yang48] theorem:

dd

() =

4[1 + P2 (cos )] (2.1)

This splits the problem into a geometrical part P2 (cos ) and the parameter thatcomprises the photoionization dynamics. Therein is the angle between the polari-sation vector of the ionising light and the momentum vector of the ejected electron inthe plane perpendicular to the radiation (so called dipole plane). P2(x) = 12(3x

2 1)is the second Legendre polynomial, and is the angle independent cross section.At the so called magic angle = 54.7 a spectrum directly proportional to can bemeasured since the term containing vanishes: P2(cos(54.7)) = 0.

The allowed values for range from -1 to 2. Zero means isotropic emission, whilenegative values describe an emission preferring the plane perpendicular to the polar-ization vector. Positive numbers for finally correspond to emission patterns havinga minimum in the direction of this perpendicular plane. For the ionization of s-levelsone expects an energy independent value of 2, as the original isotropic electron distri-bution is ejected in a p-wave only. For all other levels carrying an angular momentum` in general two outgoing waves with either ` 1 or `+ 1 are possible. Due to interfer-ence effects delicately involing the outgoing phases (see below) will have differentvalues for the same shells in different atoms and be in general energy dependent.The formal calculation of is considerably more complex, than the calculation of via Fermis golden rule.

According to the excellent article by S. Baier and coworkers [Baier94] on the theoryof atomic angular distributions, as used above, can be expressed in terms of thegeneralized anisotropy parameters k0kk :

=

103

022 (2.2)

with

k0kk =

3Bk0kkB000

. (2.3)


The coefficients Bk0kk are given by

Bk0kk =3 J0 J J

ll jj

(1)J+J f +k1/2 J J j j l l(l0, l0|k0

)

{

j l 12l j k

} {j l J fJ j k

} J0 1 JJ0 1 J

k0 k k

f J f , l j : J||D||0 J0 f J f , l j : J||D||0 J0.

(2.4)

Here, J0, 0 (J f , f ) characterize the initial (final) state of the atom (ion), l, j are theorbital and angular momenta of the photo electron, and f J f , l j : J||D||0 J0 arethe multi-channel dipole amplitudes. The standard notations for the Clebsch-Gordancoefficients and the Wigner nj coefficients are used and J =

2J + 1. Now can be

calculated using the HF dipole matrix elements f J f , l j : J||D||0 J0 in Eq. (2.4).Fortunately the calculation is carried out using computer programs. But it should

be obvious from the presented formulae, that the parameter is prone to be moresensitive to incorrect wavefunctions. Therefore it will pose the stronger test to theory.

As stated above, the use of a dipole approximation is well justified in most cases.There always exist small non-dipolar contributions, however, that can lead to a for-ward/backward asymmetry with respect to the photon beam [Krssig95] or even tosecond order contributions [Derevianko00]. The equation for the differential crosssection with second order corrections is given here just for illustration, featuring asecond angle between ejected electrons and the photon propagation axis:

dd

(, ) =

4[1 + ( + )P2 (cos )

+ ( + cos2 ) sin cos + P2 (cos ) cos 2 + cos 2 + (1 + cos 2) P4 (cos )]

With and being first order corrections and , , , and as parameters of thesecond order multipole effects. It can be seen easily that at = 90 (in the so calleddipole plane, perpendicular to the photon propagation axis) first order effects (secondline in the equation) vanish with the cosine factor. Second order parameters survivein principle. But in general these parameters are small and careful measurements athigh photon energies are necessary to observe them.

3 Instrumentation and Experiments

3.1 Photon Source

To carry out inner shell photoexcitation experiments one of course needs a photonsource in the desired energy range. Only synchrotron radiation facilities are able todeliver photons in a tunable energy range from roughly 300 to 1000 eV, required forL shell experiments on 3d metals. There is also need for high photon flux, whichis available only at third generation synchrotron radiation sources with their undu-lators, to reach a sufficiently high resolution and signal to noise ratio in acceptableamounts of time. According to [Yeh85] the cross sections for direct 2p ionisation ofthe 3d metals are roughly of the same order of magnitude as those for the 3p ioni-sation. So the reason for experimental atomic data being rather rare in the L shellenergy region before this work is more that the giant resonances were more popularearlier.

The author feels no need to introduce the dear reader into the all of the very basicsof synchrotron radiation, so only a concise summary will follow in the next para-graphs. Two text books can serve as a starting point for people new to the field:The book by K. Wille on accelerators and synchrotron radiation sources [Wille96] andPeatmans Gratings, Mirrors and Slits [Peatman97]. Both will not cover the latestdevelopments, like for example SASE free electron lasers, very well. But those topicsare of no relevance here either.

Synchrotron radiation is the continous radiation emitted by electrons (or in general:charged particles) traversing a magnetic field at relativistic energies. Todays sourceshave a usable radiation range from the infrared THz regieme to hard X-rays. Thefirst experimental observation was made by naked eye at the 70 MeV synchrotron ac-celerator (hence the name) of the General Electric Research Laboratory, Schenectady,New York, in 1947 [Elder47, Elder48]. Theoretical predictions date back into the 19thcentury coming from Lienard. Schwinger presented a solid theoretical treatment in1949 [Schwinger49].

As synchrotron radiation is a broadband and thus versatile source, with many otheradvantages as well, storage rings with stable beam conditions have been built as userfacilities later. To further increase photon flux the dipole bending magnets have beenaccompanied by periodic magnet structures (undulators) along the electons traje-tory to constitute sources of the so called 3rd generation (local example: BESSY II inBerlin, Adlershof [Follath99]). The undulators magnetic field accelerates the stored

16

3.1 Photon Source 17

electrons not only once, like the bending magnet, but N times, with N being thenumber of magnet periods, in the order of a few dozens. If the electron excursionsperpendicular to the primary propagation axis at each indidivdual bend are smallenough, i.e. when the magnetic field is rather weak, the emitted photons will only bevery slightly faster than the higly relativistic electrons. This allows for an interferenceeffect of the individual photon bursts produced at each bend, amplifing the photonflux for constructive interference with O(N2). As a result an undulator generateshigh intensity radiation, no longer in a featureless broadband range but in severalyharmonics, mostly one selected fundamental photon energy and their (odd) multiples,due to the interference effect. With most experiments requireing a monochromatizedbeam, the preferred production of the desired energy is an additional advantage. Byincreasing the magnetic field on the device and thereby enlarging the excursing theinterference fades out and the emitted intensity will scale with O(N) only (this iscalled a Wiggler). The de- and increase of the mangetic field is performed by mov-ing permanent magnets nearer to the electron beam or further away. The changedparameter is referred to as gap.

The numerous advantages of the radiation, besides the desireable energy range andhigh flux (or brilliance), include small source size, clean vaccum operation conditions,well defined time structure and the emitted spectral power can be exactly calculatedfrom well accessible properties. Additionally the radiation is usually linearly polar-ized in the horizontal plane with high purity. Linear polarisation in the perpendicularplane is possible at BESSY using special undulators (UE, with E for elliptical), were allsorts elliptical polarization (with the elliptic half axies along the vertical and horizon-tal direction) are offered aswell [Sasaki92, Weiss99]. These UE type undulators consistof an upper and lower half, as well as a left and right half. The lateral structures nowcan be shifted with respect to each other, creating a magnetic field that drive the elec-trons into a helical movement. At the UE52 undulator arbitrary linear polarizationcan be produced by an antiparallel shift of the lateral halves. Setting the undulatorto a shift of half the undulator period (in this case 26 mm, as the UE52 has a periodof 52 mm) results in 90 linear polarization. The in between values require evalua-tion of a non-linear function with the shift setting being gap dependent. A computerprogram for this calculation is available running on the beamline computers.

Undulators harmonics are still a rather broad distribution of photon energies, sofor a mode defined energy setting monochromators are needed. Spherical GratingMonochromators (SGM) [Petersen95] and the Plane Grating Monochromators (PGM)[Follath97] are employed in the VUV region at BESSY (II). In addition to the gratingas dispersive element the beamlines contain curved shape mirrors for pre- and re-focussing, as well as slits, baffles and further diagnostic elements. The experiments,whose data will be presented here, were carried out at the beamlines U49/1-SGM,U49/2-PGM1 and UE52/1-SGM at BESSY (II) in Berlin Adlershof. The U49/1-SGMand UE52/1-SGM are in fact the same beamline with a different undulator structure,which has been upgraded to a device delivering radiation of arbitrary elliptical po-larization in 2002. All beamlines offer reasonable photon flux in the energy range of

3.2 Atomic Vapour Source 18

roughly (at least) 100 to 1000 eV with an energy resolution E/E of better than 10000[Schwarzkopf03, Schwarzkopf05].

Experiments to be connected to the beamline are required to have oil-free vacuumconditions of at least 108 mbar or better, enforced by an interlock system. This re-quirement prevents the optical surfaces inside the beamline from (carbon) contami-nation and minimises absorption of the VUV radiation in the beamline.

3.2 Atomic Vapour Source

The investigation of single atoms, free from interaction with other surrounding mat-ter, depends on the production of a sufficient target density in the interaction region.With the given geometry this requires a vapour pressure on the order of 102 mbarinside the furnace. In table 3.1 the temperatures needed for this vapour pressureare summarised. Temperatures as high as needed cannot be reached in a furnace bystraight forward resistive heating, electron bombardment has to be used instead. Inthe evaporation furnace a grounded crucible is therefore impinged by electrons ther-mally ejected from a resistively heated tungsten wire cathode and accelerated by atypical voltage of 1000 V. [Ross95]. Heating power (electron current accelerationvoltage) is in the order of 200 W. This value is valid for the equipment employedonly and cannot be readily transfered to other setups. It strongly depends also on thecrucible surface. When properly assembled, the furnace directs the electrom impactpower completely to the molybdenum or tantalum rod forming the crucible. Themain loss, except for evaporated target material in the high temperature regieme, istherefore black body radiation. The crucible contact to its mount is designed to createa small thermal bridge only. Finally, the cylindrical rod has a cylindrical borehole,leaving only 1 mm thin walls to be filled with the sample material.

The electron bombardment region has to be well shielded. Otherwise the electronsfrom the furnace will create an enormous background signal inhibiting electron spec-troscopy. The shielding and the supporting mount of the heating wire cage aroundthe crucible are water cooled. In some experiments a device repelling charged par-ticles from the crucible was deployed, to reduce some background. Consisting of aceramic ring with metal pinholes, plates or wires attached inside, it was mountedon top of the furnace right between crucible exit and the -metal shielding of theinteraction region. By applying a small voltage ( 10 V) electrons and ions couldbe deflected or either of them repelled, depending on the geometry of the electrodesinside. This device is traditionally called Haase-Kfig. Its benefit was limited, somost of the time no voltage was applied and only a plain pinhole was used. As forsome targets this led to clogging and obstructions of the atomic beam, instead of animprovement of beam quality, the device was skip completely on these occasions.

For the 3d metals the melting point is also given in table 3.1. As can be seen, sev-eral of these elements are liquid at the required temperatures. That makes them oftenhighly reactive; i.e. the the metallic crucible will be rapidly destroyed by forming


Table 3.1: Initial states of the 3d elements, populated in an atomic beam at evaporationtemperature. This temperature corresponds to a 102 mbar vapour pressure [SPD81]for the element. States are sorted lowest energy first. Contributions are rounded, sothe sum does not always yield 100% excatly. Melting point is given to identify metalsliquid at required conditions.

vapour meltingtemp. point initial configuration and states Contribution

[K] [K] [%]Sc 1660 1810 4s2 3d 2D5/2, 3/2 56, 44Ti 2000 1940 4s2 3d2 3F2, 3, 4 28, 34, 38V 2120 2160 4s2 3d3 4F3/2, 5/2, 7/2, 9/2 14, 19, 22, 24

4s 3d4 6D1/2, 3/2, 5/2, 7/2, 9/2 2, 3, 5, 6, 7Cr 1670 2130 4s 3d5 7S3 100Mn 1240 1520 4s2 3d5 6S5/2 100Fe 1740 1810 4s2 3d6 5D4, 3, 2, 1, 0 48, 27, 15, 8, 2Co 1810 1770 4s2 3d7 4F9/2, 7/2, 5/2, 3/2 58, 24, 12, 6Ni 1800 1730 4s2 3d8 3F4, 3, 2 41, 11, 4

4s 3d9 3D3, 2, 1 27, 11, 4Cu 1530 1360 4s 3d10 2S1/2 100

alloys of lower melting point than the original crucible material. To avoid this corro-sion process insets made of Al2O3 or carbon (graphite) are used where necessary, i.e.Al2O3 for iron, C for titanium.

The stability of the atom flux from the furnace is rather important, as the spectraare recorded by sweeping the photon energy (absorption measurements) or kineticenergy of photo electrons over time. A photo electron sweep took in the order of100 seconds to complete and is repeated many (e.g. 500) times to result in a decentsum spectrum. For the absorption measurements only few sweeps (typically five orless) were recorded which took up to three hours each. So the (long term) stabilityrequirements are more strict for the absorption measurements of course.

Unfortunately monitoring the target density is not easy, so there is currently nopossibility to record it and correct later. Earlier it was tried to measure the targetmass transport using a surface thickness monitor that is routinely employed in theproduction of thin metallic films [Richter00]. The measured precision of the depositedmass was limited and measurements were hampered by thermal effects of the sensor,because it directly experienced the radiant heat of the furnace. So the results did notlead to an improvement of the experiment.

Instead one could try to measure the crucible temperature hoping that a stable tem-perature will lead to a stable beam. The electron bombardment nature of the furnace


does not allow the use of thermocouples for direct temperature measurement on theother hand. A contactless optical method was tried earlier but was discarded becauseof focussing and transmission problems [Sladeczek95]. So temperature measurementis not easily feasible either.

Fortunately in the high temperature regime thermal equilibrium or to be more pre-cise stable thermal conditions are quickly reached as radiative loss is in the sameorder as heating power. Therefore it is deemed sufficient to maintain a stable heatingto have a fixed temperature and thus a time invariant atomic beam. When radiativeheating from the tungsten wire is small compared to the electron bombardment it canbe neglected and only the product of electron current and acceleration voltage has tobe kept constant in order to keep the total heating power constant.

Due to the highly non-linear nature of the thermodynamics involved, a number ofprocesses can inhibit stable operation. For example slightly more heat will generatemore free electrons from the wire, which will result in even more heat, and vice-versa.Additionally the effect of material loss from the evaporation cannot be neglected, thecrucible weight is only double the usual sample load (roughly 10 g vs. 5 g). Left unat-tended at fixed power settings on the supply for the electron bombardment and onthe one for the filament (wire) heating, the furnace can show almost chaotic behaviouras a result.

A separate controller has to be used therefore, which is done in the following way:

The bombardment power supply is set to a fixed voltage (usually 1000 V tohave a Watt power reading on the mA current scale). Bombardment current (inorderly operation) does not follow Ohms law but is limited by the amount offree electrons provided by the heated filament.

The controller monitors the bombardment current.

Filament voltage is governed by the controller.

A bombardment current target value is reached by an increase or decrease ofthermal electron emission from the tungsten wire.

Initially in this work a full blown PID controller provided by the Fritz-Haber-Institut was employed. Later then only an integrative circuit with adjustable timeconstant is used with even better results, being less delicate in its settings. The timeconstant in this controller circuit is in the order of one second, imposing some prob-lem to the electrical design of the controller to avoid high frequency oscillations. Thisfavours a stripped down setup. To saveguard against different modes of failure themaximum voltages on the supplies are set to reasonably low values.

The assumption that a stable heating leads to a stable target beam was made un-der the condition of high temperatures. Of course any time independent heatingwill eventually result in a thermodynamically stable state (which could be a failiurecondition). But with heat transport being still the dominating balancing mechanismthe time to reach stability is much longer than with radiation. Therefore the furnace

3.3 Time of Flight Spectrometer 21

setup presented here is not best suited for most molecular samples or elements withlow melting points as sodium, potassium or cesium, although there was quite somesuccess in experiments with these. When resistive heating is sufficient (i.e. below1000 K) it should be used instead, preferrably combined with a temperature con-trol/stabilisation.

On further display in table 3.1 are the atomic states that are populated by thermalenergy at the evaporation temperature. The states are sorted by energy, not by pop-ulation. Due to Hunds third rule (spin-orbit coupling) for the light elements (Sc, Ti,V) with their less than half filled 3d shell lower J values have lower energy. But thestatistical weighting (2 J + 1) overrules the slight energy difference, so the most pop-ulated states is different from the energetic ground state and the whole ordering isreversed. As with more than half-filled shells higher angular momenta are favoured,both energy level and statistical weighting then work in the same direction. So forthe heavier elements, namely Fe, Co and Ni, ordering is the same for low to highenergy level and population. Cr, Mn and Cu have a special structure with an ex-actly half-filled (Mn and Cr) or closed shell (Cu), leading to low lying ground stateswith virtually no population of other levels. The unlike in chromium the unpaired 4selectron in copper has only one coupling possibilty.

To fulfill the required vacuum conditions despite the operation of this rather prob-lematic high temperature equipment a differential pumping stage is employed. Itsmain feature is a 100 mm aluminum rod with a 5 mm bore hole mounted on a blankflange with an equal size hole. It is installed between the main experiment and asecondary pumping stage on the beamline side. Under high vaccum conditions, thistight long tunnel, can establish an pressure difference of two order of magintude.Typical main chamber pressure with hot furnace was 4 107 mbar. In the pump-ing stage connected to the beam line 1 109 mbar could be maintained. During cal-ibration measurements with noble gases injected through a gas inlet pressure valuesinside the main vessel were roughly half an order of magnitude higher, with virtuallyno increase in the pumping stage.

3.3 Time of Flight Spectrometer

As laid out in the phenomenological section of the preceding chapter, true absorptionmeasurements are carried out detecting the difference in photon flux in front of andafter passing an absorption cell. This is very difficult for low density samples andsmall absorption lengths. Instead of recording the loss of photons, one can count theequivalent number of excitations. The detection of an excitation is feasible (via probepulses, e.g.) but impractical, it is much easier to record the number of decays fromthe excited state.

Here one could think of detecting fluorescence photons, Auger electron yield ortotal electron yield. But with the 3d metals most inner shell excited atoms will finallyend in an ionic state, so detecting the number of ions can be a means to measure an


approximate absorption rate. Long living excited states are not accounted for then,but they are hardly excited via an electric dipole transition from the ground state.One of course also neglects decays back into the neutral atom, but for the metalsinvestigated the fluorescence yield after 2p photoexcitation/-ionisation is in the sub-percent region [Hubbell94], being 0.27% for scandium up to 0.94% for copper. So theerror made is roughly of the order of the signal noise, as a look on the spectra laterwill show.

Due to the dilute sample no saturation effects are expected. It is, however, not fea-sible to derive absolute absorption values by ion yield spectroscopy with the setupused. On the other hand an ion mass spectrometer is sensitive to the mass to chargeratio, i.e. one gains information on the charge state of the final state. For the absorp-tion equivalent spectra (in the following we will mostly skip this restrictive attribute)presented here, a time of flight (TOF) analyser was used to discriminate differentionic states of the sample atoms. A TOF, with its slitless design, has a high collectionefficiency as all charge to mass ratios can be observed at the same time. At relativelylow cost a high transmission device can be built.

To compensate for temporal, spatial and initial kinetic energy distributions, thesetup used follows Wiley and McLaren [Wiley55] loosely, employing two pulsed ac-celeration meshes. But for strong practical reasons no real termination mesh could beinstalled, as the device had to be fitted into the 20 mm tube of the -metal shielding ofthe electron analyser and still allow electron measurements when mounted. Thus anaperture plate on ground level with a hole in it is employed for field termination onthe electron analyser side. With only 100 mm flight patch the device is also quite com-pact but still allowed to identify the three most abundant naturally occurring isotopesof Xe ions (129, 131 and 132). That is more than good enough for our experiments,where isotope effects play no role and only different charge stated of one atom haveto be distingushed from rest gas signal. The achievable photon energy resolution de-pends on target density and beamline capabilities only. For more information on theTOF setup see [Obst00].

Due to the (for our purposes) near cw character of the incident SR in multi-bunchmode, pulsed acceleration voltages have to be used to define a start for the time offlight measurement. Typical pulses were about 100 V in height, in the order of somes in length and at a 10 kHz repetition rate. Ions hitting the MCP detector afterpassing the drift tube produce the signals used as stop pulses. These stop pulses canbe processed in three different ways.

A non multi count capable variant is quickly rejected: feeding the signals into atime to amplitude converter (TAC) and record the amplitudes using a multi channelanalyser (MCA). This was the initial method for calibrating and test only, as for realmeasurements the count rate would have to be severely limited to prevent pile upeffects. Under good working conditions 10 stop pulses per start were not uncommon,as the TAC produces only one signal per start no slow (low charge) ion would becounted inside a resonance. Additionally there is no convenient way to measure anabsorption curve over a larger number of photon energies in this scheme.


So two multi count options remain: One is to filter the stop pulses by timed gatesand record signals from interesing charge to mass ratio (ranges) using counter de-vices. The most advanced method is to employ dedicated electronics combined withsome software. The filtering method can be setup using counters, computer and soft-ware provided by BESSY. Only the gating technique has to be brought in. The BESSYpackage already includes the ability of setting and scanning monochromator energiesand recoding beamline parameters along with the counter signals in software, result-ing in partial ion yield spectra. Still the method has its limitations as the number ofhardware devices, like counters, delays, gates, wires, etc. cannot be scaled arbitrarily.So only a restricted number of channels can be recorded. But with atomic species withpossible charge states only from 1+ to 5+, this limitation can be dealt with requiringjust five sets of electronics. And even a total ion yield spectrum with no gating isuseful. It provides absorption-like data, just what most theoreticians calculate, onlyno additional information.

To retain a maximum of information an allow for a flexible choice of channels anentire TOF spectrum can be recorded at each energy with the dedicated TOF electron-ics. That is a great advantage at the cost of some amount of computer memory andstorage. The software side and more details are given section 3.5.2. Additionally thereis no need to know the interesting channels prior to measurement, so that for examplepeaks emerging only at certain photon energies will not be missed. A main reason todevelop this technique was laid by trial measurements on molecular samples, wherea bigger wealth of charge to mass ratios are generated, sometime changing heavilyover a resonance. However upon completion the atomic data were already recodedin gating mode.

When recording time of flight counts over photon energy, some parameters haveto be observed to yield reliable data. For the energy scale, which is given by themonochromator drive, non-linearities are neglected. Thus to establish the correct en-ergy scale known features are measured and the energy positions adjusted to conformwith literature values. The intensity scale is mostly influenced by target density andphoton flux. Target density has been addressed in section 3.2, while not exactly stableits variations are deemed negligible during time periods needed to take a spectrum.Photon flux has to be recorded and corrected for. Not only is the electron ring currentdecreasing due to synchrotron lifetime, but with changing photon energy the com-bined undulator and monochromator photon output can easily change by a factor oftwo or more. Usually a gold mesh can be introduced in the photon beam inside thebeamline. When grounded through a precision galvanometer the current reading willbe proportional to photon flux in good approximation. To receive a corrected spec-trum the intensity at each energy is divided by the corresponding current. Intead ofthe mesh the ground current onto the last refocussing mirror was often used in theidentical way.

As one problem the detector efficiency remains. The probability to detect differ-ently charged ions from the same element increases with their kinetic energy, i.e. theircharge [Gao84, Hayaishi96, Gerth00]. A plateau in that detection efficiency curve is

3.4 Electron Analyser 24

reached at high particle energies above some keV. The small device used does notallow for voltages that high, typical values were below 2 kV. This is below saturationfor 1+ ions. No attempt for a correction of this effect has been made for the measure-ments presented here, which means we will give no absolute values for ion chargeratios, but report only on changes of such ratios with photon energy.

3.4 Electron Analyser

Photo emission experiments are carried out using a known photon energy and de-tecting the kinetic energy of the emitted electrons. To acquire electron spectra with ahigh precision and transmission, commercially available hemispherical analysers arevery popular. The basic operation principle of a Scienta SES-2002 electron analyser,which was used in the work presented here, will be laid out in the following.

The electron energy is determined by the analyzer via the flight path through twoconcentric metallic half spheres with an electric field between them. Electrons witha trajectory following the mean radius of the two half spheres have a kinetic energyequal to the so called pass energy. Nine fixed pass energies are supported by the highprecision power supplies. A set of low energies 1, 2, 5, 10, 20, and 50 eV, as well as aset for higher kinetic energies 50, 100, 200, and 500 eV. The detection system consistsof a 40 mm diameter, chevron mounted multi channel plate (MCP) assembly with afluorescence screen and an additional digital CCD camera. This 2D position sensitivedetector images the electrons along a energetic and one spacial axis, when operatedin transmission mode. According to the fine manual [Sci96] the spatical resolution is200 m. Alternatively an angular resolving mode is available, most useful for surfacescience. The energetic axis captures (slightly less than) 10% of the pass energy. Thisenergy is fixed for an individual measurement, to yield a constant energy resolutionthroughout the spectrum. One can switch the pass energy within the low or high passenergy set by software. Choosing a different set, requires a quick recabling (


pending on the desired energy range and resolution, 90% or more deadtime is possi-ble. The fixed modes quickness comes at the cost of detector effects. In order to avoidcomplicated and extensive calibration measurements necessary for a careful correc-tion of those effects, the fixed mode was completely avoided for the measurementspresented here. Instead settings were chosen to minimize deadtime when possible.

The lens system is not only employed to adjust the kinetic energy of the incomingelectrons to the pass energy, but also to focus the electrons. The focussing both im-proves the transmission by imaging the electrons onto the analyser slits as well as itimproves the resolution by parallelising the electron path prior to the acceleration.With five lens elements there is one degree of freedom for adjustments. This voltagecan be set to maximize the transmission function. The other four are needed to

maintaining constant magnification level on the entrance slit

maintaining constant focus spot on the entrance slit

match the desired pass energy

matintain sample potential (first element)

In addition to the just mentioned purposes lens system introduces a spacial dis-tance between the analysers half spheres and the source volume. This allows easyaccess to the sample volume, e.g. to place the target producing furnace in close vicin-ity of the interaction region, which is very fabourable.

Eight additional deflexion plates allow for small spacial adjustments of the probedsource volume, to account for the fact that the setup is mobile and a perfect geo-metrical alignment is hard to reach. It is not unusual to gain more than one orderof magnitude in signal intensity by adjusting these voltages, or (worse) to have nosignal at all without adjustments. Most important is the so-called down elementtogether with left/right. The improvement is checked and carried out often, it canalso minimise effects of stray electric or magnetic fields near the source volume. Itis important to note, that the setting has to be adjusted for every pass energy usedindividually. Other stray fields with more remote origin should already be dimin-ished by a double wall -metal shielding attached to the entrance lens of the electronanalyser. Two futher lens elements called slit deflection and focal plane should beleft at zero, they have effects only at lowest pass energies and are present for use inthe manufacturing process of the device.

The analyer houses a slit carousel to control the intruments resolution. Both en-trance slit and exit slit (apperture) are controlled simultaneously. See Appendix A(lower part) for an overview of the available settings. The imaging by two halfspheres introduces an abberation, electrons entering the spheres with pass perfectenergy and velocity vector originating from a rectangular area will be distorted intoa curved area at the exit plane. To overcome this effect slits smaller than 1 mm areof curved shape themselves. Therefore at high resolution a curved source region isprobed. With common beam sizes (SR and target) or cross sections this is not an issue,


however. For coarse slit settings the abberation effect is negligible according to thefine manual.

Mounted in the magic angle of 54.7 with respect to the horizontal polarization axisand in the plane perpendicular to the propergation axis of the radiation, the instru-ment detects a signal proportional to the total (angle integrated) cross section. Only avery small fraction of the 4 solid angle is probed by the lenses, in the order of 0.5%,when considering aperture and slits as well. This small amount is countered by themulti-hit detection system covering a whole (pass energy dependent) energy rangesimultaneously to deliver a very reasonable count rate in the end. The spectrometer ismounted to accept only electrons emitted perpendicular to the propagation directionof the ionising radiation and with the DA magic angle between the electron momen-tum vector and the horizontal linear polarisation axis. The count rate recorded is thusproportional to the angle integrated cross section (see equation 2.1 on page 14), unaf-fected by first order non-dipole effects [Cooper90, Amusia01, Grum-Grzhimailo01].

To specificly measure the anisotropy parameter either the instrument angle hasto be scanned or the polarization axis of the incident photons must be changed inorder to measure the cross section for different angles and derive from a fit routine.As reported in section 3.1 the latter is possible at beamline UE52/SGM offering totake the very favourable approach. Rotatable vaccum hardware the size of the SES2002 is mechanically challanging. This goes hand in hand with the problem that itwould be hard to ensure that the identical cross section region is probed regardlessof the angle setting. That opens the door to a world of uncertainty, because as notedabove transmission is considerably dependent on the spatical alignment. With anuncertainty in transmission it is demanding to compare the different intensities andderive a value. Additionally the hardware rotation will potentially be complicatedand require recalibration, favouring infrequent changes in the angle setting. But toavoid implications of long term instabilities (target beam, etc.) angle changes shouldbe made frequently.

Rotatable linear polarization eliminates these problems elegantly. Optical con-straints ensure photon beam movements are kept to a minimum. The movementis carried out using motor drives in the storage ring tunnel at the press of a button.Movement is not instantaneous but takes less than a minute with no further calibra-tion or other action needed. As a result many measurements at the each of the desiredangle settings can be acquired averaging out the effects of most instabilities.

On the other hand two issues have to be addressed using this measurementscheme: With changing gap and shift settings unfortunately the photon flux changesas does to some extent the degree of polarization. At a zero shift setting (normalundulator mode) polarization is near 100%. For increasing shift values this figuredrops slightly, but stays above 96% with no exceptions. This has been confirmed us-ing the BESSY polarimeter setup, the respective measurement curve can be found in[Godehusen03a]. For the expected accuracy of the measurements this deviation fromperfection can be neglected. Beam intensity variation on the other hand has to bedealt with, by recording the photon flux and applying a correction. The most reliable


approch is to record the mirror or mesh current with every spectrum and calibrate thisreading using an angle integrating signal like the time of flight ion yield. By this twostep correction possible magentization effects leading to anisotropies in the electronyield cross sections from the mesh or mirror surface are eleminated. These anisotropyhas been observed to be important near absorption edges of elements composing therespective beamline component. For photon energies away from these edges the cor-rections needed are very small.

Finally, after comparable intensity values for a set of usually four different anglesare determined, the parameter for this photon energy is derived from a numericalfit to the cross section relation, see 2.1:

I() =

4

[1 +

2

(3 (cos )2 1

)]This equation contains at least two free paramters: and of course . So at least twomeasurements at two angles are needed to yield an unambigious result for . Theoffset angle should represent the magic angle as the instrument coordinate systemis inclined relative to the photon system by this amount. As additional confirmationof the experimental data it can be left as a free parameter, too, requiring an additionaldata point at a different angle. For consistency should be approxminately 54.7 afterthe fit. Now, in the degenerate case that there are exactly as many data points as thereare parameters, all errors from the fit will be zero by definition. So to get a better ideaof the quality of the data one further angle is measured as stated above.

In the course of this work an upgrade was installed to the original Scienta SES-200 spectrometer (unit U60). With updated power supplies, detector, data acquisitionand software the instrument is now equivalent to a Scienta SES-2002, neglecting slighthardware design changes. Table 3.2 lists the instrument resolution for different passenergies achieved during the acceptance test for the upgrade installation in 2001 forthe Xenon 5p3/2 line using a (Gammadata) He I lamp. The instrumental resolution iscalculated by deconvoluting Doppler broadening ( 3.25 meV) and VUV light sourceline width ( 1.2 meV) from the measured full width half maximum (FWHM). Atthese settings and with the light element helium Doppler broadening is a noticeableeffect, unlike in the experiments with metal atoms.

Optimal performance for real world applications using synchrotron radiation wasreached on HI molecules, where it was possible to observe rotational fine structuresof the outer valence 2 state. Total experimental resolution (beamline U125/2-SGMplus Scienta) was less than 6 meV, using 2eV pass energy. Unfortunately the collab-orators have not yet published these results (even not in the BESSY Jahresbericht).On metal vapours the resonant 3d photo emission of Manganese sets our benchmarkwith a resolution of approx. 15.5 meV (see section 3.5 and [Richter02]).

For the 2p photo electron spectra presented here, however, transmission is more im-portant than resolution. To get rid of low kinetic energy background the spectra weretaken at kinetic energies around 100 eV, mostly using the 200 eV pass energy setting.With an additional coarse slit setting the experimental resultion settled in the range


Table 3.2: Measured FWHM and deconvoluted instrumental resolution reached forXenon 5p3/2 using a He I lamp (Ekin 9 eV). See text for the estimation of the instru-mental resolution.

pass energy measured FWHM instrumental resolution(eV) (meV) (meV)

1 3.7 < 1.32 3.8 < 1.55 4.8 3.3

10 7.420 13.850 29.7

of some 100 meV up to almost 2 eV. Due to lifetime effects, the natural line widthsare almost in that order of magnitude, but it was mainly needed in order to reachdecent statistics in reasonable time. Still aquiring the data for nickel photo emissionpresented in section 4.2 took several days. The operation mode then was to measurea number of e.g. 50 individual spectra (sweeps), each taking about one minute, to havea signal to noise ratio that allows to identify the main features. Several of these runswere performed between two injections of the storage ring comprising one shift.

Apart from the resolution improvement by the analyzer update the data acquisitionspeed was increased leading to a higher detection rate. Additionally the source codeof the new acquisition software was made public, allowing for user customisations(see section 3.5).

A photo electron spectrum showa an electron count rate plotted versus bindingenergy. As with the time of flight spectrometer flux and target density affect thesignal intensity. So the respective corrections and precautions are very similar andare not repeated here. But with an energy dispersive analyser one also has to keep inmind that the transmission function of the analyser will not be constant.

The analyser transmission function with respect to the original electron energy andthe pass energy is can be a very important factor in measurements. In the trans-mission function there is a distinct minimum at low kinetic energies, going down tozero transmission, and when going to higher kinetic energies a slower degradation oftransmission after an intermediate maximum. In general the transmission is higherwith higher pass energy, corresponding to a lower resolution, the expected give andtake relation.

A transmission curve for the entire range can be established, if one succeeds to com-pare the transmission of arbitrary points on the kinetic energy scale. Several effectsforbid the direct comparison of intensity of one photo line produced by photons ofdifferent energies, resulting in different kinetic energies. These effect either have to dowith energy dependency, e.g. the changing cross section of the line and varying pho-ton flux, or time dependency, e.g. a changing target density. Our process to determinethe relative transmission function used follows the one laid out in [Jauhiainen94]. It


uses the special properties of electronic Auger decays. An Auger decay probability isindependent from the photon energy. So for a given number of photo electrons cre-ated in photo ionization, the fraction of corresponding Auger electrons should be thesame, regardless of ionization cross section changes. As Auger electrons have a fixedkinetic energy, they are measured with the same relative transmission regardless ofthe photon energy. The relative transmission T12 between to points (1 and 2) on theenergy scale can therefore be derived by measuring two spectra and calculating:

T12 =I1I2 A1

A2

With In being the photo line intensity in spectrum n and An the respective Augerintensity. This scheme compares the kinetic energies at the photo lines positions. Themost prominet targets used for this calibration here are Krypton (M4,5NN Auger linesbetween 20 and 60 eV, thresholds 95.0 and 93.8 eV) and Xenon (N4,5OO Auger linesbetween 10 and 35 eV, threshold 67.5 and 69.5 eV

Electronic Structure of the 3d Metals: An Investigation by ... · phase atom. Both laser...

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