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Characterization of Interfaces Between
Metals and Organic Thin Films by
Electron and Ion Spectroscopies
Charakterisierung der Grenzflächen zwischenMetallen und
organischen Dünnschichten
mittels Elektronen- und Ionenspektroskopie
Der Naturwissenschaftlichen Fakultät derFriedrich-Alexander
Universität Erlangen-Nürnberg
zur Erlangung des Doktorgrades Dr. rer. nat.
vorgelegt vonMartin Schmid
aus Zwiesel
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Als Dissertation genehmigtdurch die Naturwissenschaftliche
Fakultätder Friedrich-Alexander Universität Erlangen-Nürnberg
Tag der mündlichen Prüfung: 18. 01. 2012
Vorsitzender der Promotionskomission: Prof. Dr. Rainer Fink
Erstberichterstatter: Prof. Dr. Hans-Peter Steinrück
Zweitberichterstatter: Prof. Dr. Andreas Görling
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Für meine Familie
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Contents
1 Introduction 11.1 Coordination chemistry of tetrapyrroles on
Ag(111)
and Au(111) surfaces . . . . . . . . . . . . . . . . . 2
1.2 Chemical reactions at metal/organic interfaces . . . . 4
1.2.1 Covalent adsorbate structures on Ag(111) . . 4
1.2.2 The polymer poly(3-hexylthiophene) as sub-
strate for metallic Ca layers . . . . . . . . . 6
1.2.3 Ionic liquids on solid substrates: The solid/liquid
interface studied with surface science tech-
niques . . . . . . . . . . . . . . . . . . . . . 7
2 Experimental Methods 92.1 Photoelectron Spectroscopy . . . . .
. . . . . . . . . 9
2.1.1 The photoeffect and thermodynamic relations 12
2.1.2 Spin effects in XPS: Spin-orbit splitting and
multiplets . . . . . . . . . . . . . . . . . . . 15
2.1.3 Quantitative XPS . . . . . . . . . . . . . . . 18
2.1.4 Approximating a Voigt profile . . . . . . . . 21
2.1.5 Introducing asymmetry . . . . . . . . . . . . 22
2.1.6 Investigating valence levels with UPS . . . . 38
2.1.7 Further reading . . . . . . . . . . . . . . . . 39
2.2 Low-Energy Electron Diffraction – LEED . . . . . . 40
2.3 Low-Energy Ion Scattering Spectroscopy – LEIS . . 43
3 Results 463.1 Coordination chemistry of metallotetrapyrroles
on Ag(111)
and Au(111) surfaces . . . . . . . . . . . . . . . . . 46
3.1.1 Cobalt(II) phthalocyanine adsorbed on Ag(111)
[P1] . . . . . . . . . . . . . . . . . . . . . . 46
3.1.2 Co(II) and Fe(II) tetrapyrroles on Au(111) [P2,
P3] . . . . . . . . . . . . . . . . . . . . . . 50
3.2 Chemical reactions at the organic/metal interface . . 54
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3.2.1 Covalently linked adsorbate structures on Ag(111)
[P4, P5] . . . . . . . . . . . . . . . . . . . . 54
3.2.2 The interface calcium/rr-poly(3-hexylthiophene)
[P6] . . . . . . . . . . . . . . . . . . . . . . 56
3.2.3 Pd nanoparticles and their interaction with ionic
liquids [P7] . . . . . . . . . . . . . . . . . . 60
4 Summary 63
5 Acknowledgement 69
6 Bibliography 71
7 Appendix: [P1] – [P7] 82
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List of Figures
1 2H-Porphyrin and 2H-Phthalocyanine . . . . . . . . 3
2 The interfacial formation of poly(p-phenylene-terephthal-
amide) . . . . . . . . . . . . . . . . . . . . . . . . . 5
3 The regio regular morphology of the polymer poly(3-
hexylthiophene) . . . . . . . . . . . . . . . . . . . . 6
4 The ionic liquid [EMIM][EtSO4] . . . . . . . . . . . 8
5 XPS and UPS survey spectra of Au(111) . . . . . . . 10
6 Asymmetric Pseudo-Voigt functions . . . . . . . . . 24
7 The finiteness of the integral of an asymmetric Lorentzian
curve . . . . . . . . . . . . . . . . . . . . . . . . . 26
8 The finiteness of the integral of an asymmetric Gaus-
sian curve . . . . . . . . . . . . . . . . . . . . . . . 28
9 Auxiliary function for the convergence proof of an
asymmetric Gaussian peak . . . . . . . . . . . . . . 29
10 The finiteness of the integral of an asymmetric Gaus-
sian curve; asymmetry induced by a shifted sigmoidal
FWHM-function . . . . . . . . . . . . . . . . . . . 31
11 Fit results: Sulphur on Pd(100) . . . . . . . . . . . .
33
12 Fit results: C2H2/Pd(100) . . . . . . . . . . . . . . 35
13 Fit results: Pd 3d signal of Palladium nanoparticles . 37
14 LEIS spectra from the system Ca/Au(111) . . . . . . 44
15 Co 2p core level spectra of cobalt phthalocyanine . . 47
16 Least-squares fit: Co(II) phthalocyanine multilayer . 48
17 LEED patterns: Au(111) and iron phthalocyanine mono-
layer on Au(111) . . . . . . . . . . . . . . . . . . . 51
18 Fe 2p3/2 spectra of iron tetrapyrroles on Au(111) . . 52
19 Terephthaloylchloride and p-phenylene dicarbonyl . 54
20 Deposition of Ca onto Au(111) and rr-P3HT . . . . 56
21 Ca 2p spectrum of Ca depostited at 130 K and 300 K
onto rr-P3HT . . . . . . . . . . . . . . . . . . . . . 58
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22 [BMIM][Tf2N] adsorbed on Pd/Al2O3/NiAl(110) . 60
23 Stoichiometry of the ionic liquid [BMIM][Tf2N] on a
Pd based model catalyst . . . . . . . . . . . . . . . . 62
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List of Tables
1 Fit results S 2p; sulphur on Pd(100) . . . . . . . . . 34
2 Fit results C 1s of C2H2/Pd(100) system . . . . . . . 36
3 Fit results Pd 3d; Laboratory XPS setup . . . . . . . 37
4 Fit results Ca 2p deposited on rr-P3HT at 130K . . . 59
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1 INTRODUCTION
1 Introduction
The surface of a macroscopic object comprises only of an
extremelysmall fraction of the atoms that build up the whole
object. However,the interaction of this object with its environment
is in many casesdetermined by the response of this thin, outer
layer to the physicalor chemical forces associated with the
interaction. This is a generalconcept. The stability of several
metals on air is caused by the for-mation of a protective oxide
layer on the surface of the object, i.e.,a thin interfacial layer
controls a macroscopic property of the object.The same holds true
for effects like friction, electrical conductivity,wetability and
optical appearance, to name only a few examples.1
Furthermore it was shown that by choosing a suitable adsorbate,
thoseinterfacial properties can be modified in a specific way, for
instanceto meet requirements within a scientific or industrial
application. Inrecent years it became clear that also organic
molecules, and in par-ticular biomolecules, can be utilized for
such a purpose. The greatvariability of organic compounds, in
connection with the possibil-ity to synthesize adsorbates
particularly tailored to specific applica-tions, gave rise to
fields like organic electronics2–4 or solar energyconversion5–7
based on organic molecules. In order to obtain a fun-damental
understanding of the complex inorganic/organic interfacesinvolved
in such applications, it has been a general approach to
studyrelatively simple prototype-like model systems with surface
sciencetechniques. A reduction of the complexity should reveal the
basicmechanisms. The aim of the present work is to elucidate
several as-pects of interfaces between metals, like Ag, Au, and Ca
and organicmatter, as for instance polymers or large, functional
biomolecules.Thereby, the focus is set on two different classes of
metal/organicinterfaces. First, interfaces determined by
coordinative ligand inter-actions and self-assembly of the
adsorbate, and second, interfaces de-termined or even created by a
chemical reaction between adsorbateand substrate. The
adsorbate/substrate systems were examined un-der ultra-clean
ultra-high vacuum UHV conditions with photoelectronand ion
spectroscopies.
1
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1 INTRODUCTION
1.1 Coordination chemistry of tetrapyrroles on Ag(111)and
Au(111) surfaces
Tetrapyrroles, such as porphyrins and phthalocyanines (Figure
1), andtheir metalated derivatives play a major role in many
biological andbiochemical processes. The oxygen and carbon dioxide
transport inthe blood stream of mammals is mediated by iron
porphyrins embed-ded into the heme-protein8,9 and the
photosynthetic process of plantsis based on the light absorption by
magnesium porphyrin units inchlorophyll,10–12 to name a few
examples. It were the interesting andversatile properties of
porphyrins, and in particular their metalatedderivatives, that
motivated the examination of their electronic struc-ture with
photoelectron spectroscopy, starting already in the
early1970s.13–19 While most of the early work on tetrapyrroles
focusedon their bulk properties, it were, e.g., Nishimura and
co-workers20,who demonstrated the ex-situ metalation of a thin,
well defined inter-facial layer of porphyrins. Exposition of a
self-assembled monolayer(SAM)21 of thiol-derivatized
2H-tetraphenylporphyrin (2HTPP) tosolutions of various metal salts
resulted in the formation of the cor-responding metalated
derivatives, i.e., in the substitution of the twohydrogen atoms in
the central cavity of the porphyrin macrocyle witha metal ion,
usually in its +2 state. Similar metalation processes at
thesolid-liquid interface have been reported for instance by
Hanzlikovaet al.22 and Tsukahara and co-workers.23 It was later
shown by Got-tfried et al.24 that the metalation of free base
porphyrins and phthalo-cyanines can be achieved in an ultra-clean
ultra-high-vacuum envi-ronment (UHV) in a two step process; first,
the preparation of a mono-layer of the free base
porphyrin/phthalocyanine, and second, a phys-ical vapor deposition
of the respective metal atoms onto the sample,under certain
conditions followed by annealing.25 This experimentalapproach
opened up the field for the in-situ synthesis and examinationof
extremely thin films of metallotetrapyrroles that are not stable
un-der regular ambient conditions, like for instance iron(II)
tetraphenyl-porphyrin (FeTPP). The recent scientific interest in
the propertiesof monomolecular films of porphyrins and
phthalocyanines on solidsubstrates stems from the fact that
substantial interfacial modifica-tions can be achieved by the
adsorption of those molecules; a find-
2
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1 INTRODUCTION
Figure 1. 2H-Tetraphenylporphyrin (2HTPP) and 2H-Phthalocyanine
(2HPc).
ing that has been utilized for instance in heterogeneous
catalysis,26,27
molecular electronics,28,29 or gas sensors30. Moreover, it was
shownthat tetrapyrrole molecules form well ordered, flat lying
adsorbatestructures on Ag(111) and Au(111) surfaces. The resulting
well-defined, prototypical interfaces can be used for a further
examina-tion of substrate-adsorbate interactions. Following this
approach, itwas demonstrated that the interaction between Fe and Co
metallo-tetrapyrroles, and an Ag(111) surface can be described by
consider-ing the surface as a further, macroscopic ligand to the
central metalion.31–36 While the metal centers of the free
metallotetrapyrroles arefourfold coordinated, a fivefold
coordination is achieved in moleculesin direct contact to metal
substrates. It was further shown that anattachment of nitrogen
monoxide (NO) to the remaining sixth coordi-nation site of
cobalt(II) tetraphenylporphyrin (CoTPP) molecules onAg(111)
efficiently weakens the coordinative bond between the Co-ions and
the Ag(111) substrate;32 this finding has been interpretedin
analogy to the well known trans-effect in coordination chemistryas
surface-trans effect.37 The present study aims to further
elucidate
3
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1 INTRODUCTION
the coordinative interfacial interactions between
metallotetrapyrrolemonolayers and Ag(111) or Au(111)
substrates.
1.2 Chemical reactions at metal/organic interfaces
While the interfacial properties of tetrapyrrole/metal
interfaces aremainly determined by relatively weak coordinative and
van der Waalsinteractions, more severe chemical modifications of
adsorbate and/orsubstrate play a major role at the interfaces
discussed in the next sec-tions.
1.2.1 Covalent adsorbate structures on Ag(111)
The well ordered tetrapyrrole adsorbate structures on Ag(111)
andAu(111), discussed in the previous paragraph, arise from
relativelyweak intermolecular interactions; beyond van der Waals
interactions,there is no significant covalent coupling between the
adsorbed mole-cules. In a recent study, Grill and co-workers38 have
demonstratedthat the halogen-substituted porphyrin compound Br4TPP
can be uti-lized for the fabrication of well ordered, but
covalently interlinkedadsorbate structures. After a thermal
cleavage of the C−Br bonds,located at the para-positions of the
four phenyl substituents, the ad-sorbate molecules interlink with
each other via the formation of newC−C bonds between different
porphyrin units. The approach of de-positing halogen-substituted
molecular building blocks to fabricatecovalent 2D networks was
successfully applied with different combi-nations of adsorbates and
substrates.39–41 Recently, Schmitz et al.42
demonstrated the fabrication of chains of
poly(p-phenylene-terephthal-amide) (PPTA, trademark Kevlar) on an
Ag(111) interface, achievedby the co-adsorption of the precursor
molecules terephthaloylchloride(TPC) and p-phenylenediamine (PPD).
Figure 2 illustrates the corre-sponding reaction. The resulting
polymer chains were self-assembledinto well ordered clusters on the
Ag(111) interface. This underlinesthe influence of the
two-dimensional environment to the morpholog-ical structure of the
reaction products. However, it was not clearwhether the Ag(111)
substrate plays an active role in the formationof the PPTA chains.
In solution, the formation of PPTA proceeds via
4
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1 INTRODUCTION
a nucleophilic acyl substitution, resulting in a release of
HCl.42,43 Itis not clear if this holds true for the PPTA synthesis
on the Ag(111)interface as well. While Schmitz and co-workers so
far demonstrated
Figure 2. The reaction mechanism for the formation of
poly(p--phenylene-terephthalamide).
the successful formation of PPTA by means of scanning tunneling
mi-croscopy (STM),42 the present study will further investigate the
reac-tion mechanism and in particular the adsorption behaviour of
tereph-thaloylchloride. This is motivated by the fact that several
halogen-substituted molecules are known to adsorb dissociatively on
Ag(111).44,45
5
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1 INTRODUCTION
1.2.2 The polymer poly(3-hexylthiophene) as substrate for
metal-lic Ca layers
The formation of interfaces between polymer structures and
metalscan be achieved as outlined above, where the adsorbate is
subjectto a polymerization reaction, or alternatively in a reverse
approach,by using the organic polymer matrix as a substrate and
depositing ametal on top. An example is the interface between
metallic calciumand regioregular poly(3-hexylthiophene),
abbreviated rr-P3HT (Fig-ure 3); this combination is of great
interest since it comprises of aπ-conjugated, semiconducting
polymer and the low work-functionmetal calcium. Such
metal-semiconductor interfaces are of majorimportance in organic
electronics or optoelectronics, for example inorganic
light-emitting diodes,46 field-effect transistors,47,48 or
solarcells49. Recently, Zhu and co-workers51 investigated the
properties
Figure 3. Basic unit of the regioregular polymer
poly(3-hexylthiophene), rr-P3HT; modified reprint from Hugger and
co-workers.50 The lattice parameters a, b, and c are as follows: a
=0.168 nm, b = 0.766 nm, and c = 0.77 nm.
of this interface by vapor depositing calcium onto a ≈ 100 nm
thick
6
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1 INTRODUCTION
film of rr-P3HT. By employing a variety of surface science
techniquesit was possible to obtain a comprehensive picture of the
interface be-tween Ca metal and the rr-P3HT polymer. A close
inspection of theCa/P3HT interface revealed the presence of a
reaction layer wherethe sulphur atoms within the rr-P3HT matrix
react with diffused Caatoms. The thickness of this diffusion layer
was estimated to approx-imately 3 nm. An improved preparation
procedure, resulting in betterdefined interfaces between Ca and
rr-P3HT, i.e., interfaces with a sig-nificantly smaller reacted
layer, will be addressed in the present work.
1.2.3 Ionic liquids on solid substrates: The solid/liquid
interfacestudied with surface science techniques
A further type of metal/organic interface, which was not
discussed upto now, is formed between solids and liquids. Unlike
the solid/solid orsolid/vacuum interfaces discussed so far, the
properties of solid/liquidinterfaces are usually not accessible by
UHV surface science tech-niques; the low-pressure environment of
UHV experiments (p < 1×10−8 mbar) leads to an instantaneous
evaporation of liquid (organic)compounds. However, a special class
of liquid materials, suitable forUHV experiments, is known as ionic
liquids (ILs). An ionic liquid isan organic salt, which is in its
liquid state at temperatures below 100◦C. Figure 4 illustrates
typical cations and anions in ionic liquids.Those compounds have
usually vapor pressures below p < 1×10−10mbar, thus furnishing a
liquid media that can be stored and examinedunder UHV conditions.
Since ionic liquids are made from easy tosynthesize organic
compounds, there are potentially > 1×106 differ-ent ionic
liquids accessible.52–54 Thus it is feasible to design ionicliquids
with respect to given technological or scientific demands. Re-cent
applications of ionic liquids can be found in the field of
hetero-geneous catalysis, where their application gave rise to
novel conceptslike SILP55–57(Supported Ionic Liquid Phase) or
SCILL58 (Solid Cat-alyst with Ionic Liquid Layer). While in a SILP
approach the ionicliquid acts as a solvent for a catalytically
active compound, a SCILLcatalyst comprises of a solid heterogeneous
catalyst, covered with anionic liquid with particularly designed
properties. In both cases, theionic liquid may act as a
semipermeable membrane or solvent for
7
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1 INTRODUCTION
educts or products of the catalytic process.
Figure 4. The ionic liquid [EMIM][EtSO4]; the first ionic
liquidshave been synthesized already in 1914 by Walden.59
Since it was recently demonstrated that thin and ultra-clean
filmsof ionic liquids can be prepared by physical vapor deposition
(PVD),60
the examination of ionic liquid interfaces is possible with
conven-tional surface science techniques, as for instance
photoelectron spec-troscopy.60–63 This offers an experimental route
to examine electronicstructures and chemical processes at the
solid/liquid interface in typi-cal SCILL or SILP type
experiments.64 The present study will focuson the interfacial
interactions between the room temperature ionic liq-uid
1-butyl-3-methylimidazolium
bis(trifluoromethylsulfonyl)imide,[BMIM][Tf2N], and the model
catalyst surface Pd/Al2O3/NiAl(110).Briefly, this Pd-nanoparticle
based model catalyst has been exten-sively utilized to approximate
catalytic processes at a level of com-plexity still resolvable by
conventional surface science techniques.65–68
The active sites of this model catalyst, the Pd-nanoparticles,
consist ofapproximately 3000 atoms (600 surface atoms), and adopt a
cubocta-hedral shape where the major facets (top-facet and
side-facets) showa (111) orientation. A (100) orientation of a part
of the side facets canbe observed, nevertheless the majority of the
sites (≈ 80%) exhibit(111) orientation. Typically ≈ 20% of the
aluminium oxide substrateis covered with those particles.64–68
8
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2 EXPERIMENTAL METHODS
2 Experimental Methods
In this section we will briefly review the most fundamental
aspects ofthe experimental methods which have been utilized in this
thesis. Wewill concentrate in particular on those aspects that are
essential to theinterpretation of experimental results. The reader
who is interestedin further details is referred to the literature
listed at the end of thischapter.
2.1 Photoelectron Spectroscopy
Photoelectron spectroscopy measures the energy distribution of
elec-trons in a sample. Beyond qualitative information as, e.g.,
the exis-tence of valence states, it is possible to obtain
information on bandstructures in solids or oxidation states in
molecules. The method isbased on the photoelectric effect, i.e.,
the phenomenon that irradiationof a sample with photons of a
sufficient energy (typically hν > 5 eV)results in an emission of
electrons from the sample. The kinetic en-ergy of an individual
photoelectron is determined by the photon en-ergy hν and its
binding energy prior to ionization by the followingequation:a
Ekin = hν−Ebind
Hence, by measuring the distribution of the kinetic energy of an
en-semble of photoelectrons one can deduce the binding energy
distri-bution within the sample. Depending on the energy range of
the uti-lized photons it is common practice to distinguish between
UPS (UVPhotoelectron Spectroscopy) and XPS (X-ray Photoelectron
Spec-troscopy, or synonymous ESCA - Electron Spectroscopy for
Chemi-cal Analysis). Common photon energies employed for UPS are
21.22eV (HeI discharge) or 40.8 eV (HeII discharge), and for XPS
1253.6eV (Mg Kα line) or 1486.6 eV (Al Kα line).
aHere we define the binding energy as the amount of energy
necessary to remove anelectron completely from the sample. However,
in applications it is more practicable todefine the binding energy
relative to the Fermi edge of the corresponding solid.
Bothdefinitions differ by the work function φ , i.e., the energy
required to move an electronfrom the Fermi edge into the
vacuum.
9
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2 EXPERIMENTAL METHODS
Figure 5. Survey spectra of Au(111) acquired with (a)
X-ray(1486.6 eV) and (b) UV (21.2 eV) radiation. The intensity
axisshows typical intensities in XPS and UPS experiments; the
UPSspectrum of the Au 5d band clearly demonstrates the higher
reso-lution of UPS in a more narrow spectral range close to the
Fermiedge. Moreover, UPS resolves the Au(111) Shockley type
surfacestate.69 With UPS, the work function of the sample can be
de-termined as the difference between the photon energy (21.2
eV)and the spectral width (energy range of the gray shaded region
inframe b) of 15.8 eV); see text for details.
An example for a typical X-ray photoelectron spectrum is shownin
Figure 5 a). The core level spectrum is comprised of relativelyfew,
narrow lines, each representing a certain electronic state.
Theintensity of such a line is directly proportional to the
abundance ofthe corresponding binding energy level within the
sample, and thus
10
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2 EXPERIMENTAL METHODS
to the abundance of the corresponding atom. Each atomic
specieshas an individual characteristic photoelectron pattern, as
indicated inFigure 5 b) for the case of gold. We will come back to
the nomen-clature of the photoelectron lines in Chapter 2.1.2. In a
compoundmaterial, e.g., a metal alloy, the photoelectron spectrum
is the sum ofthe photoelectron patterns from each of the individual
components.The relative intensity of those different photoelectron
patterns, cor-rected for individual atomic sensitivity factors,
directly reflects thestoichiometric composition of the sample.
Aside from the possibilityto quantify the atomic composition of a
sample, changes in the chem-ical state of a given atom usually
shift the binding energy positions ofits photoelectron lines in the
range of several electron volts. Thus, themethod can be used not
only to identify and quantify different atoms,but also to
distinguish between atoms of the same element in differ-ent
chemical environments. As depicted in Figure 5 a), the discreteline
pattern is superimposed to a background signal, which
mainlyoriginates from inelastic interactions of photoelectrons
during passingthrough the sample material. These interactions lower
the kinetic en-ergy of the photoelectrons, therefore the respective
structures appearat higher binding energies. It is common practice
to subtract back-ground features by algorithms proposed by
Shirley70 or, more rarely,Tougaard.71 It is an essential feature of
photoelectron spectroscopythat only electrons from a relatively
thin surface layer of the samplecontribute significantly to the
signal. The flux of photoelectrons ex-cited inside the bulk
material of the sample is attenuated according toLambert-Beer’s law
by the surrounding sample material. Therefore,only photoelectrons
which were excited in the first few nanometersbelow the surface can
leave the sample and enter the spectrometer,rendering photoelectron
spectroscopy an extremely surface sensitivemethod. The inelastic
mean free path λ , i.e., the average distance thatan electron can
travel through a solid without suffering energy loss, isgenerally a
function of its kinetic energy. We will discuss this quantityin
more detail in a later chapter, but note that it has typically
valuesin the range of some 1×10−9 m. In contrast to XPS, UV
photoelec-tron spectroscopy cannot be used to acquire quantitative
informationon the chemical composition,72 since the direct
proportionality be-
11
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2 EXPERIMENTAL METHODS
tween the signal intensities and the abundance of the
correspondingelectronic level does not hold here; nevertheless,
qualitative informa-tion, e.g., on the existence of valence states
can be derived with UPSwith a higher energy resolution compared to
a common XPS setup.72
A UPS survey spectrum of a clean Au(111) surface is displayed
inFigure 5 b). We will discuss some selected facets of
photoelectronspectroscopy, in particular those in direct relation
to the results pre-sented in this work, in the following
sections.
2.1.1 The photoeffect and thermodynamic relations
This paragraph is dedicated to a justification of the simple
relationbetween the kinetic energy of photoelectrons, the energy of
the im-pinging photons, and the binding energy of the electrons
within thesample. The simple relation (1) between those quantities
is the funda-mental equation of photoelectron spectroscopy. Instead
of discussingthe quantum mechanical treatment of the photoeffect,
which can befound for instance in the textbook of Hüfner,72 we will
follow the his-torical development of the theory. Based on the
classical descriptionof the energy density of the radiation field
of a black body, we willfollow the argumentation of Einstein.73 By
employing fundamentalthermodynamic principles, we will find
evidence that the energy of anelectromagnetic radiation field
appears to be evenly distributed to anensemble of smallest,
discrete quanta, each of the size hν . Here, h isPlanck’s constant
and ν is the frequency of the radiation. By referringto such a
quantum of radiation energy as a photon, one can directlyidentify
the intensity of a radiation field with the number of photonsand
explain the experimental result that a higher intensity of the
ra-diation field does not, as classical electrodynamics demands,
lead toan increased kinetic energy, but to a higher number of
photoelectronswith a kinetic energy of:
Ekin = hν−Ebind (1)
The starting point of our calculation is Wien’s approximation
(equa-tion (2)), which gives the energy density of the radiation
field of ablack body in the limit of high frequencies.
ρ = α ν3 e−hνkT (2)
12
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2 EXPERIMENTAL METHODS
Or, after rearranging
1T
=− khν
ln( ρ
αν3)
(3)
The next step is the definition of an auxiliary function ϕ ,
related tothe entropy (according to Wien)73,74
S =V ·∫ ∞
0ϕ(ρ,ν) dν
which represents the entropy of the radiation field per
frequency andvolume. For black body radiation Einstein
deduces:73
∂ϕ∂ρ
=1T
A comparison with equation (3) results in a differential
equation:
∂ϕ∂ρ
=− khν
ln( ρ
αν3)
Here, simple integration b results in an analytical expression
for ϕ:
ϕ(ρ,ν) =−ρk
hν
[ln( ρ
αν3)−1]
Considering the entropy of quasi monochromatic radiation with a
fre-quency between ν and dν within a volume V , we find
dS(ν ,ν+dν) =V ϕ(ρ,ν) dν =−V ρk
hν
[ln( ρ
αν3)−1]
dν
Substituting the total energy of this radiation, dE = ρV dν , we
obtain:
dS(ν ,ν+dν) =−dEk
hν
[ln(
dEV αν3dν
)−1]
(4)
This is an expression for the entropy of the radiation of
energydE, contained in a volume V . In a final step, we discuss the
changeof the entropy associated with a variation of the volume.
Consideringan entropy of dS0 related to a volume V0 and calculating
the entropydifference, we obtain:
b∫ ln(x)dx = x ln(x)− x13
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2 EXPERIMENTAL METHODS
dS−dS0 = dEk
hνln(
VV0
)or dS−dS0 = k ln
(VV0
)dE/hν(5)
For the sake of clarity, we will follow the original work73 and
sim-plify the equations by writing simply S instead of dS(ν ,ν+dν)
of thequasi-monochromatic radiation. Analogue, we will express the
en-ergy of the quasi-monochromatic radiation with E instead of dE(ν
,ν+dν)Thereby, Equation (5) changes into:
S−S0 = k ln(
VV0
)E/hν(6)
Considering an ideal gas of N particles contained in a volume
V0,the statistical probability of a spontaneous assembly of all
particles ina sub-volume V is given by
P =(
VV0
)NThe change in entropy by such a process is:
S−S0 = k ln(
VV0
)N(7)
Equations (6) and (7) are identical if setting N = E/hν . The
en-tropy of a quasi-monochromatic radiation field with the energy E
de-pends on the volume in a similar fashion as the entropy of an
idealgas with the total energy E. This result is only valid as long
as thetotal energy of the radiation field is infinitesimal small
and the radi-ation frequency is large enough to guarantee the
validity of Equation(2). Thus, Equation (6) only holds true as long
as a high frequencyradiation field has a small total energy
density, like for instance X-rayradiation with a small total energy
contained in a large volume.
The finding that the entropy of the radiation field is well
describedif one assumes that its total energy is evenly distributed
to N = E/hνenergy quanta, led Einstein to his conclusion regarding
the photoef-fect. Equation (1) follows directly from this
assumption.
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2 EXPERIMENTAL METHODS
While those arguments help to rationalize the energy
quantifica-tion of a radiation field and Equation (1), they fail to
explain moreadvanced features of the photoeffect, such as the
quenching of cer-tain photoelectron lines by symmetry selection
rules during experi-ments with polarized photons. Those effects can
be understood onlyby applying the more advanced quantum mechanical
description ofthe interaction between radiation and matter. The
interested reader isreferred to the literature at the end of this
chapter.
2.1.2 Spin effects in XPS: Spin-orbit splitting and
multiplets
In this section, we will discuss effects that lead to the
generation ofmultiple lines in XPS core level spectra, due to the
presence of spins,or generally angular momenta.
As a first effect, we will consider the spin-orbit splitting
which ispresent in the photoelectron lines from non-s orbitals.
This effect isresponsible for the splitting of the atomic p, d, and
f states into dou-blets and is clearly visible in the XPS spectrum
in Figure 5 b). Thisphenomenon arises because the angular momentum
of the electron,orbiting the atomic nucleus, couples with the
electron spin. Depend-ing on the relative orientation of both
magnetic moments, parallel oranti-parallel, the signal appears at a
reduced or higher binding energy.This explains, for instance, the
splitting of the Au 4d level (l = 2)into 4d3/2 and 4d5/2
sub-levels, as shown in Figure 5. The total angu-lar momentum j of
each doublet state, as indicated by the subscripts3/2 or 5/2,
simply results from the corresponding angular momen-tum l and the
electron spin s = 1/2 according to j = l − 1/2 andj = l + 1/2.75
The magnitude of the corresponding doublet splittingon the binding
energy scale is proportional to 1/〈r3〉, where 〈r〉 repre-sents the
average radius of the corresponding orbital.75 Thus, orbitalswith
different spatial dimensions will show a different spin-orbit
split-ting. As Figure 5 a) illustrates for the case of gold atoms,
the spin-orbit separation is largest for p electrons and smallest
for f electrons.This reflects the fact that 〈r〉p electrons <
〈r〉d electrons < 〈r〉 f electrons.The intensity ratio between the
individual doublet states is given bytheir degeneracy. Accordingly,
the 2p1/2 and 2p3/2 sub-levels willshow an intensity ratio of 2 :
4, since the 2p1/2 level is twofold de-
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2 EXPERIMENTAL METHODS
generated, while the 2p3/2 is of fourfold degeneracy.75
Generally, both peaks of a doublet, may it emerge from a p, d,
orf state, differ only in their relative intensity, but are of
virtually iden-tical shape. Exceptions from this general behaviour
can be observedin particular in the core level spectra of
transition metals.76 There,a broadening of the 2p1/2 state relative
to the 2p3/2 state is evident.Since the natural line width of a
photoelectron signal is determinedby the lifetime of the respective
core-hole,72 it follows that the life-time of the 2p1/2 core hole
has to be smaller than the lifetime of thecorresponding 2p3/2
state. This finding can be explained by the factthat the 2p1/2 core
hole has an additional decay channel, i.e., the de-cay via a
L2L3M4,5 Coster-Kronig Auger electron process, resultingin a higher
decay probability and accordingly a shorter lifetime.77,78
During this process, an electron originating from the 2p3/2
level fillsup the 2p1/2 core hole; the energy difference between
those two statesis released via an Auger-Electron. The resulting
broadening of transi-tion metal 2p1/2 states compared to the
corresponding 2p3/2 lines iswell described in the
literature.77,78
A further effect that complicates in particular the analysis of
tran-sition metal core level spectra is the appearance of multiplet
effectsdue to the presence of further, unpaired spins, for instance
in the d-subshell of transition metal complexes.79,80 The coupling
betweenunpaired electrons in the d-shell with the photoion
core-hole givesrise to several energetically different final
states. This phenomenoncan be observed in all core-levels,
including s orbitals.79 The detailedmechanism of this coupling, and
subsequently the resulting peak pat-tern has been subject to
several theoretical approaches. In the follow-ing section we will
briefly review this topic, since it is essential forthe
interpretation of the photoelectron spectra acquired from
metal-lotetrapyrrole samples.
Multiplet effects were detected in the s orbitals of
paramagneticmolecules, such as O2 or NO,81 as well as in transition
metal com-pounds79,82,83. This phenomenon has been interpreted as a
final stateeffect. Since the process of photoionization obeys
energy conserva-tion, the different results of the coupling
process, i.e., the differentmagnetic states of the photoion, are
reflected by different correspond-
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2 EXPERIMENTAL METHODS
ing kinetic energies of the detected photoelectron. The
magnitude ofthis splitting is enhanced by correlation effects if
the s-core hole andthe unpaired electrons belong to the same atomic
shell, as for instancein the case of a 3s core-hole in a 3d
transition metal complex.84 Theinterpretation of a corresponding
multiplet splitting in p or d levelsproved to be more complex; in a
first approximation one could de-scribe the resulting lines as the
result of a core-spin + core-orbit + d-spin + d-orbit coupling. In
particular Gupta and Sen85,86 developeda theory that additionally
takes an influence of excited states of thed -electrons into
account, resulting in a relatively complex multipletpattern in the
2p levels of 3d transition metal complexes. Neverthe-less, their
results were applied successfully in several studies.80,87–89
Alternatively to the Hartree-Fock calculations of Gupta and Sen,
arelatively simple angular momentum coupling scheme was
success-fully applied, in particular to cobalt high-spin (S=3/2)
and cobalt low-spin (S=1/2) compounds.15,16,90–92 This coupling
scheme is based ontheoretical considerations of Nefedov.93
Essentially, it neglects anyangular momentum of the d-electrons,94
while coupling the 2p1/2and 2p3/2 core hole states exclusively with
the resulting spin of thed-electrons. To give a short example, an S
= 1 spin state of the d-subshell will result in J = 5/2 ,3/2 , and
1/2 states, originating fromthe 2p3/2 state in the photoion, and a
doublet of J = 3/2 ,1/2 states,arising from the 2p1/2
core-hole.15,92
Since the state of the d-electrons strongly affects the 2p
spectra,the spin-orbit separation – usually considered as the
constant distancebetween the maxima of the 2p3/2 and 2p1/2 peaks –
is not well de-fined any more; there is a variety of different
multiplet states thatemerge from the 2p3/2 and 2p1/2 levels and it
is not unambiguouslyclear which to take to measure the spin-orbit
splitting. However, it iscommon practice to measure the distance
between the most intenselines within each multiplet to define the
spin-orbit separation. Theinfluence of the d-electrons to the
spin-orbit separation was closelyexamined for instance for various
cobalt compounds. Co(II) high-spin compounds generally show an
apparent spin-orbit separation of≈ 16 eV, while diamagnetic Co(0)
or Co(III) complexes show a valueof only≈ 15 eV.15,90,91 For a
cobalt atom in a Co(II) (S=1/2) low-spin
17
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2 EXPERIMENTAL METHODS
state, usually a spin-orbit separation of ≈ 15.5 eV is
found.92Further specific properties of the core level spectra of
paramag-
netic transition metal compounds have to be mentioned at this
point.It is an established experimental fact that the spin state -
at least ofcobalt compounds - has a direct influence on the
intensity of satellitelines in the corresponding 2p
region.15,16,90–92 While Co (II) (S=3/2)compounds show an intense
satellite structure, no satellites are ob-served in the spectra of
diamagnetic Co(0) or Co(III).15,90–92 Co(II)(S=1/2) low-spin
compounds, such as cobalt(II) phthalocyanine, whichis discussed in
more detail in the experimental part, show an interme-diate
behavior by exhibiting an appreciable, but not dominant
satellitestructure.16,92 In conclusion, it can be inferred that
each configurationof the d-electrons of cobalt compounds has a
distinct spectral finger-print in the core levels.
2.1.3 Quantitative XPS
As mentioned in the preceding chapter, XP spectra contain
informa-tion originating nearly exclusively from a thin surface
layer with athickness of several nanometers. In the following
section we willelaborate this statement in more detail. The flux of
electrons trav-elling through a solid is exponentially attenuated
according the lawof Lambert-Beer; the longer the travelled distance
x, the lower theresidual electron flux I(x).
I(x) = I0 exp(− x
λ
)Therefore, only electrons that have travelled a relatively
short distancethrough the sample material, until they have reached
and left the sur-face, contribute significantly to photoelectron
signals. The quantityλ is commonly referred to as attenuation
length or electron inelasticmean free path, and is in general a
function of the kinetic energy of theelectrons. It gives the
distance after which an initial electron flux isreduced by a factor
of 1/e≈ 0.37. The other electrons lost kinetic en-ergy or were
absorbed during their passage through the sample. Theseelectrons
contribute significantly to the background signal of photo-electron
spectra. In this study, we use an empirical expression for the
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2 EXPERIMENTAL METHODS
dependency of λ on the kinetic energy E according to λ = 0.3 E
0.64;this expression is only valid for the typical kinetic energies
of photo-electrons as observed in XPS measurements.95 It appears
noteworthythat the mean free path of electrons that pass through a
solid, showsonly a minor dependency to the particular composition
of the solidmaterial. A plot of the mean free path as a function of
the kineticenergy of the electrons is often referred to as
universal curve, sinceit is remarkably independent from any
material properties.96,97 Thesmallest mean free path, i.e., the
highest interaction probability of theelectrons with the
surrounding material occurs at an energy of ≈ 50eV. At higher
energies, the mean free path increases with increasingenergy. The
relation for λ - as given above - is thus only an approxi-mation to
the universal curve in the region of kinetic energies typicalfor
XPS measurements. The depth from which 95% of the
detectedphotoelectrons of a given photoelectron peak emerge is
commonlyreferred to as information depth. It equals approximately 3
times theattenuation length.
If photoelectrons, excited at a depth d inside the bulk
material,travel towards the surface under an angle ϑ 6= 0, i.e.,
not on a tra-jectory parallel to the surface normal, their route
through the samplewill be of the length d/cos(ϑ), resulting in a
stronger attenuationof the signal. The following equation describes
the influence of thedetection angle ϑ to Lambert-Beer’s law.
I(d) = I0 exp(− d
λ cosϑ
)This result allows to vary the effective information depth
simply byrotating the sample relative to the spectrometer, and thus
detectingonly photoelectrons that travelled through the sample
under an angleϑ ≥ 0. Accordingly, the depth λ after which the
initial flux is reducedto a fraction of 1/e ≈ 0.37 decreases to a
value of λ cosϑ , resultingin a higher surface sensitivity of the
method. Rotating a sample dur-ing XPS measurements furthermore
furnishes a method to distinguishsurfaces that are built up from
subsequent layers of different chemi-cal compounds from surfaces
that consist of a random mixture (as e.g.alloys). The latter case
shows no variation of the relative intensitiesof the different
elements with the detection angle.
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2 EXPERIMENTAL METHODS
Assuming a layer by layer growth, the intensity of
photoelectronsoriginating from an overlayer of a thickness d, e.g.,
organic moleculeson a metal substrate, can be calculated according
to
Iad(d) = Iad∞
(1 − exp
(− d
λad cosϑ
))In a real experiment the quantity Iad would correspond for
instanceto the intensity of the C 1s line, or any other intense
photoelectronline originating exclusively from the adsorbate. In
this equation, Iad∞represents the intensity measured if the layer
thickness is allowed toincrease to infinity, thus the highest
possible count rate. Consideringthe attenuation of a substrate peak
(e.g., the Au4f5/2 line with pris-tine intensity Isub∞ ) due to the
presence of an adsorbate layer of thethickness d, one finds
Isub(d) = Isub∞ exp
(− d
λad cosϑ
)Accordingly, the thickness of an adsorbate layer can be
calculatedfrom the ratio of the measured intensities of the
substrate and adsor-bate,98 Iad(d)/I
sub(d) , by solving the transcendental equation
Iad(d)Isub(d)
=Iad∞Isub∞
(1 − exp
(− dλad cosϑ
))exp(− dλsub cosϑ
) ≈ σadσ sub
(1 − exp
(− dλad cosϑ
))exp(− dλsub cosϑ
)The factors σad and σ sub represent the photoionization
sensitivityfactors of the photoelectron lines of adsorbate and
substrate, respec-tively. Numerical values for different elements
are tabulated in theliterature.99,100 A correct application of the
latter equation requiresthat the spectrometer is operated at
identical settings during the ac-quisition of the substrate and
adsorbate spectra.
We have seen in the preceding paragraph, how the intensity of
aspectral line can be used to quantify the interfacial composition
ofa sample, as for instance by calculating the thickness of an
adsor-bate layer. In many cases the required extraction of a line
intensity iscomplicated by an overlap of several different peaks.
In such a situa-tion, only a numerical deconvolution of the signal
by a least-squares
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2 EXPERIMENTAL METHODS
fit allows further interpretations. While, in a first-order
approxima-tion, each photoelectron peak can be modeled as a
Gaussian curve,accurate results require the application of peak
functions with certainspecific properties. The next chapter is
dedicated to this issue.
2.1.4 Approximating a Voigt profile
We have seen in the previous chapter that the intensity of a
photo-electron line can be used to quantify the amount of the
correspond-ing element on a sample. A reliable measure for the
intensity is thearea below a photoelectron line. The measurement of
this quantity iscommonly achieved by a least-squares fit with a
suitable peak profile.Such profiles are for instance Doniach-Sunjic
curves72,101 or, in par-ticular in this work, Voigt
profiles.102–104 A Voigt profile is the resultof the convolution of
a Lorentzian profile with a Gaussian curve. InXPS, the Lorentzian
curve represents the actual energy distributionof photoelectrons,
originating from a distinct atomic level, as theyleave the sample.
The spectral width of this line is inversely propor-tional to the
lifetime of the corresponding core-hole in the photoion,a result
that follows from the quantum mechanical uncertainty prin-ciple
between time and energy.77,78,102 The subsequent imaging ofthe
photoelectrons by the spectrometer results in a distinct
perturba-tion of the initial shape of the spectral line. This
perturbation canbe described by a convolution with a Gaussian
curve. In numericalapplications, however, it is an established
procedure to approximatethe real convolution with a numerically
less costly algorithm. Ac-cordingly, it is a widespread practice to
approximate the convolutionbetween Gaussian and Lorentzian profiles
by the calculation of a sumof Gaussian and Lorentzian curves
according to equation (8); m repre-sents a weighting factor with
possible values between 0 and 1. Such aweighted sum is commonly
referred to as Pseudo-Voigt curve.105,106
Gauss⊗Lorentz ≈ (1−m)Gauss+mLorentz (8)
Although the shape of Gaussian and Lorentzian curves can be
con-sidered as common knowledge, some modifications, which are
oftenapplied in the context of photoelectron spectroscopy, have to
be men-tioned. In an XPS least-squares fit procedure it is
favorable to have the
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2 EXPERIMENTAL METHODS
peak area A as a direct coefficient, rather than the amplitude
h. Thiscan be achieved due to the finite area of Gauss as well as
Lorentzcurves. In the following sections we will write x instead of
E−E0 forthe sake of simplicity; E represents the binding energy
scale of XPSspectra, and E0 the binding energy of a distinct peak.
The areas of theGauss and Lorentz curves are given by
Ag =∞∫−∞
Gauss =∞∫−∞
hg e−a2x2 dx = hg
√π
a
Al =∞∫−∞
Lorentz =∞∫−∞
hl1
b2 + x2dx = hl
1b
arctan( x
b
)∣∣∣∣∞−∞
= hlπb
or in terms of the full width at half maximum (FWHM) ωg =√
4ln2/aand ωl = b/2
Ag = hg ωg
√π
4ln2
Al = 2hlπωl
This analysis allows to substitute hg and hl as functions of
area andFWHM.
hg =
√4ln2
πAg/ωg ⇒ Gauss =
√4ln2
πAgωg
e−4ln2(x
ωg )2
hl =1
2π(Al ωl) ⇒ Lorentz =
Al2π
ωl(ωl/2)2 + x2
=2Alπ
ωlω2l +4x2
2.1.5 Introducing asymmetry
General considerations The signal background of core level
spec-tra is, as mentioned above, the result of energy-loss
processes of pho-toelectrons. Thus, those electrons have a lower
kinetic energy andappear accordingly at a higher binding energy.
The situation can becomplicated if the background shows an
irregular shape due to com-plex energy loss mechanisms, and in
particular if those loss-structures
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2 EXPERIMENTAL METHODS
overlap with the main peak. Such a situation is frequently
observedin the presence of plasmon excitations, i.e., collective
oscillations ofthe sample electrons.107 Further discrete loss
structures are shake upand shake off satellites, where another
electron of the photoion is ex-cited to an initially unoccupied
state (shake up), or is even removedfrom the photoion (shake off -
leads to a twofold ionization). Furtherloss structures, typical for
organic molecules are vibrational excita-tions of the photoion.
There, according to the Frank-Condon princi-ple, the exciting
photon transfers energy not only to the photoelec-tron, but also to
a molecular vibration.102,108,109 A situation which isfrequently
found, specifically in spectra from metallic samples, is adistorted
peak shape due to a screening of the photoion core-hole
byconduction electrons, and the creation of an electron-hole pair.
Thisloss mechanism usually creates a distinct, asymmetric tail in
the rangefrom 0 to 5 eV above the main line.104 A possible way to
introducesuch an asymmetry in Pseudo-Voigt functions105 is the
redefinition ofthe FWHM ω according to ωg = ωl = ω(x). If this
method is chosen,one has to be aware of several consequences:
(i) FWHM related parameters that enter the fit represent not
nec-essarily the actual FWHM of the resulting curve.
(ii) The simple relation between peak area and amplitude, as
de-duced in the previous chapter, is no longer valid; the
area-parameterthat enters the fit is not the real area of the
peak.
(iii) Depending on the detailed function ω(x), it is possible
thatthe resulting curve has no finite area; in this case a suitable
cut-offcriterion for integration has to be chosen.
It follows from the first two points that the actual width and
area ofthe resulting peak have to be measured on the resulting
curve; in gen-eral, there is no simple, analytical relation between
the correspondingfit parameters and the actual values. Furthermore,
it is favourable ifthe function ω(x) would result in a Pseudo-Voigt
curve with a finiteand well defined area. In that case no arbitrary
cutoff criterion hasto be chosen. Recently Stancik and
co-workers110 suggested a sig-moidal variation of ω(x), according
to the equation
ω(x) =2ω0
1+ exp(−ax)(9)
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2 EXPERIMENTAL METHODS
Figure 6. Several asymmetric Pseudo-Voigt functions; the
param-eter a controls the degree of asymmetry.
In this equation, ω0 represents the FWHM of the corresponding
sym-metric Pseudo-Voigt peak, while the parameter a determines the
de-gree of asymmetry. In the case of a = 0, the resulting curve is
simplya symmetric Pseudo-Voigt profile with a FWHM of ω0. Figure 6
il-lustrates the resulting curves for several choices of a. The
asymmetryparameter a is constrained to positive values only.
Although this func-tion was proposed in the context of vibrational
spectroscopy, we willsee in the following chapters that, after a
modification, it furnishes apeak profile usable for XP spectra as
well.
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2 EXPERIMENTAL METHODS
Unique profile areas A significant drawback to several
asymmet-ric peak shapes, as for instance, Doniach-Sunjic
profiles,101,104 is thefact that the area below the curve is not
well defined. In contrast to thesymmetric Gauss and Lorentz
functions, where an integration from−∞ to ∞ results in an unique
and well defined area, a similar integra-tion of asymmetric
profiles yields possibly an infinite area.72 There,to obtain a
finite area, one has to decide for an arbitrary integrationrange.
Hence it is difficult, if not impossible in most cases, to
comparedifferent peak areas in an unambiguous way, since it is not
possibleto decide for an unique, physically justified integration
range. Theasymmetric Pseudo-Voigt function, as defined above, does
not sharethis disadvantage. Similar to the symmetric Gauss and
Lorentz func-tions, it has a unique profile area. We will prove
this statement in thefollowing section. To do so, we will prove the
convergence of the in-tegral of the Gauss and Lorentz contributions
in the peak separately.The sum of two profiles, each with a
convergent integral, is again aprofile with a convergent
integral.
Since it is difficult to obtain an antiderivative of asymmetric
Pseudo-Voigt profiles and deduce the integral directly, we will
utilize the fol-lowing
Theorem 1 The integral of a curve f (x) ≥ 0 on a given interval
isfinite, if one can find a different curve G(x), with G(x) ≥ f (x)
and∫
G(x)dx = finite. We will refer to such a curve as a majorant.
Ifwe can show the existence of a majorant in a given interval, we
haveshown the finiteness of the integral over f (x) over that
interval.
We are now in a position to prove the important finiteness of
the inte-gral.
Lorentz Let f (x) be an asymmetric Lorentzian curve, where
theasymmetry is specified by the parameters ω0 and a according to
Equa-tion (9). The relation f (x) ≥ 0 is true for all possible x.
To ob-tain a majorant for the Lorentz curve, we will choose a
symmetricLorentzian curve with a width of 4ω0. This choice is
indicated inFigure 7. We will now deduce the intervals where f (x)
< G(x), i.e.,the coordinates of the intersection points between
f (x) and G(x). On
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2 EXPERIMENTAL METHODS
this interval the relation∫
f (x)dx ≤∫
G(x)dx holds true; since it isknown that the integral over G(x)
is finite there, one can concludethen that the integral over f (x)
is finite on that interval as well. Towork out the intersection
points we set:
Figure 7. Determination of the intersection points between
theasymmetric Lorentz profile, f (x) and its majorant curve G(x).
Thedashed regions in frame b) illustrate the codomain of the
intersec-tion points xs0 and xs1, as deduced from the intersection
betweenthe parabola and sigmoidal curves for a = 0 and a→ ∞.
ω(x)ω2(x)+4x
2 =4ω0
16ω20 +4x2
or
x2 = ω0 ω(x) =2ω20
1+ exp(−ax)= H(x)
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2 EXPERIMENTAL METHODS
The solution of the latter transcendent equation is given
graph-ically in Figure 7. From the basic shape of the sigmoidal
functionand the parabola it is evident that there are two and only
two inter-section points, xs0 and xs1. For all x < xs0 and x
> xs1 the relationx2 > 2ω20/(1+ exp(−ax)) is true. Thus, f
(x) < G(x) is true in theintervals [−∞ : xs0] and [xs1 : ∞] and
the integral of f (x) is finite there.
Since f (x) has no singularities in the interval [xs0 : xs1],
the inte-gral of f (x) is finite in the range form [−∞ : ∞].
The latter argument would not hold, if the intersection points
xs0and xs1 could, for a certain choice of the asymmetry parameter
a,diverge to ±∞. Fortunately, this case can be excluded by the
elemen-tary properties of the sigmoidal function and the parabola;
the dashedregions in Figure 7 b) illustrate the codomain of xs0 and
xs1 for anychoice of a from the interval [0 : ∞]. In fact, both
intersection pointsare restricted to finite values.
Gauss We will proceed with the proof of the convergence of
theGaussian part of the asymmetric Pseudo-Voigt in a similar way.
Letf (x) be a Gaussian curve, where the asymmetry is specified by
theparameters ω0 and a according to equation (9). The relation of f
(x)≥0 is true for all possible x. Accordingly we choose as majorant
asymmetric Gauss curve with the width of 4ω0. This configuration
isillustrated for ω0 = 1 in Figure 8 a). As above, we have to work
outthe intervals where G(x) is larger than f (x). The intersection
pointsof both curves are given by:
1ω(x)
exp
(− x
2
ω2(x)
)=
14ω0
exp(− x
2
16ω20
)
or
x2 =(2ω0)2 ln(2 + 2exp(−ax))
3/4+2exp(−ax)+ exp(−2ax)= H(x)
Since the function H(x) is not as elementary as the
correspondingsigmoidal function in the preceding chapter, we will
briefly discuss
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2 EXPERIMENTAL METHODS
Figure 8. Determination of the intersection points between
theasymmetric Gauss profile, f (x) and its majorant curve G(x).
Thedashed area indicates the codomain of the intersection points
asdeduced from the intersection of the parabola x2 with the
auxiliaryfunction H(x) for a = 0 and a→ ∞.
its properties. Figure 9 illustrates the appearance of H(x) for
variousasymmetry parameters. It is evident that H(x) closely
resembles asigmoidal function.
28
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2 EXPERIMENTAL METHODS
The following properties can be derived from the equation:
limx→−∞
H(x) = 0
limx→ ∞
H(x) = (16/3) ω20 ln(2)
lima→ 0
H(x) = (32/15) ω20 ln(2)
H(0) = (32/15) ω20 ln(2)
Figure 9. The dependency of H(x) to various asymmetry
param-eters a. The function can be described as a modified
sigmoidal.
After these preparations, we can proceed in discussing the
inter-section points and the intervals in a similar way as in the
latter para-graph. Figure 8 b) illustrates the solution of the
transcendental equa-tion. The intersection points between the
asymmetric Gauss f (x) andits majorant G(x) can be deduced as the
intersection points betweenthe parabola x2 and H(x). Thus, for the
intervals [−∞ : xs0] and [xs1 :∞] the relation f (x)< G(x) is
true, and so is
∫f (x)dx <
∫G(x)dx.
Since the integral of f (x) is finite in the interval [xs0 :
xs1] as well,the integral of f (x) is finite in the range form [−∞
: ∞]. As in thepreceding chapter, the finiteness of the
intersection points ensures ageneral validity of the given
arguments.
29
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2 EXPERIMENTAL METHODS
Conclusion Since we have shown that the integrals of the
Lorentzianas well as Gaussian parts of the asymmetric Pseudo-Voigt
functionconverge, we can conclude that the integral of the
Pseudo-Voigt func-tion on the interval [−∞ : ∞] is well defined,
just as in the case ofsymmetric Gaussian and Lorentzian curves.
Although its value can-not be given as an analytical function, a
numerical integration over alarge enough interval will approximate
the area from −∞ to ∞ suffi-ciently.
Application to XPS In the following section, we will see that
thereproduction of real asymmetric photoelectron spectra requires
thatthe sigmoidal FWHM function ω(x) is allowed to shift relatively
tothe peak position E0; a further degree of freedom that leads to a
fur-ther parameter b.
ω(x) =2ω0
1+ exp(−a(x−b))(10)
Before proceeding with the applications of Equation (10), we
willbriefly exemplify the convergence behaviour of the Gaussian
part ofthe resulting Pseudo-Voigt profile. However, we omit a
convergenceproof of the Lorentzian part since it can be done in an
identical way.We will constrain the discussion to values of the
asymmetry parame-ter a > 0. In the case of a = 0, the shift
parameter b has no influenceon the curve whatsoever.
As shown in the preceding sections, the intersection points
be-tween an asymmetric Gaussian curve and its majorant can be
deducedgraphically by intersecting the parabola x2 with an
auxiliary functionH(x). Applying Equation (10) in the definition of
a Gaussian curve,one obtains:
1ω(x)
exp
(− x
2
ω2(x)
)=
14ω0
exp(− x
2
16ω20
)
⇒ x2 = (2ω0)2 ln(2 + 2exp(−a(x−b)))
3/4+2exp(−a(x−b))+ exp(−2a(x−b))
30
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2 EXPERIMENTAL METHODS
The graphical solution for this equation is illustrated in
Figure 10for several choices of b. For decreasing values of b from
0 to −∞,the intersection point xs1 approaches its maximum position
xmaxs1 =√(16/3) ln(2) ω0. Similarly, the intersection point xs0
approaches its
minimum value of xmins1 = −√(16/3) ln(2)ω0. Thus, for all values
of
b ∈ [−∞ : 0] the intersection points between the asymmetric
Gaussianand its majorant curve are limited to the interval [−
√(16/3) ln(2)ω0 :√
(16/3) ln(2) ω0]. Outside this interval, the majorant curve is
al-ways larger than the asymmetric Gauss curve. This proves that
forany choice of b ∈ [−∞ : 0], the asymmetric Gaussian curve has a
fi-nite and unique area.
Figure 10. Intersection points of the parabola x2 and the
auxiliaryfunction H(x) – illustrated for various values of b –
accordingto Equation (11). These intersection points are identical
to theintersection points between an asymmetric Gauss profile and
itsmajorant curve. The dashed regions mark the codomain of
bothintersection points xs0 and xs1.
We will now consider a choice of b from the interval [0 : ∞]
andshow the convergence of the area of the asymmetric Gaussian for
thiscase. For a shift of b towards infinity, both intersection
points xs0 andxs1 converge towards x = 0.
Thus, for any choice of b∈ [0 : ∞], the resulting intersection
points
31
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2 EXPERIMENTAL METHODS
will be constrained to the interval [xs0 : xs1]; outside this
interval themajorant is always larger than the asymmetric Gauss
curve, irrespec-tive of the choice of b. This proves the
convergence of the asymmetricGaussian curve for all b ∈ [0 : ∞].
Note that for the limit of b→∞ theasymmetric Gaussian curve
approaches the shape of a δ -function.
In summary, we have shown that for any choice of b from [−∞ :
0]and [0 : ∞], and hence for any choice of b from [−∞ : ∞], the
profilearea remains finite.
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2 EXPERIMENTAL METHODS
Examples In this paragraph we will discuss in particular
spectraacquired with synchrotron radiation. Although the present
work doesnot cover synchrotron based measurements, it is important
to com-ment on the general validity of the asymmetric Pseudo-Voigt
func-tion, introduced in the latter section. Accordingly, we will
use XPSspectra acquired with synchrotron radiation as a benchmark.
Prior topeak fitting, a Shirley type background70 has been
subtracted from allspectra presented in this section.
Figure 11 shows a least-squares fit to a spectrum of elemental
sul-phur on Pd(100), acquired by synchrotron radiationc. The fit
residual(calculated as difference between the raw data and the fit
result) showsin the range of the peak maximum an oscillating
behaviour. This nu-merical phenomenon is characteristic for
least-squares fits that usePseudo-Voigt instead of Voigt
curves.105,106
Figure 11. Least-squares fit of the S 2p region of sulphur;
theparameters of the peaks 1 - 4 are given in Table 1.
The numerical results of this fit are given in Table 1. The
values ofthe peak area, FWHM, and position exemplify the previous
statementthat, if asymmetry is present in a photoelectron line, the
mere fit co-
cCourtesy of Dipl.-Phys. Michael Lorenz and M.Sc. Karin
Gotterbarm
33
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2 EXPERIMENTAL METHODS
efficients do not reflect the corresponding physical values any
more.However, those values can be extracted numerically from the
result-ing curves. In Table 1, those quantities are indicated as
measured.
Peak
1 2 3 4Area (Parameter) 782300 392300 18640 9504Area (Measured)
932600 467600 12200 11200Position (Parameter) 161.97 163.17 163.80
164.95Position (Measured) 161.93 163.12 163.75 164.90FWHM
(Parameter) 2.51 2.51 2.51 2.51FWHM (Measured) 0.70 0.70 0.70 0.70m
(Gauss-Lorentz ratio - parameter) 0.68 0.68 0.68 0.68a (Asymmetry -
parameter) 0.92 0.92 0.88 0.88b (Asymmetry shift - parameter) 2.1
2.1 2.1 2.1
Asymmetry: 1− FWHMrightFWHMleft 0.28 0.28 0.28 0.28
Table 1. Numerical parameters of the least-squares fit of the S
2pregion of elemental sulphur on Pd(100).
The signals at 161.92 and 163.13 eV (peak 1 and 2), and the
peaksat 163.8 and 164.95 eV (peak 3 and 4) comprise each a sulphur
2pdoublet. Accordingly, the intensity ratio between peak 1 and peak
2,as well as peak 3 and peak 4, should be 2 : 1, as given by the
degen-eracies of the 2p3/2 and 2p1/2 states. The intensity ratio
between peak1 and 2 is found to be 1.9985 : 1 and the corresponding
ratio betweenpeaks 3 and 4 is 1.9887 : 1. The strong deviation of
the FWHM coef-ficient from the actual FWHM of the peaks underlines
once more thatone should be aware of numerical effects while
interpreting the fittingresults of XPS data.
34
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2 EXPERIMENTAL METHODS
As a further example, we will consider a fit to the C 1s
spec-tra of C2H2/Pd(100)d (Figure 12). This spectrum was chosen,
sinceit comprises a relatively simple sub-structure and shows
clearly thecharacteristic of an isolated peak. In comparison to the
example ofthe last paragraph, the C 1s level appears to be
reconstructed in aslightly higher quality than the S 2p spectrum.
The oscillation of thefit residuum is significantly smaller than in
the previous spectrum.Peaks 2 and 3 presumably represent
vibrational excitations of the ad-sorbed C2H2 molecules, while the
signal at 286.49 eV possibly orig-inates from traces of carbon
monoxide.109
Figure 12. Least-squares fit of the C 1s region of the
systemC2H2/Pd(100) ; the parameters of the peaks 1 - 4 are given
inTable 2.
d Courtesy of M.Sc. Oliver Höfert
35
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2 EXPERIMENTAL METHODS
Peak
1 2 3 4Area (Parameter) 1847000 234400 17580 40590Area
(Measured) 2145000 272200 20420 47130Position (Parameter) 283.78
284.19 284.97 286.55Position (Measured) 283.75 284.15 284.93
286.49FWHM (Parameter) 1.52 1.52 1.52 1.52FWHM (Measured) 0.54 0.54
0.54 0.54m (Gauss-Lorentz ratio - parameter) 0.76 0.76 0.76 0.76a
(Asymmetry - parameter) 1.79 1.79 1.79 1.79b (Asymmetry shift -
parameter) 0.9 0.9 0.9 0.9
Asymmetry: 1− FWHMrightFWHMleft 0.33 0.33 0.33 0.33
Table 2. Numerical parameters of the least-squares fit of the C
1sregion of the C2H2/Pd(100) system.
As a final example, we will demonstrate a least-squares fit to
thePd 3d region, acquired from a sample covered with Pd
nanoparticles[P7]. In contrast to the latter examples, this
spectrum was recordedwith a regular, monochromatized AlKα X-ray
source. The raw data(Figure 13) were modeled with three peaks; two
representing the3d5/2− 3d3/2 doublet, while the third can be
attributed to plasmonexcitations.111 As above, we can use the
reproduction of the nomi-nal intensity ratio of the doublet as a
benchmark for the quality ofthe fit. The procedure resulted in an
intensity ratio between the 3d5/2and 3d3/2 components of 1.504 : 1,
in close agreement to the nomi-nal ratio of 1.5 : 1. The fit
results, listed in Table 3, underline againthat if asymmetry is
applied in a fitting procedure, the fit coefficientsdo not
represent the corresponding physical quantities any more, butmerely
describe the shape of the curve. The oscillating behaviour ofthe
fit-residual is comparable to the S 2p fit above. The
relativelyhigh value of the parameter b, representing a strong
shift of the corre-sponding sigmoidal function, exemplifies the
necessity of this degreeof freedom for a satisfying fit result.
36
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2 EXPERIMENTAL METHODS
Figure 13. Pd 3d signal, recorded with a standard lab source;
thenumerical results are given in Table 3.
Peak
1 2 3Area (Parameter) 23680 15740 229Area (Measured) 29480 19600
229Position (Parameter) 334.31 339.60 345.79Position (Measured)
334.20 339.49 345.80FWHM (Parameter) 5.88 5.88 1.02FWHM (Measured)
1.54 1.54 1.04m (Gauss-Lorentz ratio - parameter) 0.15 0.15 0.15a
(Asymmetry - parameter) 0.44 0.44 0.1b (Asymmetry shift -
parameter) 4.7 4.7 0
Asymmetry: 1− FWHMrightFWHMleft 0.35 0.35 0.35
Table 3. Fit results of a Pd 3d spectrum fitted with the novel
fitfunction.
37
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2 EXPERIMENTAL METHODS
Summary In this section, we have shown that the introduction of
asigmoidal FWHM function into a regular Pseudo-Voigt function
hasvarious advantages. The application of the function
Pseudo-Voigt = (1−m)√
4ln2π
Agω(x)
e−4ln2( xω(x) )
2
+mAl2π
ω(x)(ω(x)/2)2 + x2
withω(x) =
2ω01+ exp(−a(x−b))
in least-squares fits of asymmetric spectra results in a good
repro-duction of the experimental curves and stoichiometric
relations. But,more importantly, the numerical properties of this
approach guaran-tee a finite and well defined area of the fit
curves, thus no arbitraryintegration cutoff criteria have to be
applied. This property makes itfeasible to compare curves with
different asymmetry and a differentFWHM in an unambiguous way.
2.1.6 Investigating valence levels with UPS
After the discussion of the most relevant aspects of XPS, we
willnow continue elucidating some relevant facts concerning UV
photo-electron spectroscopy. In contrast to XPS, UV photoelectron
spec-troscopy is not suitable to acquire quantitative information
on thechemical composition of a sample. This is mainly due to a
substantialvariation of photoionization cross sections of different
energy levels.Furthermore, diffraction effects of photoelectrons at
very low kineticenergies can not be excluded. In the context of the
present work,however, UPS was used for the following
applications:
(i) Show the presence of adsorbate-substrate valence states.(ii)
Measure work-function changes ∆φ of the sample upon depo-
sition of adsorbates.(iii) Follow adsorbate-induced
modifications of substrate surface
states.
38
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2 EXPERIMENTAL METHODS
(iv) Monitor the modification/creation of valence states by
inter-facial chemical reactions.
While most of those aspects follow directly from features in
theobserved spectra, the modus operandi for the determination of
thework function φ , and its changes, possibly needs a brief
explanation.Figure 5 a) shows an UPS survey spectrum of a clean
Au(111) sur-face, acquired with HeI radiation (21.2 eV). It is
apparent that thespectral cut-off, which represents electrons with
the highest sampledbinding energy, is well below 21.2 eV, the value
which could be ex-pected at a first sight. The reason for this
finding is that even electronswith a binding energy of 0 eV, i.e.,
those directly at the Fermi edge,require a certain amount of energy
to be released from the solid. Thisenergy is commonly referred to
as work function φ . Thus, the energyrequired to excite a
photoelectron is actually the sum of the bindingenergy (measured
relative to the Fermi edge) and the work function ofthe sample.
Therefore, the energy provided by a 21.2 eV photon canonly excite
electrons with a binding energy up to Emaxbind = 21.2 eV−φ
.Accordingly, by measuring the maximum binding energy position
asthe distance from the spectral cut-off to the Fermi edge (Figure
5 a),one can directly calculate the work function φ .
Adsorbate-inducedwork function changes that result in a shift of
the spectral cut-off, canthus be quantified accordinglye. Typical
values for work functions arein the range of several electron
volts, for a gold(111) sample φ equalsca. 5.4 eV.
2.1.7 Further reading
Since a comprehensive discussion of all aspects of photoelectron
spec-troscopy would be far beyond the scope of the present work, it
appearsnecessary to refer the interested reader to further
literature. A thor-ough discussion of photoelectron spectroscopies,
with a modern focuson theoretical aspects is to be found in the
textbooks of Hüfner72 andBriggs and Seah.112 A more experimental
approach can be found in
eThe photoelectrons at the spectral cut-off have a very low
kinetic energy; to avoidscattering effects or artefacts due to the
spectrometer, those electrons have to be accel-erated towards the
spectrometer. Commonly, applying a bias of -5 V to the sample
issufficient for this purpose.
39
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2 EXPERIMENTAL METHODS
the textbook of Grasserbauer98 together with a short
introduction toelectron spectrometers. The electron spectrometer
used in this workis described in the paper of Gelius et al.,113
while the basic designof electron spectrometers is described in an
article of Roy114. Sincean electron spectrometer is principally
based on an array of electricallenses, it appears necessary to
mention the textbook of Grosser115 onthis topic.
2.2 Low-Energy Electron Diffraction – LEED
Since Low-Energy Electron Diffraction (LEED) was utilized to
con-trol the long-range order of the Au(111) and Ag(111)
single-crystalsurfaces, and, on some occasions, the long-range
order of tetrapyr-role monolayers, we will briefly review this
method. We will developa principal understanding of this
experimental tool based on the math-ematics of the Fourier
transformation. LEED is performed by irradi-ating sample surfaces
with low energetic electrons with a kinetic en-ergy in the range
between tens and several hundreds of electronvolts.According to
fundamental quantum mechanical principles, we caninterpret the
ensemble of impinging electrons as a plain wave. Thiswave is
scattered and reflected as it hits a sample surface,f
placedperpendicular to its initial direction of propagation.
Following theprinciple of Huygens, each atom or molecule on the
surface acts thenas a point source for a scattered wave. The sum
over all point sourcesresults in an interference pattern that can
be observed experimentallyby installing a luminescent screen in
front of the sample. This diffrac-tion pattern has in fact a close
connection to the spatial distributionof the scattering objects on
the sample. Under the approximation ofFraunhofer diffraction116, it
represents the Fourier transformed of thescattering surface
structure.1,116,117 If this surface structure has a pe-riodicity,
i.e., if the scattering occurs on a two-dimensional lattice,
itsFourier transformed will show a corresponding characteristic
struc-ture. The interpretation of the structures in the Fourier
transformedis possible in a straight-forward way, since it can be
shown that the
fIn a first-order approximation it is justified to neglect the
scattering on bulk atomsdue to the low mean free path of electrons
in solids. Thus the scattering only occurs atthe very first atomic
layer.
40
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2 EXPERIMENTAL METHODS
Fourier transformed of a lattice is identical to its reciprocal
lattice.118
Hence, LEED experiments allow to directly image the reciprocal
lat-tice of a sample surface, and thus to draw conclusions on the
surfacelattice itself.
In the following section, we will briefly discuss the key result
thatthe Fourier transformed (and hence the Fraunhofer diffraction
pat-tern) of a lattice is identical to its reciprocal lattice. The
proof will begiven for the more general case of a three-dimensional
lattice, includ-ing the scattering on a two-dimensional surface
net, as it is observedin LEED measurements. We will take for
granted that the diffrac-tion pattern is identical to the Fourier
transformed and show that theFourier transformed is identical to
the reciprocal lattice.
We will start our discussion with the case of an
one-dimensionallattice, i.e., a regular, infinite chain of atoms.
Mathematically, thischain of atoms (mutual distance a) can be
expressed as a series ofδ -functions.
∞
∑n=−∞
δ (x−na)
Such a function is often referred to as comb(x).116 The Fourier
trans-formed of this equation is by itself a series of δ
-functions, however,in k-space and with an inverted
periodicity.116,118
∫ ( ∞∑
n=−∞δ (x−na)
)exp(ikx) dx =
∞
∑n=−∞
δ (k−2πn/a) (11)
Extending our considerations to a three-dimensional lattice, we
mayuse the lattice vectors~a,~b, and~c as a basis.
~r = ra~a + rb~b + rc~c
Accordingly, we can describe the lattice by an array of δ
-functions inthe following way:
∑δ (ra−naa) ∑δ (rb−nbb) ∑δ (rc−ncc) (12)
Similarly, the ~k-vector required for the Fourier transformed
can bewritten as
~k = kA~A + kB~B + kC~C
41
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2 EXPERIMENTAL METHODS
where the length and orientation of the three basis vectors in
not spec-ified yet. We will show now that the three-dimensional
Fourier trans-formed of Equation (12) can be calculated in a
straight-forward man-ner, if the basis vectors ~A, ~B, and ~C are
chosen in an advantageousway.
∫c
∫b
∫a
(∑δ (ra−naa) ∑δ (rb−nbb) ∑δ (rc−ncc)
). . . (13)
. . .× exp(i~k~r) dra drb drc
For any other choice, the resulting Fourier transformed will
havethe same appearance, but the computation process and the
resultingequations appear more difficult.
The exponential term in Equation (13), in particular the
product~k~r, has generally the effect that one cannot rewrite the
threefold inte-gral (13) as a product of three one-dimensional
integrals, which wouldbe favourable for the analytical solution.
However, it is possible tofind a certain set of basis vectors of
k-space ~A, ~B, and ~C that allows toperform this operation, and
thus obtain the solution of the threefoldintegral. The product~k~r
writes as
~k~r = ~A~akAra + kA~A(~brb +~crc) +~B~bkBrb + kB~B(~crc +~ara)
+~C~ckCrc + kC~C (~ara +~brb)
At this point, vector ~A is chosen to be perpendicular to the
latticevectors ~b and ~c; in other words, ~A is chosen parallel to
~b×~c. Thisresults in ~A~b = ~A~c = 0. Proceeding in a similar way
and choosing ~Bperpendicular to~a and~c, and ~C perpendicular to~a
and~b, we obtain:
~k~r = ~A~akAra + ~B~bkBrb + ~C~ckCrc
Introducing this in the exponential function of the Fourier
transfor-mation leads to
exp(i~k~r) = exp(i ~A~akAra) exp(i ~B~bkBrb) exp(i ~C~ckCrc)
42
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2 EXPERIMENTAL METHODS
It is possible to achieve a further simplification by
restricting thelengths of the vectors ~A, ~B, and ~C such that ~A~a
= ~B~b = ~C~c = 1. Then,the Fourier integral (13) can be factorised
into three one-dimensionalintegrals, each of the form of Equation
(11).(∫
a∑δ (ra−naa)exp(i kAra) dra
)(∫b∑δ (rb−nbb)exp(i kBrb) drb
). . .
. . .×(∫
c. . . drc
)Hence, the result can be written in the form
∞
∑n=−∞
δ (kA−2πn/a)∞
∑n=−∞
δ (kB−2πn/b)∞
∑n=−∞
δ (kC−2πn/c) (14)
where the first factor is a sequence of δ -functions along the
directionof ~A, the second along ~B, and the third along ~C. The
mutual distanceof the δ -functions is 2π/a, 2π/b, and 2π/c
respectively. The twoconstraints ~A || (~b×~c) and ~A~a = 1 can be
expressed simultaneouslywith the equation
~A =~b×~c
~a (~b×~c)(15)
This relation is precisely the definition of a reciprocal
lattice vector.g
Thus, Equations (14) and (15) reflect the point-distance and
orienta-tion within the reciprocal lattice. Similar conclusions can
be drawnfor ~B and ~C. Thus, we have shown that the Fourier
transformed of alattice is identical to its reciprocal lattice.
A further discussion of LEED, from a more experimental point
ofview, can be found in the textbooks of Zangwill117, or Henzler
andGöpel1.
2.3 Low-Energy Ion Scattering Spectroscopy – LEIS
In contrast to photoelectron spectroscopy, Ion Scattering
Spectroscopy(ISS or LEIS) is only sensitive to the atomic
composition of the top-most atomic layer and no information
concerning the chemical state
g This definition matches the definition which is commonly used
in crystallography;however, in solid state physics it is more
common to define the reciprocal lattice basedon ~A~a = ~B~b = ~C~c
= 2π . Thus, the definitions differ by a factor of 2π , resulting
in~AsolidState = 2π×~Acryst.. 119
43
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2 EXPERIMENTAL METHODS
of the atoms can be derived. In an ISS measurement, an ion-beam
isscattered on surface atoms. Considering an elastic collision
betweenthe ions and the surface atoms, one can derive the residual
energy ofthe ions after the collision. Its value is a function of
(i) the initial en-ergy of the ions, (ii) the mass of the ions and
the surface atoms, and(iii) the scattering angle, according to the
following equation:
E f = Ei
(cosΘ+
√(matom/mion)2− sin2 Θ
)2(1+matom/mion)2
The backscattered ions posses, due to energy and momentum
con-servation, a well defined residual energy, which is given by
their ini-tial kinetic energy, their mass, the mass of the
scattering partner, andthe scattering angle. Their kinetic energy
distribution shows a sharppeak.
Figure 14. 1 keV He LEIS spectra of a deposition series of
Caonto Au(111); the peak at a kinetic energy of 920 eV
originatesfrom elastic collisions with Au atoms, the peak at 690 eV
fromcollisions with Ca atoms.
Applying the latter equation, it is possible to calculate from
theposition of this peak the atomic mass of the scattering partners
on the
44
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2 EXPERIMENTAL METHODS
surface, and thus identify their atomic species. In the present
work,ISS was mainly used as a deposition monitor. This is possible
dueto the fact that effectively only the topmost atomic layer
contributesto the ISS signal. If, in a deposition series, the
substrate intensitydropped by 50%, one can directly conclude that
only 50% of the sub-strate surface remain uncovered by the
adsorbate. For illustration,Figure 14 shows LEIS spectra, acquired
during the deposition of Caonto a Au(111) surface. Due to the fact
that only the upmost atomiclayer contributes to LEIS signals, it
follows that a closed layer of anadsorbate shows the same intensity
as a bi- or multilayer. Thus, LEISexperiments are less suitable for
multilayer deposition experiments.For further reading please be
referred to the works of Niehus120,121
or the textbook of Henzler and Göpel1.
45
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3 RESULTS
3 Results
The results presented in this chapter were acquired with
photoelec-tron and ion spectroscopies. It should be noted, however,
that the cor-responding publications were partly done in
cooperation with othergroups and thus contain additional
information acquired by differentexperimental methods. The
following section gives a brief survey ofthe most essential results
from the publications [P1] - [P7].
3.1 Coordination chemistry of metallotetrapyrroleson Ag(111) and
Au(111) surfaces
3.1.1 Cobalt(II) phthalocyanine adsorbed on Ag(111) [P1]
The adsorption of cobalt(II) phthalocyanine (CoPc) on Ag(111)
wasexamined with XPS and UPS. From previous investigations, a
sub-stantial modification of the electronic states of the central
cobalt atomwas to be expected;33 thus, the aim of the article [P1]
was to fur-ther elucidate details of this coupling. In particular,
the modificationof the Co 2p core levels contains much more
information than onewould expect at the first glance. The cobalt 2+
ion in CoPc possessesan unpaired electron in its 3d sub-shell,
corresponding to a molecularspin of S=1/2. Since cobalt 2+ ions
also occur with a net-spin of S= 3/2, CoPc is referred to as Co(II)
low-spin complex. Due to thisopen shell-character, multiplet
effects can be observed in the cobaltcore levels. Briefly, such
multiplet effects arise if the unpaired spin ofthe core-hole after
photoionization couples to the spin of the unpairedelectrons in
outer shells. Hence, one can find for instance multiplelines in an
s core-state, but also in all other core level signals. Itwas shown
for cobalt that each spin configuration has an individualspectral
fingerprint in the 2p region.15,90,92 The multilayer spectrumin
Figure 15 exhibits a typical Co(II) S = 1/2 pattern. The
apparentspin-orbit splitting is with 15.7 eV significantly larger
than in metalliccobalt and the shape of the peaks suggests the
presence of an unre-solved sub-structure; nevertheless, the intense
satellite structures ofCo(II) high-spin complexes are absent. A
least-squares fit of the Co2p region of the CoPc multilayer is
shown in Figure 16. The relative
46
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3 RESULTS
Figure 15. Co 2p3/2 spectra of a CoPc multilayer and
submono-layer on Ag(111). The background subtraction of the
submono-layer spectrum was performed in a way that the ratio
between thetotal 2p3/2 and 2p1/2 intensities, i.e. including the
gray-shadedsatellite features, matches the nominal value of 2 : 1.
Reprintfrom [P1].
intensities of the individual peaks have been constrained to the
nom-inal values given by the degeneracy of corresponding J states,
in linewith the interpretation of Frost15,90 and Briggs92.
Interpreting thefeature at 782.5 eV as a satellite, due to a
spin-dependent process, itsrelative intensity is in accordance with
theory.16 One has to note thatthe latter mechanism results possibly
in different satellite structuresfor the 2p3/2 and 2p1/2 levels.
However, alternatively the feature at782.5 eV was associated with
further multiplet peaks.92
47
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3 RESULTS
Figure 16. Least-squares deconvolution of the Co 2p
region,recorded from a cobalt(II) phthalocyanine multilayer. The
relativeintensities of the photoelectron lines were constrained to
the val-ues given by the degeneracy of the corresponding J states.
The ex-istence of those states results from a coupling of the
spin-orbit j =3/2 and j = 1/2 states with the S = 1/2 state of the
d-electrons. Theangular momentum of the d electrons was assumed to
be quenchedby the ligand field of the phthalocyanine macrocycle.
The relativeintensity of the satellite in the 2p3/2 spectrum
matches the valuegiven by Borod’ko.16 See text and [P1] for
details.
A more detailed analysis of the shape of 2p core levels of
CoPc(sub-)monolayers and comparison to the well known 2p line
patternsof different cobalt spin states reveals that the molecules
in direct con-tact to the Ag(111) substrate are in a diamagnetic
state. The spin-orbitseparation is identical to the value obtained
for diamagnetic Co(0), orCo(III) compounds. The absolute binding
energy positions are closeto Co(0) values. Those findings confirm
previous DFT calculationsthat predict a charge transfer from the
substrate to the cobalt ions,associated with a quenching of the
molecular spin.122 The completeremoval of any multiplet effects
from the CoPc monolayer spectrumis further corroborated by the fact
that the ratio between the FWHMof the Co 2p3/2 and 2p1/2
components, as determined by the addi-tional broadening of the
2p1/2 level due to the Coster-Kronig process,
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3 RESULTS
is in agreement with literature values.77,78 UPS measurements of
thevalence levels of CoPc monolayers resulted in the observation of
adoublet-like peak structure close to the Fermi energy, as
previouslyanticipated with DFT.122 The latter results further
confirm the currenttheoretical understanding of the interaction
between Co-tetrapyrrolesand the Ag(111) surface.
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3.1.2 Co(II) and Fe(II) tetrapyrroles on Au(111) [P2, P3]
In the previous chapter, it was shown that the interaction
betweencobalt tetrapyrroles and an Ag(111) surface can be
understood interms of a charge transfer from the substrate to the
central metal ionof a porphyrin or phthalocyanine. In the
following, we will discussthe corresponding situation on an Au(111)
interface. One of the mostsignificant differences between the
Ag(111) and Au(111) surfaces,apart from chemical aspects, is their
fundamentally different surfacemorphology due to the reconstruction
of the Au(111) surface. Theupmost atomic layer of gold atoms
suffers an uniaxial compressionalong a [11̄0] direction; as a
consequence, 23 surface atoms occupy22 bulk sites, leading to a
geometrical mismatch between the surfacelattice and the bulk
structure below. Thus, a periodical alternation offcc and hcp sites
is generated on the surface. The pattern is furthercomplicated
since, on a larger length scale, a periodic change of thedirection
of compression by ± 120◦can be observed. This leads tothe
herringbone appearance of the reconstructed Au(111) interface,a
morphological feature which is still present after the adsorption
oftetrapyrrole monolayers.123,124 Figure 17 a) shows the LEED
patternof a clean Au(111) surface. The hexagonal fine-structure
around eachspot directly reflects the herringbone reconstruction (6
fold symmetrydue to the 120◦ herringbone variation).
The rich LEED pattern of a Fe(II) phthalocyanine (FePc)
mono-layer on Au(