Digital Comprehensive Summaries of Uppsala Dissertations from
the Faculty of Science and Technology 890
Angle-Dependent Electron
Spectroscopy Studies of C60
Compounds and Carbon Nanotubes
BY
J OACHIM S CHIESSLING
ACTA UNIVERSITATIS UPSALIENSIS
UPPSALA 2003
Dissertation for the Degree of Doctor of Philosophy in Physics presented at Uppsala University in
2003
A BSTRACT
Schiessling, J. 2003. Angle-Dependent Electron Spectroscopy Studies of C60 Compounds and
Carbon Nanotubes. Acta Universitatis Upsaliensis. Digital Comprehensive Summaries of Uppsala
Dissertations from the Faculty of Science and Technology 890. 71pp. Uppsala. ISBN 91-554-57487
Fullerenes have been shown to constitute a prototypical building block for truly nanometer-sized
devices and exotic nanounit-based materials, e.g., high-temperature superconductors. This makes
the detailed understanding of fullerene electronic states in compounds and at interfaces of primary
importance, since the high symmetry of the molecule greatly simplifies the starting point of the
analysis. Carbon nanotubes, which combine one macroscopic with two nanoscopic dimensions, are
perhaps of even greater practical interest.
Angle-dependent electron spectroscopies have been employed in the present work to study these
materials, characterizing their structure, bonding, and electronic states. For solid C60 , the photoelectron angular distribution has been found to be essentially that of the free molecule, modified
by solid state scattering; a similar distribution is found for K3 C60 . The surface and bulk electronic
structure of K3 C60 has been identified by angle-dependent core and valence photoelectron spectroscopy (PES) and x-ray emission spectroscopy. An insulating surface layer has been identified for
this high-temperature superconductor.
Angle-dependent valence PES is used to investigate the electronic states of C60 /Al(110). Electron
correlations are found to be the origin of the splitting observed in the molecular orbitals, which
is quite sensitive to the molecular orientation. The components of the highest occupied molecular
orbital are differentiated according to their overlap with the substrate.
A rigid shift of valence- and core-levels has been observed even for ionic and covalent C60 compounds, reflecting the efficient static polarizability screening of the molecule.
The alignment of multi-walled carbon nanotubes has been investigated by x-ray absorption spectroscopy, using the spectral intensity ratio of π ∗ - and σ ∗ -resonances. Core level combined with
valence PES shows that the degree of defect structure varies from position to position on the sample. Valence photoelectron spectra of defect-free sample spots closely resembles the total DOS of
graphite.
Key words: fullerenes, C60 , K3 C60 , multi-walled carbon nanotubes, molecules, clusters, electron
spectroscopy, synchrotron radiation, x-ray absorption, x-ray emission, molecular orbitals, charge
transfer, electron correlation, surface physics
Joachim Schiessling. Department of Physics. Uppsala University. Box 530, SE-752 21 Uppsala,
Sweden ([email protected])
c Joachim Schiessling 2003
ISBN 91-554-5748-7
ISSN 1104-232X
Printed in Sweden by Kopieringshuset AB, Uppsala, 2003
”It’s a Snark!” was the sound that first came to their ears,
And seemed almost too good to be true.
Then followed a torrent of laughter and cheers:
Then the ominous words ”It’s a Boo-”
Then, silence. Some fancied they heard in the air
A weary and wandering sigh
Then sounded like ”-jum!” but the others declare
It was only a breeze that went by.
They hunted till darkness came on, but they found
Not a button, or feather, or mark,
By which they could tell that they stood on the ground
Where the Baker had met with the Snark.
In the midst of the word he was trying to say,
In the midst of his laughter and glee,
He had softly and suddenly vanished away—
For the Snark was a Boojum, you see.
from The Hunting of the Snark
by Lewis Carroll
ii
List of Papers
This Thesis is based on the following papers, which will be referred to in the text by their
Roman numerals.
I. Polarization-Dependent Angular Photoelectron Distribution of Solid C60
J. Schiessling, L. Kjeldgaard, T. Balasubramanian, J. Nordgren, and P. A. Brühwiler
Accepted for publication in Phys. Rev. B
II. Molecular Orbital Components of C60 on Al/(110)
J. Schiessling, M. Stener, T. Balasubramanian, L. Kjeldgaard, P. Decleva, J. Nordgren, and P. A. Brühwiler
Submitted
III. Orbital splitting and molecular orientation for C60 /Al(110)
J. Schiessling, M. Stener, L. Kjeldgaard, T. Balasubramanian, P. Decleva, J. Nordgren, and P. A. Brühwiler
In manuscript
IV. Angle Dependent Photoemission of K3 C60 : Bulk and Surface Charge States
J. Schiessling, L. Kjeldgaard, T. Käämbre, I. Marenne, J. N. O’Shea, J. Schnadt,
C. Glover, M. Nagasono, D. Nordlund, M. G. Garnier, L. Qian, J.-E. Rubensson, P.
Rudolf, N. Mårtensson, J. Nordgren, and P. A. Brühwiler
In manuscript
iii
V. A Soft X-ray Study of K3 C60 : Bulk Electronic Structure and Intermolecular
Charge Transfer Rates
T. Käämbre, J. Schiessling, L. Kjeldgaard, L. Qian, I. Marenne, J. N. O’Shea, J.
Schnadt, D. Nordlund, C. Glover, J.-E. Rubensson, P. Rudolf, N. Mårtensson, J.
Nordgren, and P. A. Brühwiler
In manuscript
VI. Core-hole screening efficiencies in molecular π systems estimated from a comparison of valence and core excitons
J. Schnadt, J. Schiessling, and P. A. Brühwiler
Submitted
VII. Beamline-induced Chromium Structure in Carbon K-edge Absorption Spectra
J. Schnadt, J. Schiessling, J. N. O’Shea, L. Patthey, M. Shi, C. Puglia, N. Mårtensson,
and P. A. Brühwiler
Nucl. Inst. Meth. Phys. Res. B 184, 609 (2001)
VIII. Synchrotron radiation study of the electronic structure of multiwalled carbon
nanotubes
J. Schiessling, L. Kjeldgaard, F. Rohmund, L. K. L. Falk, E. E. B. Campbell, J.
Nordgren, and P. A. Brühwiler
J. Phys.: Condens. Matter 15, 6563 (2003)
iv
Comments on my own participation
The experiments described in this thesis are carried out at the synchrotron radiation facility MAX-lab in Lund. Surface science experiments performed at a synchrotron light
source are always effort of many persons. In all scientific projects I played an active role
in the experimental work, data analysis and preparation of the manuscript. The position
of my name in the author list reflects my contribution to some degree. Where my name
stands first, I was the person with primary responsibility for all aspects of the scientific
work including manuscript preparation.
v
Contents
List of Papers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Comments on my own participation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1 Geometry and Electronic Structure of C60 . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 C60 in Solid State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Intercalation of C60 fullerite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 C60 Adsorbates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Electron Correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Carbon Nanotubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 Experimental Techniques and Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1 Photoelectron Spectroscopy (PES) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Photoelectron analyzer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 X-ray Absorption Spectroscopy (XAS) . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 X-ray Emission Spectroscopy (XAS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Synchrotron Light Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 The Surface Instrument in Uppsala . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6 Sample Preparation and Ultra High Vacuum Conditions . . . . . . . . . . . . . . .
4 Photoemission Lineshape of Fullerene Compounds . . . . . . . . . . . . . . . . . . . . .
4.1 Angular Distribution of Photoelectrons for solid C60 . . . . . . . . . . . . . . . . .
4.2 Lineshape Analysis of K3 C60 and C60 /Al(110) . . . . . . . . . . . . . . . . . . . . .
4.2.1 K3 C60 C 1s analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.2 C60 /Al(110) Valence Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5 Surface Electronic Structure of K3 C60 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6 C60 Monolayer on Al(110) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.0.3 Splitting of the HOMO-band . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7 Rigid Energy Shift in Core-Level and Valence Photoemission . . . . . . . . . . . . . .
8 Multi-Walled Nanotubes (MWNT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.1 Sample Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.2 Orientation of MWNT on Nanoscopic Scale . . . . . . . . . . . . . . . . . . . . . . .
8.3 Electronic Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
vi
iii
v
1
3
3
4
6
7
7
8
10
10
14
16
17
18
21
22
25
25
33
33
36
40
48
52
54
56
56
56
61
64
Introduction
Figure 1.1: Collage of geodesic houses.
This is the story of a tiny house and its inhabitants. The house is made of carbon and
has a geodesic shape. This shape is a reminder of the geodesic domes designed by the
architect R. Buckminster Fuller, as shown in Fig. 1.1. In analogy to this design this type
of house is often called Fullerene.
Just as the domes by R. Buckminster Fuller offer a new and exciting look into future
architecture, these small houses have started a wide field of scientific activity, ranging
from fundamental research to applications as a prototype device for future technologies.
Whereas the largest of the domes is more than a hundred meters in diameter the size
of the house is only tiny. In fact, it is so small that it is not possible to see with bare eye,
and not even with the best optical microscope is it possible to obtain an image, therefore,
a different method with which to investigate this house has to be chosen.
One possibility to investigate the interactions is by interviewing the inhabitants of
the house. The inhabitants are electrons which each sit at unique levels. Every level is
1
associated with a characteristic energy and the house can be identified by the arrangement
of these levels.
Before the electrons can be interviewed they have to leave their home. Electrons can be
kicked out by a photon in a process called photoionization. To measure the kinetic energy
of that released electron (photoelectron) it is forced to pass through an electric field, in
which its path changes. The electric field is chosen to obtain a deflection of the electron
path. By measuring this deflection the kinetic energy of the photoelectron is achieved and
the electron levels can be determined.
The influence of the environment on this house is of particular interest. The quality
of the modifications in the electronic levels is a measure of this influence on the house.
Many researchers have interviewed electrons living in houses on a metal or on a semiconductor. The answers researchers have obtained in the past where not very clear, and it
seemed that the metal induced a big change in the levels of the house.
Many of these houses put together form a crystal called fullerite. A so-called superconductor can be made by adding alkali atoms to this crystal. Superconductivity is a
phenomenon describing the ability of electrons to travel without any energy loss (in a
closed pathway for years!). This phenomenon is of great interest from both the fundamental and applicative point of view. However, if electrons of this special crystal are
interviewed about what is happening to them and their house, they give only very ”broad”
answers. Speculation are that the houses are extremely modified throughout the system,
which would be in contrast to the expectations of the current model.
To help the electrons in understanding what is happening to their house in these systems a series of photoelectron measurements at a set of emission angles has been done.
A careful look at the collection of answers and empirical work gives more insight into
this system. In the following pages more details are given and show to what extend the
electrons have to be worried about their homes.
2
Background
2.1
Geometry and Electronic Structure of C60
The fullerenes were discovered in 1985 by a group lead by R. F. Curl, H. W. Kroto and
R. E. Smalley[1]. They synthesized carbon structures in order to analyze the infra-red
spectrum of carbon rich giant stars observed by H. W. Kroto. The clusters were formed
by laser ablation from carbon material. They found a high stability structure with 60
carbon atoms. This suggests a molecular structure of great symmetry. The structure of
C60 is shown in Fig. 2.1. In analogy to the shape of the geodesic domes designed by the
architect R. Buckminster Fuller the newly-discovered structure is was called ”buckminsterfullerene”. For their discovery of fullerenes R. F. Curl, H. W. Kroto and R. E. Smalley
were awarded with the Nobel Prize in Chemistry in 1996.
In the first years after their discovery only small quantities of fullerenes were available
for further investigations due to the costly production via laser ablation.The breakthrough
came 1990 when W. Krätschmer and D. R. Huffman found a method to produce macroscopic quantities[2] of fullerenes by subliming graphite in a light arc. The fullerenes could
be extracted out of the carbon condensate using an organic solvent. In the following years
a vast amound of research has started, and entirely new branches of fullerene chemistry,
superconductivity and materials chemistry and physics have evolved.
Figure 2.1: The buckyball structure consists of 60 carbon atoms, forming 20 hexagonal
and 12 pentagonal faces.
All atomic sites in the C60 structure are equivalent. C60 has 360 electrons, whereof
120 are core electrons, leaving 240 electrons for the valence levels localized on a (almost)
spherical shell. The molecule belongs to the icosahedral point group (Ih ). In Fig. 2.2 the
electronic structure as obtained by Hückel calculation[3] is shown. The valence orbitals
3
can be described as superposition of the hybridized sp2 − sp3 atomic orbitals, forming σ
and π bonds. Because all levels are completely filled, the C60 ground-state symmetry is
totally symmetric. Experimentally the diameter of the shell is determined via NMR[4] to
7.1 Å. Accounting the size of the π-electron cloud associated with the carbon atoms, the
outer diameter of the C60 molecule can be estimated as 7.1Å + 3.35Å = 10.34Å, where
the thickness of the electron cloud of 3.35 Å is an estimate from the distance between
graphite layers.
(a)
Spectroscopic View
8
Binding Energy(eV)
6
4
2
0
PES
LUMO+2
LUMO+1
LUMO
HOMO
HOMO-1
Intensity
IPES
Number of States
(b)
10
8
6
4
2
0
Hückel Calculation
hg+gg
hu
gu
hg
t1u
t2u
4
3
2
t2u
t1g
-1
1
0
Energy (eV)
-2
-3
Figure 2.2: (a) Photoelectron (PES) and inverse photoemission (IPES) spectrum show
the occupied and the unoccupied states (IPES is from reference [5]). The
spectroscopic features are labeled in accordance with Martins et al., Ref. [6].
The binding energy is referenced to the vacuum level. (b) Molecular orbital
levels from Hückel calculations after [3]. Arrows indicate the occupied levels.
The notation in the diagram are the names of the irreducible representations
in the icosahedral point group (Ih ).
As seen in Fig. 2.2, C60 has just enough electrons to fully fill the hu molecular level,
which forms the highest occupied molecular orbital (HOMO), while the next higher
t1u level remains empty and becomes the lowest unoccupied molecular orbital (LUMO).
The peaks appering in photoemission consist of one or more molecular orbitals: (HOMO
(hu ), HOMO-1 (hg +gg ))[7].
2.2
C60 in Solid State
The photoemission spectrum of solid state C60 , or C60 fullerite, resembles closely the gas
phase spectrum [8, 9] demonstrating the absence of strong intermolecular interactions.
4
The rather week interaction in the condensed phase are induced dipol-dipol interactions
(van der Waals forces) leaving molecular properties preserved [10]. One of the fascinating
properties of the fullerites in particular is, that many of the macroscopic properties are
related to properties of the isolated molecules [11, 12, 13]. Electron spectroscopy plays
a central role in elucidating the fullerene electronic structure [14]. The bandwidth of the
HOMO band has been predicted by local density approximation (LDA) for solid C60 to be
about 0.6 eV [15]. However, a distinct band dispersion for solid C60 has not been observed
and the width in the photoemission spectrum is rather explained as due to vibrational
broadening [16, 17]. Recently band dispersion in the range of 150 meV has been reported
for the alkali doped monolayer C60 on silver [18].
(a)
10
]
[0
[001]
(b)
]
11
[-1
[11
-1]
[1
11
]
[100]
[1
1]
-1
Figure 2.3: (a) Crystal structure of solid C60 . At room temperature the molecules rotate
freely. Void positions of the face centered cubic structure are indicated by the
cross (octahedral void) and the tetrahedral (tetrahedral void). The filled side
of the tetrahedron indicates the (111) plane which consists the surface plane
of vacuum grown samples. (b) At lower temperature the rotational axis are
aligned along the four 111 axes and the lattice structure is simple cubic.
Single crystals grown from vapor deposition of C60 molecules form a single crystal
with the molecular centers arranged on a face-centered-cubic (fcc) lattice1 . The crystal
structure is illustrated in Fig. 2.3(a). The fcc lattice constant is 14.17 Å giving a neighbor
distance of 10 Å[19]. The separation between two atoms on different molecules is large
(≈ 3 Å) compared with the length of a C-C bond (≈ 1.4 Å). At room temperature the
molecules are rotating almost freely [4, 20, 21, 22] around their lattice positions. Since
there is no orientational order all lattice positions are equivalent. In the temperature range
of 250 K - 260 K[23] the molecules loose two of their three degrees of rotational freedom,
and the orientation relative to the the cubic axes becomes important. This is a rotational
ordered cubic phase, in which the molecules of the fcc phase assume discrete orientations
about a set of 111 directions, as shown in Fig. 2.3(b).
1 A similar kind of systems are the noble gases, which have like C
60 a closed-shell electronic configuration.
They all (except for helium) crystallize into monoatomic fcc Bravais lattices.
5
2.2.1
Intercalation of C60 fullerite
In 1991 it was found that adding alkali atoms to solid C60 leads to charge transfer from the
atoms to the molecules and the previously unoccupied LUMO is getting filled. Potassium
atomes can penetrate deep into C60 films and they intermix well with C60 molecules
in a very short time at ambient temperature, due to the low activation energy of the
diffusion[24]. A representative overview for successive potassium intercalation is shown
in Fig. 2.4. Solid C60 is an insulator with a gap of 1.6 eV[25]. Upon intercalation the
previously insulating fullerite can become metallic and even superconducting[26]. The
intercalated fullerite is called fulleride.
Unoccupied Levels
Occupied Levels
Figure 2.4: Photoemission (l.h.s.) and x-ray spectroscopy (r.h.s) by Chen et al.[27]. This
study shows that the PES (XAS) LUMO is increasing (decreasing) for successive intercalation with potassium. At a stoichiometry of x=5.8 the LUMO is
almost filled and the corresponding peak in the XAS spectrum has vanished.
At a stoichiometry of about x=3 a step at EF is seen.
Stable phases for the intercalated solid C60 are found for stoichiometries K1 C60 ,
K3 C60 , K4 C60 , K6 C60 . In the begining it was not clear, if Kx C60 samples were composed of one, two or more phases. E.g., for successive intercalation up to x=1.5 phase
separation into K1 C60 (all octahedral sites are filled) and K3 C60 (all octahedral and all
tetrahedral sites filled) was found [28]. Hopping within the tetrahedral and octahedral
voids of the fcc lattice the alkali atoms can diffuse easily through solid C60 , however,
diffusion should be more difficult in K3 C60 , since all interstitial sites are occupied. All
stable phases are non-metals except K3 C60 which is even a superconductor and makes
this compound of special interest.
In 1994 a recipe for growing a pure phase crystal K3 C60 has been found by Poirier et
6
al. [29] and K3 C60 has become the testing ground for investigations of fulleride superconductivity. Such K3 C60 films are flat with grains with lateral dimensions commonly
greater than 1000Å[30] and show a close-packed fcc (111) plane as the preferred crystal
surface termination [30].
2.3
C60 Adsorbates
On most surfaces C60 tends to form well-ordered quasi-hexagonal close-packed overlayers with a nearest neighbor separation close to that of the van der Waals bonded C60 solid.
A variety of bond strength and character is observed in C60 substrate interaction ranging
from van der Waals[31, 17] to ionic[32, 33, 34] and covalent interaction[35, 36, 37]. The
substrate-induced modification of the electronic and structural properties of C60 is an
important issue for future technology[38, 39].
2.4
Electron Correlations
In a simple metal, every electron can move freely through the periodic potential of the
lattice formed by the positive cores and the field of the other electrons in a mean-field
manner. Many of the most interesting properties of materials, such as magnetic ordering
in, e.g., giant magnetoresistance compounds, charge/spin density waves or superconductivity in,e.g., the high-TC cuprates go beyond the independent-electron approximation and
the electron-electron correlations have to be taken into account explicitly. The simplest
approach taking the many-body effects into account is the Hubbard-model[40, 41]. The
correlations are described in the Hubbard model by on-site (U ) and nearest-neighbor (V )
interaction. U reflects the Coulomb repulsion between pairs of electron on the respective
atomic/molecular site. Interaction with neighboring sites is described by the Coulomb
interaction V . In many regards C60 -based salts serve as model systems for exploring
strongly correlated systems[42].
The simplest estimate of U for C60 is obtained from the Coulomb integral[43, 44]
assuming the charge forms a thin shell of a sphere with radius R=3,5 Å
ρ(r)ρ(r )
UCoulomb =
d3 r d3 r (2.1)
|r − r |
= 4.1eV,
(2.2)
where ρ(r) is the charge density of the electron. Taking many-body effects into account
the value for the free molecule[44] is U free = 2.7 eV. In solid state C60 the Hubbard
repulsion will be smaller than for the isolated molecule due to the polarization screening
of neighboring molecules. The theoretical expectation for C60 solid is U = 0.8 − 1.3 eV.
Experimentally values of U = 1.6 ± 0.2 eV[25] and U = 1.4 ± 0.2 eV[45] are found
for solid C60 , and similar for K3 C60 U = 1.6 eV[45]. The value of U depends on the
screening efficiency of the surrounding of the molecule. For C60 monolayer on metal, e.g.,
it can be expected to be reduced with respect to the value of solid C60 due to the image
charge screening of the metal. For a C60 /Ag(111) a Coulomb repulsion of UML =0.6 eV
has been measured[46].
7
Another way to think of the Hubbard U is in terms of electron-hole excitation[25], the
creation of an electron-hole pair costs one U. This is illustrated for a linear chain with
periodic boundary conditions. A chain with M sites has the total Coulomb energy EU
plus the energy due to the nearest-neighbor interaction EV . The initial state energy E i of
a system with n electrons at every site is:
Ei
EUi
EVi
= EUi + EVi
1
= M n(n − 1)U
2
= M n2 V
(2.3)
(2.4)
(2.5)
After creation of an electron-hole pair and separating electron and hole the final state
E f of the system is:
Ef
EUf
EVf
= EUf + EVf
1
1
= (M − 2) n(n − 1)U + M (n − 1)(n − 2)U +
2
2
1
+M (n + 1)nU
2
= (M − 4)n2 V + 2(n + 1)nV + 2n(n − 1)V = M n2 V
(2.6)
(2.7)
(2.8)
(2.9)
The energy difference is:
∆E
= Ef − Ei = U
(2.10)
Thus the energy involved in creation of a electron-hole pair is always U .
The simplest approach to estimate the nearest-neighbor interaction V is by considering
two site, A and B. The energy of an electron at site A is increased when an electron is
added to the neighboring site B at distance d leading to V = e2 /d. The polarization
screening of the surrounding molecules will lower the value of V. The nearest-neighbor
interaction for solid C60 is calculated to V = 0.3 − 0.5 eV[44].
2.5
Carbon Nanotubes
Carbon nanotubes are beside the spherical shaped fullerenes another form of novel carbon
allotrope that has been synthesized. As shown in Fig. 2.5 nanotubes and graphite are very
similar in their basic structure as being made of carbon hexagons. A sp2 /sp3 hybridization
forces the layer into a curvature and nanotubes are often regarded as rolled-up graphene
sheets.
Small diameter tubes show quantization effects in the electronic structure and their
electron dispersion relation can be explained to the first order by Brillouin zone folding
of graphene[47]. Depending on the tube helicity, e.g., the angle the graphite sheet is
rolled-up, the electronic structure can vary between insulating and metallic. The π-bands
determine mainly the optical gap and conductivity, and σ-bonds determine mechanical
properties.
Multi-walled carbon nanotube (MWNT) consist of several concentric tubes. Because
of the different numbers of carbon atoms around the various concentric tubules, it is not
8
Figure 2.5: Illustration of carbon nanotubes.
possible to achieve a graphite like ABAB. . . interlayer stacking of the planar hexagonal
networks for the curved structure in MWNTs [48]. Theses systems are used in prototypes
of technological applications like, e.g., flat screen displays [49], compact x-ray-tubes [50]
or miniaturized gas sensors [51]. These applications are profiting from a good spatial
alignments of the tubes. Nanotubes can be aligned in external fields, or grow in a selfaligning fashion. In general, the spatial alignment of these kinds of samples is very good
on macroscopic scale. Despite intensive research efforts on state-of-the-art samples, principal spectroscopy techniques[52, 53, 54, 55, 56, 57, 58, 59] like photoemission and x-ray
absorption have not yet converged in terms of lineshape. This limits the understanding of
this novel material and so far a clear spectroscopic view is still awaiting. The electronic
and geometric structure of MWNTs are investigated in Paper VIII.
9
Experimental Techniques and Equipment
The techniques used to investigate the fullerenes in this thesis are photoelectron spectroscopy (PES), x-ray absorption (XAS) and x-ray emission spectroscopy (XES). The first
step in all these processes is the photon-excitation or -ionization of the fullerene system.
In PES the fullerene is ionized and the kinetic energy of the released electron (photoelectron) is measured. XAS describes the absorption of incoming light as a function of
photon energy. For every photon energy the amount of released electron is measured.
XES is a two photon process (photon in, photon out). The energy of the outgoing photon
is measured.
The fundamental process inherent in all the spectroscopic methods used in this thesis
is the dipole transition. The process primarily probes electronic structure, however it has
a great potential to determine geometrical structure as well. In general the transition rate
w in quantum mechanics is given by Fermi’s Golden Rule[60]:
w=
2π
2
|f |Hint | i| ρf (E)δ (hν + Ei − Ef ) ,
h̄
(3.1)
where |i and f | are the initial state and final state wave functions. Ei and Ef are the
initial and final state energies, hν is the energy of the incoming photon, ρf is the final
state density of states. The δ function ensures energy conservation. The operator is the
interaction Hamiltonian describing the coupling between photon and electron
e
Hint = −
A · p.
(3.2)
mc
e denotes the charge and m the mass of the electron. c is the light velocity. The electrons
momentum is described by p. The electromagnetic vector potential A can be expressed1
, e.g, in terms of the electric field vector E for a monochromatic plane wave propagating
in direction n as[60]:
ω
A = 2E cos
n · x − ωt .
(3.3)
c
3.1
Photoelectron Spectroscopy (PES)
Experimentally, the interaction between light and electrons has been observed for the first
time in 1887 by H. Hertz. He found that zinc looses negative charge upon irradiation with
light. This has been described 1915 by A. Einstein as photoeffect.
Ekin = hν − Ebinding (−Φ),
(3.4)
where hν is the energy of the incoming photon, Ebinding the element specific binding
energy of the electron level and Ekin is the kinetic energy of the released photoelectron.
1 Justifying
the gauge condition ∇ · A = 0.
10
The PES process is illustrated in Fig. 3.1. Core-level spectroscopy, often called x-ray
photoelectron spectroscopy XPS, can give atomic specific information, e.g., via a chemical shift. Valence-spectroscopy, often called ultra-violet photoelectron spectroscopy UPS,
helps to investigate the valence electronic structure of a molecule and, e.g., its modification upon adsorption on a surface.
For a solid state sample the contribution of the work function Φ has to be added to
Eqn. 3.4. The work function describes the minimum energy required to remove an electron from the interior of a solid into the vacuum[61]. The binding energies of the electron
measured for a metallic sample is referenced to the energy of the Fermi level EF , which is
given by the lowest binding energy of the electrons in the conduction band. For insulators
like,e.g., solid C60 the binding energy has to be given with respect to another common
reference, e.g. in terms of the ionization potential to the vacuum level. See, e.g., Ref. [62]
for the ionization potential of solid C60 .
On its way out of the sample the photoelectron experiences scattering. The high cross
section for inelastic scattering of the photoelectron in the material makes this methods
extremely surface sensitive. A frequently used graph to show the attenuation length of
photoelectrons inside a solid as a function of kinetic energy is the so-called universal
curve[63, 64], see Fig. 3.2(a). The usage of a universal curve can be motivated by the
fact that electron energy loss in solids is to a large extent due to excitation of valence
electrons. The electron density in the valence band with about 0.25 electron/Å3 is similar
for most materials. Thus by collecting photoelectrons at different emission angles virtually different probing depth are achieved and the surface sensitivity in PES can be varied,
see Fig. 3.2(b). Commonly an exponential attenuation is assumed, giving a simple relation for the attenuation of the intensity with respect to emission angle. The attenuation is
characterized by the inelastic mean free path (IMFP). However, a quantitative information about the emission depth of the photoelectron cannot be achieved by only taking the
IMFP into account. Elastic scattering will change the path of the photoelectron and the
approximation of a exponential attenuation of the signal with depth is not longer valid.
Different paths are illustrated in Fig. 3.2(c).
Spectra of solids always contain a sizable background due to inelastic scattered photoelectrons. In order to isolate the ”intrinsic spectrum” this background has to be removed
by a suitable procedure. This can be realized in the simplest case by subtracting a linear
background between to carefully chosen points in the spectrum. A correction frequently
used is the ”Shirley”-background[65], where the background intensity at a particular binding energy is assumed to be proportional to the integral of the intensity from this energy
down to lower binding energy. An application of Shirley-background is shown for corelevel data in Fig. 8.5.
After emission of a photoelectron is left with the positive charge of the photo-hole.
The positive charge can be neutralized in metals, whereas an insulators is left with the
positive charge. The accumulation of photo-holes during a measurement creates a net
charge an the surface of an insulating sample. This is balanced by a charge transfer from
the, e.g., (grounded) metallic substrate to the sample surface. A net charge at the surface
can cause significant distortions in the photoemission spectrum by reducing the kinetic
energy of the photoelectrons.
The angle-dependence in the dipole approximation is determined by parity and angular momentum conservation. The angular distribution of an emitted particle after dipole
absorption for linearly-polarized light is characterized by an anisotropy parameter β [66,
67]. The differential cross section is given the Bethe-Cooper-Zare formula for polarized
11
Photoemission
(a)
Core-Level
Spectroscopy
Valence
Spectroscopy
(b)
Energy Referencing
insulator
metal
Ekin
Ekin
hν
Ekin
hν
Ekin
Vacuum Level
Unoccupied
Valence-Levels
Occupied
Valence-Levels
{
IP
Band
Gap
{
Φ
{
EF
EB
Core-Level
Figure 3.1: (a) Illustration of the photoemission process. A photoelectron is released
upon absorption of a photon with energy hν. Via measuring the kinetic energy Ekin of the photoelectron the value of the binding energy is achieved.
The valence electrons wave function is spread out over all constituting atoms.
UPS gives information about the chemical state of the system. In XPS, however, the binding energies measured are very sensitive upon changes at the
atomic site due to the strong localization of the core electron wave function.
(b) Photoionization of an insulating and metallic sample. There is no unique
energy level given for insulators. The measured binding energies (ionization
potential IP) are referenced to the vacuum level. Metals have a well defined
energy EF , which is the boundary between occupied and unoccupied state.
EF can be identified in the spectrum as Fermi edge and serves as energy reference for metallic samples.
light is [68]:
dσ
dΩ
=
σ0
(1 + β(hν)P2 (cos θ)) ,
4π
(3.5)
where σ0 describes the photoelectric cross section. P2 (x) = 12 (3x2 − 1) is the Legendre
polynomial of second degree. The relevant angle between photoelectron emission and
light polarization is denoted with θ. The molecular asymmetry parameter β(hν) is a
function of excitation energy. This distribution is shown in Fig. 3.3 together with a graph
for anisotropy values for HOMO and HOMO-1 for C60 .
12
(b)
100
8
6
4
2
10
(c)
8
6
4
IMFP
Scattering Length (Å)
(a)
l3
l2
l1
α
z
10
100
1000
Kinetic Energy (eV)
Figure 3.2: (a) Universal curve after Refs [63, 64] to describe the attenuation of photoemission signal within a solid due to inelastic scattering. (b) Illustration of the
increased trajectory of an photoelectron originating in a depth z reaching the
analyzer in different emission angles. (c) The straight trajectory of an electron for a particular value for the inelastic mean free path IMFP compared
to a trajectory for the same value of the IMFP modified by elastic scattering
resulting in the elongated path l=l1+l2+l3.
β= 2
E
(b)
β= 1
2.0
Asymmetry Parameter β
(a)
1.0
β= 0
HOMO
HOMO-1
0.0
β=−1
-1.0
20
40
60
80
100 120
Kinetic Energy (eV)
140
Figure 3.3: (a) Polar plot of the angular intensity distribution of photoelectrons after
dipole absorption for different values of the asymmetry parameter (−1 ≤
β ≤ 2) with respect to the direction of light polarization. (b) Calculated
anisotropy parameter of free C60 as a function of kinetic energy of the
photoelectrons[69]. In photoemission experiments of gas phase C60 the values for β are found to be slightly increased[70].
13
3.1.1
Photoelectron analyzer
In order to record a photoemission spectrum the photoelectrons have to be separated by
their kinetic energy. In all experiments of the present work a hemispherical deflection
analyzer was used. The spectrometer consists of two parts: a lens system, imaging (magnifying) the sample spot onto the analyzer entrance slit, together with preretardation to a
pass energy and the analyzer. This analyzer consist of two concentric hemispheres. By
applying an electric field between the hemispheres the path of the electrons is influence
depending on their kinetic energy. In order to improve the resolution photoelectrons are
decelerated (or accelerated) to a pass energy before they enter the analyzer. Since their absolute energy spread is not changed by the deceleration (or acceleration) to a pass energy
this method has a gain in resolution which is proportional to Ekin /Eret . Electron entering
the analyzer with the same kinetic energy but different incident angles at the entrance slit
are focused onto the same spot of the detection plane. Electrons with different kinetic energies are separated in the dispersive direction at the detection plane. In the perpendicular
direction the sample is mapped spatially. The impinging electron is amplified by the multi
channel plate detector (MCP) to a measurable pulse. A phosphor screen on the other side
of the MCP transforms the pulse to a visible light spot. The phosphor screen is monitored
by a charge-coupled-device (CCD)-camera. The readout of the camera and the electric
potentials of the lenses and the analyzer hemispheres are controlled by a computer during
data aquisition.
14
Principle Set Up of Photoelectron Spectrometer
entrance slit
sample
s
ton
pho
Lens System
V+
Vret
phosphor
screen
V-
trajectories
CCD-camera
MCP
Figure 3.4: Illustration of a Scienta photoemission analyzer. The analyzer consists of a
lens system and hemispherical analyzer. Electric fields focused the electrons
on the detection plane. The electron impact is amplified the MCP and a light
spot on the phosphor screen indicates the signal. The CCD camera is recording the distribution of light spots on the screen. The direction of energy dispersion of the electron at the detection plane is indicated by the arrow. In the
direction perpendicular to the dispersion the analyzer gives a spatial mapping
of the sample.
15
3.2
X-ray Absorption Spectroscopy (XAS)
In XAS [71] the electronic and geometric structure of unoccupied states of the coreexcited system can be probed. In the dipole approximation Fermi’s Golden Rule gives the
absorption cross section for linearly polarized light[71]:
2
σXAS ∝ |·f |E · p| i| ρ(Ef )δ (h̄ω + Ei − Ef ) ,
(3.6)
where E is the electric field vector and p the electron momentum. The matrix element
consists of the initial and final state of the total system. However, in a more local picture,
the states involved in the transition are the core-level as initial and the valence orbital
as final state. Thus, the overlap of the atomic core-level |i and the valence orbital f |
making it a local tool measuring the unoccupied states at the site of the core-hole
There are two aspects for XAS measurements: (1) probing the spatial orientation of the
sample, and (2) probing the electronic density of unoccupied states of a system. (1) The
dipole matrix element f |E · p| i must be totally symmetric. This sets constraints on the
final state wave function and by changing the direction of light polarization it possible to
probe the spatial orientation of the system. (2) The density of unoccupied states is probed
by sweeping the photon energy in the vicinity of an absorption edge of an atom. The
measured density of states is modified by the presence of the core hole with respect to the
ground state.
A more technical issue is that the light absorption cannot be measured directly, since
the samples investigated here are to thick and all light is absorbed. Thus the absorption
has to be monitored via a secondary process as, e.g. the electrons released in the decay
of the core-hole excited state. In Fig. 3.5 photon absorption and different decay channels
are illustrated. Upon absorption the core-hole excited state decays within a few tens of
femtoseconds by emission of a photon (fluorescence-) or Auger-electron (Auger-decay).
The number of emitted particles in the decay is proportional to the number of adsorbed
photons, thus reflecting the absorption cross-section.
A common method to measure the XAS-profile is to collect the emitted electrons using
a multi channel plate (MCP). A MCP consists of an array of small diameter glass tubes
with a high voltage applied between both ends of the tubes. An electron entering tube will
create a multitude of electrons by impinging at the tube walls resulting in a measureable
current pulse. The MCP can be biased by a retardation voltage to filter out the lower
kinetic energy part of the electrons. This is often used in XAS and the measurement is
called partial yield.
In so called total yield (TY) spectra no retardation voltage is applied and electrons of
all kinetic energies are collected. In a so-called partial yield (PY) a retardation voltage
Vret is applied to allow electrons only with the minimum kinetic energy of eVret to reach
the analyzer. This influences the surface sensitivity of XAS. Electrons emerging from
deeper regions in the bulk will be scattered inelastically on their way to the sample surface
and will leave the sample at low kinetic energy. Thus by setting a retardation voltage the
surface sensitivity in the XAS spectrum can be varied.
The measured XAS signal depends directly on the incident photon flux. The photons
are reflected on several optical elements before they reach the sample. Unfortunately the
optical elements are often contaminated with carbon particle. These particle adsorb a
fraction of the photons. As a result the synchrotron light will show a structured distribution of intensity in the energy region of interest. To overcome this problem a reference
spectrum has to be recorded on a carbon free sample, e.g., the cleaned substrate or on a
16
(a) Photon Absorption
(b) Decay of excited state
Unoccupied hν
{
Valence-Levels
hν
Occupied
Valence-Levels
hν
Core-Level
Photoemission
Auger decay Flourescence
(Spectator)
decay
(Elastic)
Excited
state
Figure 3.5: Schematic of the process in XAS. (a) The incoming photon can excite the
atom resonantly or promote a photoelectron into vacuum (direct photoemission). The first leaves the atom in an excited state. (b) Two decay channels of
the core-hole excited states are possible. In electron yield measurements both
the direct photoelectrons and the Auger-electrons are recorded.
gold mesh, placed in the beamline before the analysis chamber and with a fresh layer of
cold sublimed onto the grid before measurement.
A typical reference spectrum shows the well-known losses due to carbon contamination at the optical elements in the beamline, see the dotted line (upper curve) in Fig. 3.6,
the so-called carbon dips. The XAS raw data from the sample need to be corrected for
these variations in the photon intensity by an appropriate method. Assuming that the
structure is solely due to carbon losses the XAS raw data simply have to be divided by the
throughput. However, most of the curves in Fig. 3.6 show extra structure at 288.5 eV. This
extra structure is due to excitations by higher-order light. A correction for higher-order
light contributions is discussion in chapter 8 and in paper VII.
3.3
X-ray Emission Spectroscopy (XAS)
Soft x-ray emission spectra are recorded by monitoring the photons of a fluorescent Auger
decay as a function of energy. The probability of such a fluorescent deacy is about two
to three orders of magnitude less compared to electronic Auger decay. In contrast to the
methods described above the final state in resonantly excited XES is electrically neutral.
The spectrometer at I511 used in the present work is based on three gratings mounted at
fixed angles of incidence and a large two-dimensional detector which can be positioned
and oriented. The detector can be moved in a three-axis coordinate system in order to
cover the different Rowland curves defined by the different gratings. The spectrometer
was developed in the group in Uppsala[72]. Its principle set up is sketched in Fig. 3.7.
17
Different Beamline Throughputs at MAX-lab
Intensity
Bl22, 1992
I511
D1011, May 2000
282
284
286
288
290
292
Photon Energy (eV)
294
Figure 3.6: Clean crystal absorption spectra in total electron yield from bending magnet
(BL22, D1011) and undulater (I511) beamlines at MAX-lab. Typically three
dips are seen in the spectrum. The dips can be disentangled in components
due to carbon and due to Cr absorption. See text for more details.
Two-dimensional detection is used to allow a large solid angle in the non-dispersive direction, without suffering from loss of resolution due to imaging errors. Spatial resolution
in the dispersive direction makes it possible to recored a full spectrum in one detector
position.
3.4
Synchrotron Light Sources
For the experiments described in this thesis a synchrotron light source was used. As know
from classical electrodynamics,see e.g.Refs. [43, 73] a charged particle is emitting electromagnetic radiation when it is forced on a curved trajectory. In order to store the parti-
De
te
ct
or
ns
to
pho
Sample
Slit
Grating
Figure 3.7: Illustration of the principle of a Rowland circle for XES.
18
cles they are circulating in a storage ring. In order to keep them in the same orbit, energy
has to feed back into the particle beam, unsually done with a radio frequency (RF) electric
field. Magnet fields are used to control the trajectory of the electrons. Depending on the
energy of the charged particle and the curvature of the trajectory the energy of the emitted
radiation can be tuned. Three types of radiation sources are distinguished: bending magnet, wiggler and undulator. The experiments of the present work were done at bending
magnet and undulator beamlines at MAX-lab. The bending magnet is a dipole magnet
at a vertex in the storage ring, its synchrotron radiation gives a large range continuous
spectrum. The most selective insertion-device is the undulator. An undulator consists of
a series of permanent magnets in a way that constructive interference is achieved between
light pulses emitted at different magnets. There the particles are forced to change trajectory several times, generating a narrow cone of light at a characteristic frequency. In most
cases the insertion devices deliver polarized light with the polarization direction in the
plane of the storage-ring.
MAX-lab is based upon a race-track microtron injector, a storage/pulse-stretcher ring,
MAX I (550 MeV), and a third generation storage-ring, MAX II(1.5 GeV).
I811
I911/1-5
I1011
10 m
D1011
D811
I711
73
1.5 GeV
MAX I
52
MAX III
550 MeV
41
MAX II
700 MeV
D611
33
33 32 31
NIM
I511/1
I511/3
I411
I311
Figure 3.8: Schematic of the MAX laboratory showing the two storage rings MAX I and
m MAX II at present in operation. The new storage ring MAX III is not under
commission yet. Beamline 33 is shown at its present and future location.
Beamline BL33 at MAX-lab
Beamline 33[74, 75] is a bending magnet beamline located at MAX-I. Beamline 33 is
used for angle resolved photoelectron spectroscopy on solids in the photon energy range
15 eV to 200 eV. The monochromator has three gratings (300 l/mm, 700 l/mm and 1500
l/mm) and a movable exit slit. The spot size on the sample is 2×1mm2 . The experimental
19
station is a commercial surface science system from VG Microtec. The system consists of
a preparation chamber, a sample storage chamber, a sample introduction chamber and an
analyzer chamber. The preparation chamber is equipped with LEED, ion sputtering gun,
gas-inlet system and a number of optional ports for user owned sample preparation accessories. The analyzer chamber is equipped with LEED. The goniometer mounted angular
resolved electron energy analyzer (ARUPS10) specially designed to have an electronically variable angular resolution from ±0.4◦ to ±2.0◦ .
Experimental Geometry at BL33
(h)
(v)
n
E
e-
α φ
S
sample
Figure 3.9: Schematic of the experimental set up at BL33. The light polarization is in the
plane of the paper. The sample can be rotated around an axis perpendicular to
the plane of the paper. The analyser can be rotated around the same axis like
the sample, polar angle and perpendicular to this (azimuth angle). The light
incidence angle is φ, the polar emission angle α
Beamline D1011 at MAX-lab
Beamline D1011[74, 75] is a bending-magnet based beamline at MAX-II covering the
energy range 30 to 1500 eV with an energy resolution of about E/dE = 1x104 . The
monochromator is of modified SX-700 type (360 l/mm and 1220 l/mm gratings) with
a plane-elliptical focusing mirror and fixed exit slit. The Spot size on sample is 1(v) x
3(h) mm2 . With its flat intensity curve and its particular experimental geometry with light
incidence normal to the sample surface it is ideal for investigation of molecular orientation
with XAS. The endstation consists of a vertical arrangement of preparation and analysis
chambers accessible via a long-travel manipulator. The preparation chamber is equipped
with ion-gun, gas-inlet system, mass spectrometer and LEED. The analysis chamber is
equipped with a Scienta 200 analyzer for photoemission experiments and a multi channel
plate detector for electron yield XAS. The Scienta is placed at a fixed angle of 40◦ with
respect to the direction o light incidence.
Beamline I511 at MAX-lab
The surface branch of I511 is an undulator beamline at MAX-II, designed for surface
PES and XES measurements[76]. The monochromator is of modified SX-700 type with
250 l/mm and 1220 l/mm gratings, with a spherical focusing mirror and movable exit slit.
The available photon energies are in the range from 100 eV to 1500 eV with an energy
20
MC
P
Experimental Geometry at D1011
sa
le
mp
α
E
S
φ
Figure 3.10: Schematic of the experimental set up at D1011. The analyser position is
fixed. The sample can be rotated around the axis perpendicular to the plane
of the paper.
resolution of E/dE = 5x104 . The photon flux on sample is of the order of 1013 ph/s for
the 1220 l/mm grating. The preparation chamber includes LEED, mass spectrometer,
gas-inlet, ion sputter gun and a manipulator in horizontal mounting with a cryostat for
cooling. The analysis chamber is equiped with a grazing incidence grating spectrometer
for XES, a hemispherical PES analyser and an MCP detector for XAS. Both spectrometer
Scienta-200 and XES-300 can be rotated around the direction of light incidence, thus the
angle of polarization and emission can be varied independently.
3.5
The Surface Instrument in Uppsala
Since beamtime is coslty it is good to have a home lab to carry out preparation studies.
The surface instrument in the cluster laboratory in Uppsala consists of two preperation
chambers, which are equipped with standard instrumentation, i.e., gas inlet, ion sputter
gun, quadrupole mass spectrometers and Low Energy Electron Diffraction (LEED) optics. The manipulators have a cryostat for liquid nitrogen or liquid helium cooling. The
electron analyzer is a Scienta-200. As a light source are a rotating Al-anode for XPS and
a He-discharge lamp for UPS available.
The Al Kα radiation (hν=1486.6 eV) are produced using an aluminium oxide coated
water cooled rotating anode. Electrons are emitted and accelerated in a two stage electron
gun, operated at a power of 3.5 kW with a 14 kV acceleration voltage. The electron
beam is focused onto the rim of the anode which is in rotation at a speed of 6000rpm.
To operate at this power water cooling for the anode is necessary to prevent melting. To
reach the fast rotating rim of the anode water is injected under high pressure through the
shaft. A two-stage differential pumping achieves UHV within the anode chamber. Upon
the electron bombardment the photons are created in fluorescence processes. The photon
21
Experimental Geometry at I511
n
E
Manipulator
sample
S
MC
P
Figure 3.11: Schematic of the experimental set up at I511. Both, sample and detector can
be rotated around the axis defined by the incoming light. The PES and XES
detectors have the same rotation axis as the sample.
bandwidth of approximately 0.8 eV is monochromatised to 0.2 eV via Bragg reflection at
seven quartz crystals arranged on a Rowland circle with the anode and the analyzer focus.
The He radiation is generated with a microwave driven electron cyclotron resonance
discharge lamp of Gammadata VUV 5000 type. With a grating monochromator the component of the He I or He II radiation (the photon energy of He Iα is 21.2 eV and that of
He IIα amounts to 40.8 eV) can be set.
3.6
Sample Preparation and Ultra High Vacuum Conditions
For the experiments described in this thesis ultra-high vacuum (UHV) conditions were
necessary to prevent contamination of the sample surface with adsorbed molecules. The
low pressure is achieved with different kinds of pumping (roughing pump down to p =
10−3 mbar, turbo molecular pumps to reach p = 10−9 mbar, ionization pumps reach p =
10−9 mbar and titanium sublimation pumps working in low 10−10 mbar range). In order
to drive off adsorbed molecules from the inner walls of the experimental chambers the
instruments are baked at 150◦ for approx 18 hours. Different gauges are used to monitor
the pressure: thermocouple (10−3 mbar range), cold cathode gauge (range: 10−10 mbar),
ionization gauge (range: 10−11 mbar).
At I511 the sample was mounted at a cryostat. With liquid nitrogen cooling the
sample temperature was T=110 K. At all other experiments the were done with the sample
at room temperature. In all experiments using single-crystals sample temperature was
monitored with Cr/Al thermoelement placed in a hole drilled in the respective crystal
(except at B L33 where a pyrometer was used). The temperature of the MWNT sample
22
Yt-2 fullerene preparation chamber
StarCell
120l/s
Cluster preparation chamber
Scienta 200
Rotating anode
Scienta 200
UV lamp
UV monochromator
Mirror
Analysis chamber
X-ray monochromator
MDC
MDC
MDC
MDC
200 l
StarCell
400l/s
StarCell
120l/s
300 l
X-ray monochromator
VARIAN
SD 300
VARIAN
SD 300
Figure 3.12: The Yt-2-instrument in Uppsala.
was monitored with a thermoelement clamped to the Si-substrate. The single-crystals are
heated resistively via tungsten wires (typical diameter of 0.5 mm, typical heating power
P=30 W) fed through holes drilled parallel to the crystal surfaces.
The single-crystals used for the C60 experiments are of 10 mm diameter and 3 mm
thick. Prior to C60 deposition the single-crystal samples where cleaned using Ar-ion
bombardment (sputtering), at kinetic energies of 0.5 keV - 1 keV. In order to help surface
reconstruction the sample is annealed for half an hour after sputtering. To prevent surface
melting the annealing temperature is held below 2/3 of the crystal melting temperature.
Cycles of sputtering (typically 5 min - 20 min) and annealing are repeated and the level
of contamination is checked with XPS. The quality of the surface checked with LEED.
The C60 was deposited from a Knudsen cell spot welded on an electrical feedthrough. To
form the Knudsen cell a Ta foil is folded to from a pocket. The C60 powder is filled in and
the pocket is spot welded at al three edges and a pin hole is made on the folded side. A
thermocouple is spot welded directly on the Ta foil to monitor the temperature. A spiral
tungsten wire was placed in the imediate vincinity of the Knudsen cell to help outgassing
the device. After the bake-out of the chamber, with the chamber still at elevated temperature of approx. 70◦ the Knudsen cell was outgassed in heating (typical heating power) the
Knudsen cell up to 900 K several times, until no sign of pressure increase was observed.
Sublimations were made typically at 700 K, without significant increase of the pressure
in the chamber.
The K3 C60 crystal is prepared in-situ on a Cu(111) substrate, grown in several cylces
of C60 layer deposition with successive K-intercalation. To prevent nucleation of K4 C60
the K deposition rate was chosen to keep the ratio of C60 to potassium below 3. After
each deposition cycle the sample was checked with PES. Finally the completed sample
was annealed at 600 K for 6 hours to sublime excess C60 in order to achieve a pure phase
sample[29]. The photoemission lineshape of the present sample is in excellent agreement
with the spectra reported by Hesper et al.[77] and Goldoni et al.[78, 79].
The ordered monolayer C60 on Al(110) was formed by subliming C60 from a Ta crucible (400◦ C) onto a cleaned Al(110) surface held at 400◦ during deposition. Since this
23
temperature is well above the sublimation temperature of solid C60 , only one monolayer
sticks to the surface. The typical ML c(4x4) overlayer is identified by LEED.
The MWNT sample investigated was prepared ex situ by the group of E. E. Campbell.
Here the sample preparation[80] is described briefly: A cleaned silicon substrate was
placed in a furnace (1050 K) and exposed to a flow of H2 , C2 H2 , F e(CO)5 and Ar
as carrier gas from a water-cooled injector. The iron particles serve as catalyst for the
carbon tube groth. After 30 min the substrate was covered with an even film up to several
square centimeter size. For the synchrotron radiation study the substrate is mounted on
the manipulator prior to chamber bakeout.
24
Photoemission Lineshape of Fullerene
Compounds
Valence photoemission from the fullerenes investigated in this work is shown in Fig. 4.1.
The C60 compounds presented here involve three fundamental interactions: van der Waals
crystal C60 , ionic solid K3 C60 and covalent bonded C60 monolayer on Al(110). The
surfaces and interfaces of these systems are of special interest and are investigated in
detail in the present work.
The lineshape of C60 fullerite is a fingerprint of its molecular structure. The highly degenerated bands give rise to well separated structures in the photoemission spectrum. The
other two C60 systems, however, exhibit spectra with considerably broadened features,
and the molecular orbitals cannot be unambiguously identified .
The spectrum of potassium intercalated compound K3 C60 shows a broad structures,
see Fig. 4.4(b). The lowest energy structure shows a distinct Fermi-Dirac-like shape and
identifies the system as a metal. The large width in K3 C60 photoemission has been explained for pure phase samples as broadening due to correlation effects[25], due to plasmon excitation[81] or surface states[82].
In the spectrum of the C60 monolayer, shown in Fig. 4.4(c) the molecular orbitals are
broadened and split into components. The large width of the molecular-derived levels of
monolayer systems has generally been attributed to substrate-induced hybridization and
concomitant energy level splitting [35, 83, 37, 84].
The lineshape observed for MWNT is characterized by increasing intensity from zero
at EF up to a maximum at about 8 eV and only very little structure within the spectrum,
see Fig. 4.4(d). No molecular like peaks are seen for MWNT. For MWNT there is a general consensus that photoemission should approach that of graphite, the variety in quality
of present samples, however, hampers a conclusive interpretation and the photoemission
results are discussed in literature,e.g., in terms of photoemission from the tips[59], presence of defect sites[57] or in terms of band dispersion[54].
4.1
Angular Distribution of Photoelectrons for solid C60
In Paper I the influence of the molecular solid on the angular distribution of photoelectrons is investigated. A series of photoemission spectra of a C60 multilayer is taken for
a large range of emission angles for different excitation energies and light polarization.
The spectra are corrected for acquisition time and photon flux. The sample consists of an
in-situ prepared multilayer of C60 on top of an Al substrate. The multilayer was annealed
after deposition to achieve a smooth surface. In Fig. 4.2 the raw data of angle dependent
photoemission of solid C60 are displayed. The data are taken at beamline 33. The 3-dim
graph visualizes the smooth intensity distribution peaking close to the angle of light polarization in all cases. For the low excitation energy data it is observed that the spectra are
25
(b)
HO
MO
-1
HO
MO
Pea
Solid C60
K3C60
{
K 3p
(c)
{
Intensity
(a)
kC
Fullerene Valence PES
LUMOderived
C60/Al(110)
Al Valence
(d)
20
MWNT
15
10
5
K3C60 Binding Energy (eV)
0
Figure 4.1: Valence spectra of the C60 systems and multi-walled nanotubes (MWNT)
sample taken at hν = 110 eV. (a) Molecular orbitals are labeled in the spectrum of solid C60 . (b) Photoemission from K3 C60 shows broad lineshape with
subtile structures. The cut- at the LUMO-derived structure indicates a metallic system. (c) The lineshape of the C60 monolayer spectrum is broadened,
the Al substrate signal spectrum consists is almost constant in the displayed
spectral region. (d) Spectrum from MWNT shows no MO structure. The
spectra shown here are aligned in energy arbitrary for the ease of comparison.
shifted in energy for different emission angles. This is attributed to charging of the sample
during the photoemission process. The fact that charging is only significant in the 32 eV
data can be attributed to the difference in photoelectric cross-section which is about one
magnitude higher at 32 eV than for 110 eV excitation energy[85]. To obtain the angular
distribution of photoelectrons the individual orbitals in the series of spectra is fitted with
Gaussians. The result of the fitting is shown in Fig. 4.3. In order to model the angular
distribution of photoelectrons emerging from solid C60 the process is divided into three
steps[86]:(1) emission of the photoelectron at the molecule (primary intensity), (2) traveling of the photoelectron to the sample surface and (3) escape from the sample into vacuum. Since the molecules are rotating almost freely at their lattice position[20, 21, 4, 22]
at ambient temperature the angular distribution from the first step is assumed to be equal
to the gas phase result. The primary intensity is dependent only on molecular properties
26
Figure 4.2: 3-dim plots and corresponding intensity image of angle dependent photoemission of the three frontier bands (HOMO, HOMO-1 and Peak C) of solid
C60 . The AD is smooth without fine structure. The direction of light polarization (normal emission) is indicated by a solid-(dashed-)line in the intensity
images. The emission angle is given with respect to the sample normal.
and on the direction of light polarization with respect to the detection direction. In step
(2) inelastic scattering will attenuate the photoelectrons on the trajectory to the surface in
27
Influence of the light polarization for solid C60
(a)
(b)
1
o
Polarization 45
Polarization 5o
2
1
0
0
15
10
o
20
10
5
0
Polarization 25
o
(d)
30
hν = 32 eV
(c)
Polarization 45
Intensity (arb. units)
3
hν = 110 eV
2
0
-40
0
40
80
-40
0
40
80
Emission Angle (o)
HOMO
HOMO-1
Peak C
Model, β = 1.1
Figure 4.3: Angular distribution of the three frontier bands of C60 fullerite as shown in
Fig. 4.2. Every data point corresponds to a fit value, as explained in the text.
The solid lines are the expected AD scaled to approximate the HOMO and
HOMO-1 distribution. Light polarization is indicated by dashed-dotted- and
normal emission by dashed-lines. The analyzer cut-off is indicated by arrows.
See the text for more details.
the spectral region of interest. Thus to describe this step the solid state properties like the
emission depth z, emission angle α with respect to the surface normal and the inelastic
mean free path λ are important. Approximating the photoelectron trajectory as a straight
line the intensity will be attenuated according to an exponential decay[87]:
dI(α)
z
= e− λ cos α dz
(4.1)
with the inelastic mean free path λ. The integral for a semi-infinite sample is proportional to cos α. In step (3) another solid state effect, the refraction of the photoelectrons
at the surface potential barrier influences the angular distribution. The primary angular
distribution is essentially of the form cos2 α which is rather insensitive to photoelectron
refraction. A correction for the present data with an inner potential of V = 5 eV[88] did
not change the angular distribution in the spectral region of interest.
28
In addition to the three steps just mentioned another geometrical factor has to be considered for cases of light spot sizes larger than the analyzer acceptance angle. At normal
emission the light spot area is bigger than the analyzer acceptance area, and by moving
the analyzer away from normal emission, the acceptance area, and with it the number of
photoelectrons reaching the analyzer, increases by 1/ cos α. Thus the number of photoelectrons increases until a critical angle αc is reached at which the acceptance area covers
all of the light spot. The area of the light spot depends on the light incidence angle, and
with it on the light polarization angle, since the light polarization is perpendicular to the
Poynting vektor. The critical angles for the analyzer cut-off in the experiments carried out
at beamline 33 are given in Tab. 4.1. This geometrical factor cancels with integral over
the exponential in Eqn. 4.1. This makes photoemission from solid state proportional to
the primary free molecule photoemission for emission angles α ≤ αc .
Table 4.1: Width w of the illuminated sample area for different light incidence angles φ
at beamline 33. For emission angles greater than αc the photoelectron analyzer
acceptance area is larger than the illuminated area.
φ
w
αc
45◦
2.8 mm
57.6◦
25◦
4.7 mm
71.5◦
5◦
> 10 mm
81.4◦
The primary distribution is calculated by the differential cross section for dipole transition [66, 67] for the free molecule according to Eqn. 3.5. Model curves determined by
β[69] and corrected for the analyzer cut-off are shown in Fig. 4.3 as solid lines. The
model reproduces the gross structure in the experimental data. The light polarization
dominates the gross distribution resembling the free molecule emission. The main difference is the drastic change in slope due to the analyzer cut-off at large emission angles.
The experimental curve is more compressed towards normal emission than expected by
the model for the expected value of β. Even a model including the maximum value of
β = 2 cannot reproduce this compression. Since all intermolecular scattering is included
in the primary photoemission and the intramolecular inelastic scattering is covered by the
model discussed above a logical reason for the compression could be elastic scattering of
the photoelectrons. Typically elastic scattering is calculated by Monte Carlo simulations,
see, e.g., Refs. [89, 90, 91]. Their simulations show that the primary distribution is fanned
out more isotropically. However this is in contrast to the present experimental findings
of a compression towards normal emission. This difference could have its origin in the
granularity of the sample as compared to the continuum of scatterer assumed in the Monte
Carlo simulations. It can be imagined that the large size of the molecules and the lattice
spacing is leading to a redistribution of photoelectrons towards normal emission.
The second topic of this thesis is the charge transfer compound K3 C60 , issue of Paper IV and Paper V, ence of the light polarization on the photoemission lineshape of
C60 and K3 C60 is shown for three emission angles in Fig 4.4. From set of spectra in
Fig. 4.4(a)(b) it can be seen that the shape of fullerite MOs is constant, and even the
relative intensities are insensitive of emission angle and light polarization. Only in the
grazing emission spectrum with the lightpolarization parallel to normal emission changes
29
Influence of Light Polarization on Valence PES
Binding Energy (eV)
24
20
16
12
8
(a) Polarization = Emission
C60
hν = 133 eV
RT
Emission:
0o
45o
60o
Intensity
(b) Polarization = 0o
(c) Polarization = Emission
K3C60
hν = 110 eV
T = 110 K
Emission:
0o
45o
60o
(d) Polarization = 0o
20
16
12
8
4
Binding Energy (eV)
0
Figure 4.4: Lineshape of the valence band for C60 and K3 C60 at the indicated excitation
energy. The spectra are normalized to features in the deeper valence region.
The orientation of the light polarization plays an important role for the photoemission lineshape in the near EF valence region. The data are taken at
beamline I511.
in the relative intensities are observed.
There is no separation of the molecular orbitals seen in the valence spectrum of K3 C60 .
However, the angular dependence show in Fig. 4.4 is a reminder of the behavior observed
for solid C60 in that intensity decreases in the range from EF to 5 eV for grazing emission
if the polarization is fixed at normal emission. The K3 C60 valence lineshape is discussed
in more detail in Chap. 5.
There is a significant influence of the light polarization in the LUMO-derived region,
see Fig 4.5. In contrast to solid C60 with no inelastic losses the metallicity of K3 C60 provides a continuum of inelastic losses, which are apparent in the LUMO-derive spectrum.
Fig 4.5 demonstrates the change in background due to the inelastic scattered electrons by
30
LUMO-derived band of K3C60
a) 40o Emission
Intensity (arb. units)
0o Polarization
40o Polarization
0o Emission
b) 70o Emission
0o Polarization
70o Polarization
0o Emission
1. 5
1. 0
0. 5
Binding Energy (eV)
0. 0
Figure 4.5: PES Lineshape of the LUMO-derived band for K3 C60 for 40◦ and 70◦ emission angle taken at hν = 110 eV at T = 110 K; a spectrum taken in normal
emission is shown for comparison. All spectra are normalized to the intensity at EF . The intensity in the higher binding energy region increases with
emission angle suggesting that a significant fraction is due to inelastically
scattered photoelectrons. In addition to the dependence on the emission angle the direction of light polarization has influences on the contribution from
inelastically scattered photoelectrons in the spectrum.
optimizing the light polarization. The observation that the main emission direction is a
function of light polarization is relevant for measurements of the inelastic mean free path,
an effect, which has been neglected so far in measurement reported in literature. However, for non-optimized experimental geometries the inelastic scattered electrons from the
bulk component can contribute significantly to the surface spectral region complicating
the identification of the surface component. The decomposition of the K3 C60 lineshape
into surface and bulk structures is described in more detail in Chap. 5. As shown in Papers IV the LUMO-derived spectrum of K3 C60 constitutes photoemission from surface
and bulk molecules. In principle, surface and bulk contributions can be discriminated by
taking spectra at different emission angles.
The third topic in this thesis is the C60 monolayer. The main difference between the
bulk and the monolayer system is that the molecules have a well defined orientation with
respect to the substrate in the latter due to the interaction with the substrate. Therefore
the differential cross section can be investigated in detail. Raw data for C60 /Al(110) are
shown in Fig. 4.6. One lineshape out of the set in the raw data is shown in Fig. 4.1 above.
A visual inspection of the raw data suggests that both frontier valence orbitals are split
into two components respectively. The angular distribution of the components changes
with excitation energy. At higher excitation energy the angular intensity is emphasized
in direction of the light polarization. At lower energy, in particular at 32 eV, the distribution is more influenced by sample properties, showing a distribution almost symmetric
31
Figure 4.6: Photoemission data of C60 /Al(110) for a large range of emission angles for
the indicated excitation energies. The light polarization is at 25◦ with respect
to sample normal.
to normal emission. An analysis of the angular dependence and decomposition of the
lineshapes into components of the molecular orbitals is shown in Chap. 6.
32
4.2
Lineshape Analysis of K3 C60 and C60 /Al(110)
The photoemission spectra of the K3 C60 compound and the C60 monolayer are considerably broadened as compared to spectra from solid C60 . These complex structures are
disentangled onto components via angle-dependent PES for the first time. In order to
compare spectra taken at different emission angles the lineshapes have to be fitted to extract the angular distribution. A common way to analyze photoemission lineshapes is to
use a fit employing standard functions, like in the simplest case Gaussians (instrumental broadening and virbrations) or Lorentz functions (reflecting lifetime broadening), or
in case of asymmetric core-level lineshapes Mahan[92] or Doniac-S̆unjić[93] functions
(metals). Simulation of the present data with standard lineshapes did not result in a good
agreement with the data. Thus a different approach using empirical lineshapes was chosen to model the data for K3 C60 and C60 /Al(110). Empirical lineshapes are obtained by
taking the difference between two spectra. The ideal case would be isolated structures or
if there are at least significant difference in spectral features. The differences in LUMO
lineshape in Fig 4.5 are to small to obtain a reliable result, but the rich structure for the
monolayer valence spectra in Fig. 4.6 is an excellent candidate. The advantage of empirical lineshapes is that they do require as parameter only the relative scaling and the constant
off-set. The shape of the difference spectrum serves as criteria to find both parameters.
On the first hand the result should give a smooth lineshape with a ”physical” slope at the
low binding energy side. E.g., for a core-level a comparison to a Voigt function made of
the energy resolution and life-time broadening can give the ”minimum slope” of the tails
in the difference spectrum, since the result has to include these contributions in any case.
If possible, the analysis should be carried out on isolated structures in the data. For K3 C60
the C 1s line is an isolated structure with a significant angular dependence, as shown in
Fig. 4.7(a). First the core-level spectrum of K3 C60 fulleride is discussed. In the second
part the valence lineshape of the monolayer C60 is analyzed.
4.2.1
K3 C60 C 1s analysis
The K3 C60 spectra are analyzed with respect to contributions from surface and bulk photoemission. In order to vary the surface sensitivity and with it the respective contributions
spectra are taken at normal and at grazing (70◦ ) emission, shown in Fig. 4.7(a). The
visual impression of the K3 C60 lineshape suggests two contributions. The first contribution (surface contribution) is obtained in scaling normal and grazing emission data to
match approximately at the shoulder at 284.3 eV and taking the difference. The scaling
factor is chosen that the normal emission data are always below lineshape of the grazing
emission data. For too large values of the scaling factor the difference spectrum shows
kinks. A core-level lineshape showing kinks has no physical motivation. Thus the spectra should be scaled to be as close to each other as possible, without giving unphysical
results in the difference spectrum. From these constraints the value of the scaling factor is limited to a small range. Fig. 4.7(b) shows the difference spectrum for the scaling
shown in Fig. 4.7(a). In particular the low binding energy side serves as criteria for a
”physical” result, since the high binding energy of the peak has significant background
due to inelastically scattered photoelectrons. This background does not increase linearly
with the scaling factor and is therefore artificially increased in the difference spectrum. A
suggested correction of the artificial tail is indicated by arrows in the lineshape of surface
component in Fig. 4.7(b).
33
Empirical lineshapes of the K3C60 core-level photoemission
fer
Dif
(a)
en
70° Emission
0° Emission
ce
(b)
Surface Contribution
Surface
Component
Sum
287
(c)
286
285
284
283
0° Emission
Surface
287
286
285
284
283
Di
ffe
re
nc
e
(d)
Bulk Contribution
Bulk
Component
287
286
285
284
283
287
286
285
284
Figure 4.7: Illustration of the analysis of the core-level PES using empirical lineshapes.
(a) Experimental data show a significant angle-dependence in the shoulder
at 284.3 eV. (b) Difference spectrum of normal and grazing emission data as
shown in (a). Two symmeric lines suggest two components in the surface
lineshape. (c) Normal emission data compared to the difference spectrum
from (b). (d) Bulk component as difference of the spectra shown in (c). See
the text for more details.
Once one of the contributions is determined the procedure to obtain the second contribution, which is the bulk contribution in the present case, is straight-forward. In Fig. 4.7(c)
the normal emission data and the surface contribution are scaled. The difference spectrum
constituting the bulk lineshape is shown in Fig. 4.7(d). In principle the same criteria on
34
283
Intensity (arb. units)
Bulk and Surface Contribution
of C 1s Lineshape
0° Emission
Surface
Bulk
Surface + Bulk
Bulk(29±10)%
Intensity (arb. units)
287
286
285
284
Binding Energy (eV)
70° Emission
Surface
Bulk
Surface + Bulk
Bulk (17±10)%
287
286
285
284
Binding Energy (eV)
Figure 4.8: Surface and bulk contribution in the K3 C60 photoemission lineshape.
the value of the scaling factor as discussed above can be applied. The overestimation of
the intensity in the high binding energy region of surface lineshape leads to uncertainties
in the high binding energy region of the bulk lineshape. A conservative margin of this
uncertainty is given by the arrows show in Fig. 4.7(d).
The contributions to the core-level spectrum of K3 C60 differ in their lineshapes. The
surface component is rather symmetric, whereas bulk contribution is asymmetric. The
surface component is relatively broad as compared to the core-level FWHM of solid C60 ,
and for reasons given in Chap. 5 it is fitted with two Gaussians, as shown in Fig. 4.7(b).
The asymmetry of the bulk component is a fingerprint of a metallic system.A Gaussian in
Fig. 4.7(d) illustrates the location of the bulk component in the spectrum.
Finally the bulk contribution in the normal and grazing emission spectra can be measured. A simulation of the experimental data with the empirical lineshapes is shown in
Fig. 4.8. The simulation shows a significant bulk contribution of 29 ± 10% in normal and
17 ± 10% in grazing emission. As discussed above the value of the scaling factor is not
35
definite. The large error given reflects the results from empirical lineshapes drawn from
extreme scaling factor. This present bulk contribution is in accordance with literature
by means of that the K3 C60 photoemission spectra are derived predominantly from the
surface layer[94, 82, 95], however, the bulk contribution is found to be somewhat higher
than expected. To summarize, from the angle dependence observed in the C 1s line it is
shown for the first time that the broad lineshape consists of surface and bulk contribution.
This enables the elucidation of the surface electronic structure of K3 C60 , which is topic
of Chap. 5.
4.2.2
C60 /Al(110) Valence Analysis
Photoemission of the valence region of C60 monolayer on Al(110) shows broad lineshapes. A series of spectra taken for a large range of emission angles shows that the
broad lineshapes consist of components with individual angular dependence, see Fig. 4.6.
From the individual angular dependence the empirical lineshapes of the components can
be drawn via difference spectra. Once the empirical lineshapes known the respective
angular distribution of the components will be obtained by fitting the set of spectra using the empirical lineshapes. A visual inspection of the data in Fig. 4.6 shows that the
HOMO-derived and the HOMO-1 derived region consists of two features respectively.
The features are labeled HOMO-a and HOMO-b, respectively for the HOMO-1-derived
components.
The first step in the analysis is the subtraction of the contribution from the Al sample,
which contributes essentially a constant background in the spectral region of interest for
the excitation energies chosen in this work.
In Fig. 4.9(a)(b) the HOMO-derived components are analyzed. Two experimental
spectra out of the series shown in Fig. 4.6 with different ration of HOMO-a and HOMO-b
are chosen. The experimental spectra in Fig. 4.9(a) are scaled to match the lineshape in the
low binding energy region. The difference gives the lineshape of the HOMO-b. HOMOb and the 30◦ emission spectrum are scaled as shown in Fig. 4.9(b), and the difference
gives the HOMO-a component. In a similar manner experimental data are scaled in the
HOMO-1-derived region and HOMO-1-a and HOMO-1-b are obtained, as illustrated in
Fig. 4.9(c)(d).
The lineshapes of the components obtained by the analysis are compared in Fig. 4.10(a)
to the valence photoemission of solid C60 . The empirical lineshapes are similar in width
and shape to HOMO and HOMO-1 photoemission from solid C60 . This similarity will be
discussed in more detail in Chap. 6. The empirical lineshapes are used to fit the raw data.
The good agreement between fit and experimental data is shown in Fig. 4.10(b). There
is an excellent in the HOMO-derived region, only small deviation are found in the region
very close to EF . However, the changes where to small and could not be investigated
in more detail. The model is less accurate in the HOMO-1-derived region, however, the
visual perception of the raw data is reproduced. As a result of the fit the angular distribution of the four components is shown in Fig. 4.11. The angular distribution changes with
excitation energy. This angular dependence of C60 monolayer is basis of papers II, III.
The angular distribution is discussed in more details in Chap. 6.
36
Analysis of the C60/Al(110) Valence
(a) HOMO-derived components
HO
M
O
-b
0° Emission
30° Emission
Difference (a)
Intensity (arb. units)
(b) HOMO-derived components
30° Emission
Difference (a)
Difference (b)
-a
MO
HO
(c) HOMO-1-derived components
0° Emission
12° Emission
Difference (c)
HOMO-1-b
(d) HOMO-1-derived components
HO
MO
-1-
a
12° Emission
Difference (c)
Difference (d)
4
3
2
1
Binding Energy (eV)
0
Figure 4.9: Analysis of valence PES of C60 on Al(110). The spectra are taken at hν=
32 eV excitation energy at the indicated emission angles. The Al background
has been subtracted. In every step one of the MO components is drawn as
difference spectrum.
37
Comparison of Components to Fullerite Lineshape
(a)
HOMO-1-derived
Solid C60
a
-b
-1
1O-
O
M
O-b
HOM
M
HO
HO
Intensity (arb. units)
HOMO-derived
HO
M
O
-a
Simulation of the Data with Empirical Lineshapes
(b)
data, 12o
fit
HOMO-a
HOMO-b
HOMO-1-a
HOMO-1-b
3
2
1
Binding Energy (eV)
Figure 4.10: Empirical lineshapes extracted from the valence PES signal. (a) The empirical lineshapes of the C60 monolayer system are similar in shape to the
solid C60 spectrum. (b) Simulation of the 12◦ emission data with empirical
lineshapes. The quality of the fit shown is representative for quality of fits in
the series of spectra.
38
Intensity (arb. units)
Intensity (arb. units)
Angular Distribution of MO Components
hν = 24 eV
HOMO-a
HOMO-b
HOMO-1-a
hν = 45 eV
80
-40
-20
0
20
Emission Angle (°)
40
HOMO-1-B
Intensity (arb. units)
Intensity (arb. units)
-40 -20 0 20 40 60
Emission Angle (°)
Legend
hν = 110 eV
hν = 32 eV
-40 -20 0 20 40 60
Emission Angle (°)
80
-40
-20
0
20
40
Emission Angle (°)
60
Figure 4.11: Result of fitting the raw data of Fig. 4.6 using empirical lineshapes as discussed in the text. The light polarization direction is indicated by a straight
line. At higher excitation energy intensity is enhanced on the positive emission angle side. At 32 eV excitation energy the angular distribution is symmetric with respect to the normal emission.
39
Surface Electronic Structure of K C
3
60
The character of K3 C60 surface has been the object of intensive study and debate for
almost a decade[27, 45, 77, 81, 82, 94, 79, 95, 96]. In particular it is discussed why
all photoemission spectra of K3 C60 consistently show broad valence, to little intensity at
EF and too wide LUMO-derived band in comparison with band structure calculations[97].
The width of the LUMO-derived band of the order of 1.2 eV has been attributed to correlation effects[25] or plasmon excitation[81]. Based on essentially the same spectra
Hesper et al. conclude the surface to be on average at half-integer charge state[77],
whereas Goldoni et al. conclude the surface molecules are identical to the bulk charge of
3 electrons[96]. In contrast to K3 C60 the valence band photoemission spectrum of the
doped monolayer on Ag with 3 electrons per molecule is very much narrower and has a
much higher density of states at EF [18, 98].
The K3 C60 valence lineshape characterized is by broad main peaks with subtle structures, i.e. shoulders, in the onset (lower binding energy side) of each filled band (e.g.,
at 1.6 eV, 2.9 eV, and 5 eV) as shown in Fig 5.1. As discussed in Sec. 4.1 the photoemission spectrum of K3 C60 shows a significant angular dependence suggesting surface
and bulk contribution, as discussed in Sec. 4.2 for the core-level spectrum, locating the
bulk structure at the lower binding energy side in the spectrum. A similar analysis of the
angle dependence in the valence region is complicated due to the broad structures in the
spectrum.
However, a connection between spectral features in the C 1s data and the valence spectra can be made, as shown in Fig. 5.1. Strikingly, the separation between shoulder and
peak of the HOMO-derived band are similar to those of the C 1s and a sum of core-level
lineshapes placed a energy positions of solid C60 lineshapes approaches the broad lineshape of K3 C60 . This assumes a rigid shift between energy levels for C60 . Rigid shifts
of valence and core levels in C60 -systems have not been discussed for this system, yet
they are obvious if one compares studies of charge transfer to C60 ML and in fullerides,
as discussed in Chap. 7. The assignment of the low energy features to bulk structure is
reinforced by comparing PES and x-ray emission spectroscopy. Due to the short electron
mean free path of the order of a few nanometers PES is very surface sensitive, in x-ray
emission however, due to the long photon mean free path in the order of hundreds of
nanometer reflects mainly bulk structure. K3 C60 PES and XES is compared in Fig. 5.2.
The peaks XES lineshapes correspond with shoulders in PES lineshape. Thus there is a
strong evidence for different molecular sites in K3 C60 , with the weaker and low-binding
energy side as representative for bulk structure. Another connection be made by the common temperature dependence in the shoulders in valence[79] and core-level[78] spectra
of K3 C60 .
The present assignment of spectral features in terms of different lattice sites implies
that the Madelung potential due to screening and/or charge states is significantly different
in the surface and bulk layers. To motivate the differences in lattice site the geometrical
40
Analysis of Valence Lineshape
K3C60
Valence
C 1s
Model
5
HOMO
HOMO-1
(b)
Peak C
Intensity (arb. units)
(a)
C60
Valence
C 1s
4
3
2
1
K3C60 Valence Binding Energy (eV)
0
Figure 5.1: (a) Normal emission valence PES spectrum of K3 C60 . The solid line is a
model given by the sum of the illustrated images of the normal emission C 1s
spectrum (dashed lines), placed below the valence peaks. (b) Comparison
with a pure C60 spectrum (shifted in energy) to help illustrate the rigid band
shifts. C 1s and the first fully occupied valence level are similar in width,
lineshape and energy separation in C60 and K3 C60 .
structure is discussed. Solid C60 constitutes a closed packed fcc lattice. Upon doping with
potassium the tetrahedral and octahedral sites are occupied. At the stoichiometry K3 C60
all tetrahedral and octahedral sites are occupied by 2 and 1 potassium atoms per molecule,
respectively. Due to the difference in Madelung potential the two sites are distinguishable
in PES with the tetrahedral site higher binding energy. K 2p photoemission with Al k-α
excitation shows the bulk ratio of 3:1 [99]. In more surface sensitive photoemission with
excitation energy of 365.5 eV the ratio appears to be almost equal[78]. This suggests
differences in the surface structure, however, this has not been discussed in literature. The
angular dependence of the K 2p photoemission is discussed in paper IV.
The discussion above shows that broad photoemission lineshape can be explained consistently in terms of surface and bulk contribution, in parallel the potassium shows surface
and bulk component. In the following I want to discuss the surface structure and in particular the question of metallicity of the surface. As observed by LEED and STM[30] the
K3 C60 in-situ prepared sample has a (111) termination plane. Along the {111} directions
the sample consist of alternating potassium (tetrahedral, octahedral, tetrahedral) and C60
planes. From electrostatic consideration Hesper et al. [77] find strict boundary conditions
for the macroscopic charge distribution over the K3 C60 crystal for this system. It turns
out that there are three possible configurations for the surface balancing the electrostatic
41
Intensity (arb. units)
Bulk Signal of K3C60
PES
XES
Bulk Levels
Surface Levels
14
12
10
8
6
4
2
PES Binding Energy (eV)
0
Figure 5.2: Non resonant x-ray emission and normal emission valence PES of K3 C60 .
The XES is aligned in energy to match the first structure in the PES. Solid
lines and dashed lines connect surface and bulk contribution in PES. The
structures in XES are more narrow than features in PES and the XES peaks
coincide with bulk structure.
forces within the crystal: an outermost C60 layer with average charge −1.5, K-layers as
termination plane at charge state +1 or +1.5. During the present experiments no degradation of the sample was observed over the period of more than the 36 h a preparation
was kept in the analysis chamber during measurements. E.g., K6 C60 is very reactive[77].
From this stability against oxygen contamination it does not seem likely that the sample surface consists of the rather reactive alkali ions. This leaves the alternative of an
outermost layer consisting of relatively inert C60 molecules.
An illustration of the K3 C60 with a topmost layer consisting of C60 is shown in
Fig. 5.3(a). The bulk consist of alternating potassium (tetrahedral, octahedral, tetrahedral) and C60 planes. All bulk molecules are charged with three electrons, since each
bulk molecules is surrounded by three alkali atoms on average and the LUMO is occupied with 3 electrons. The situation is different at the surface, where C60 is missing half
of the alkali neighbors. As it turns out, in this configuration the molecules are on average
in charge state 1.5-. Because of the molecular nature of alkali fullerides, this implies that
the outer plane consists of equal numbers of molecules C60 with 1 and 2 electrons in the
LUMO.
The differences in the number of electrons in the LUMO-derived is reflected directly
in the photoemission lineshape of the LUMO-derived band. The differences in charge
state are reflected in the photoemission spectrum and explain the shape of the LUMOderived with respect to the deeper valence structure. Taking the electron multiplicity into
account the LUMO-derived region is modeled in Fig. 5.4. The analysis above motivates
to model the LUMO-derived lineshape with three components, reflecting the bulk and the
two surface sites.
Fig. 5.4 shows an expanded view of the LUMO-derived PES. The 70◦ emission spectrum compares well with previous studies[81, 95]. The angle dependence shows that
42
intensity at EF drops with increased emission angle, assigning EF to bulk electronic structure, in parallel to the finding for the C 1s, that the low binding energy component belongs
to bulk structure.
To simulate the vibrational structure of the bulk component a gas phase spectrum is
used[12] of C−
60 , which was broadened to mimic instrumental resolution and convoluted
with a plasmon loss function in line with previous work [79, 81]. The surface components
are represented by symmetric curves similar to the components in Fig. 4.7. The distance
between the three components are extracted from the fit in Fig. 4.7. The separation between surface and bulk can be obtained from the fit shown in Fig. 4.7. The fit of the
C 1s line gives an approximate energy separation between the two surface components of
0.4 eV.
The ratio between surface and bulk structure is taken from the analysis of the C 1s
lineshape. Since photoelectrons have comparable kinetic energy in both spectra and the
C 1s lineshape matches the HOMO-derived band, thus the surface and bulk contributions
are comparable in both cases, and this information is used to model the LUMO-derived
PES data. Taking surface to bulk ration into account the relative ratio between the two
surface sites and the bulk are scaled according to the assumed charge state. The charge
state 1- is assumed to lie at the highest binding energy of the three, and 2- between 1- and
3- as indicated. The solid lines in Fig. 5.4(a),(b) are the sum of these three components,
taking electron multiplicity and surface to bulk ratio into account. It is apparent that
this model gives semiquantitative agreement with the measured spectra and their angle
dependence.
Now the question of the charge distribution at the surface is addressed, and its consequences on metallicity. The LUMO-derived band is occupied with one or two electrons
for the respective surface sites. In order to minimize the electrostatic energy the differently
charged molecules will be distributed evenly within the surface layer. A charge density
wave (CDW) is the simplest conceptual starting point to realize this structure. Three energetically equivalent structure are shown in Fig. 5.5, due to frustration the surface might
consist of several domains.
It is important to note that all molecular sites are equivalent regarding their Madelung
potentials. Thus the energy separation seen in PES can be estimated by taking only
electron-electron correlation into account,e.g., the interaction of the electrons on the
molecules U and the interaction with electrons on neighboring molecules V into account.
In CDW configuration as shown in Fig. 5.5 each molecule has six neighbors, always two
neighbors have the same charge like the molecule in question.
In Tab. 5.1 relevant energies for charge transfer in the surface and for photoemission are summarized. As it turns out the energy terms involved in PES from the surface
LUMO-derived bands are 10V for the singly-charged and 8V +U for the doubly-charged
molecules. The difference in energy between two sites is calculated by taking theoretical
values of U and V for negatively-charged molecules (1.1 eV and 0.35 eV, respectively
[44]) to 0.4 eV. Thus the splitting and the ordering of the molecular charge states in the
surface layer compares well with the model developed in the present work. The present
model has implications on the ongoing debate about the metallicity of the surface and
bulk, Hesper et al., Ref [94], claim that mainly the surface is metallic, whereas Goldoni et
al., Ref [95, 96] claim that surface and bulk electronic structure is identical. Our finding
that intensity at EF drops with increased emission angle is assigning EF to bulk electronic
structure. An open question is the extent to which surface molecules could contribute
to the spectrum at EF , since the angular dependence cannot rule out minor contributions
43
Table 5.1: Correlation energies of the K3 C60 surface electronic structure as shown in
Fig.5.5
Neighbor hop(neglecting U)
Transition number I:
Initial state for starting (-2) molecule:
2V * (2 * 2 + 4 * 1)
=
16 V
Initial state for finishing (-1) molecule:
1V * (4 * 2 + 2 * 1)
=
10 V
Total
26 V - 2V
=
24 V
Final state for starting molecule:
1V * (3 * 2 + 3 * 1)
=
9V
Final state for finishing molecule:
2V * (3 * 2 + 3 * 1)
=
18 V
Total
27 V - 2V
=
25 V
nearest neighbor transfer
=
V
Initial state for starting (-2) molecule:
2V * (2 * 2 + 4 * 1)
=
16 V
Initial state for finishing (-1) molecule:
1V * (4 * 2 + 2 * 1)
=
10 V
Total
16V + 10V
=
26 V
Final state for starting molecule:
1V * (2 * 2 + 4 * 1)
=
8V
Final state for finishing molecule:
2V * (4 * 2 + 2 * 1)
=
20 V
Total
8V + 20V
=
28 V
Transition II
=
2V
Initial state, now including terms in U:
U + 2V * (2 * 2 + 4 * 1)
=
U + 16 V
Final state:
1V * (2 * 2 + 4 * 1)
=
8V
Transition number II
PES
PES:-2-site:
Difference:
U + 8V
PES:-1-site:
Initial state:
1V * (4 * 2 + 2 * 1)
Final state:
=
10 V
0
Difference:
10 V
PES difference
U - 2V
44
from surface.
For the solid C60 the large on-site Coulomb energy U = 1.6 eV[25, 45] and the one
electron bandwidth W = 0.6 eV suggest K3 C60 to be an insulator, however, the lattice symmetry and Jahn-Teller-coupling enable conduction[100, 101]. At the presence of
different charged molecules, however, there is the possibility of charge transport without involving U . In particular charge can be carried at zero energy cost via next-nearest
neighbor hopping at defects, see Hesper, Ref. [102] for a detailed discussion. A mainly
defect free structure as shown in Fig. 5.5, however is mainly insulating. In defining the
transport properties the relevant Coulomb interaction is the intermolecular repulsion V
since a hopping from a 2- molecule to a 1- molecule does not involve U .
The electron transport at the surface is determined by V . Two possible ways of charge
separation are shown in Fig. 5.5. The CDW-configuration corresponds to an insulating
surface with a gap of 2V . Recall that the seperation between EF and the shoulder in the
valence is 1.6 eV, like it is expected from the fundamental gap[25] placing the HOMO of
the metallic bulk at the expected energy position.
Recently PES of a single layer C60 doped to charge state 3- has been studied in
detail[18], clearly, in the region where the surface states of solid K3 C60 appear, less intensity is observed in the single layer spectrum. This confirms the location of the charge
states C60 −1 and C60 −2 in the solid K3 C60 spectrum. This is the first report that shows
an model reflecting the the right spectral intensity of a half filled LUMO.
Thus for the first time the picture of the distribution of bulk and surface spectra for the
C 1s, LUMO-derived, and deeper valence bands are unified. The present work shows that
the observation of a superconductivity gap at EF [94] must be due primarily to an effect in
the bulk of the sample.
45
Schematic of K3C60 Surface and Bulk Charge States
(a) Top View
Legend
T1
T2
C601-
T2
O2
O1
O1
T2
T1
T2
T1
O1
O2
O1
O2
T2
T1
O2
(b) Side View
T2
1st tetrahedral layer
T1
1st tetrahedral layer
O2
1st octahedral layer
O1
1st octahedral layer
t2
2nd tetrahedral layer
t1
2nd tetrahedral layer
T1
bulk layer, C603-
O2
O1
T2
bulk sequence surface sequence
C602-
O2
O1
T1
tB
bulk tetrahedral layer
oB
bulk octahedral layer
sample surface
surface: C601-, C602-
T2
T1
T2
T1
1st tetrahedral layer
O1
O2
O1
O2
1st octrahedral layer
t2
t1
t2
t1
t2
2nd tetrahedral layer
bulk layer: C603-
tB
tB
tB
tB
tB
bulk tetrahedral layer
oB
oB
oB
oB
oB
bulk octrahedral layer
tB
tB
tB
tB
bulk tetrahedral layer
bulk layer: C603-
continuing bulk sequence
Figure 5.3: Illustration of the lattice structure of K3 C60 with a C60 plane as topmost layer.
The differently charged molecules are indicated. The alkali ions are labeled
according to the lattice site (tetrahedral: T, t, tB; octahedral: O, oB). The surface alkali ions differ in the charged C60 surface neighbors (t1: (1-,2-,2-) and
t2: (1-,1-,2-), likewise o1, o2 and T1, T2). (a) The topmost layer consisting
of C60 with alternating charge states.(b)The cross section shows the alternating C60 and K-planes. The three lines (dashed, solid, dashed dotted) in (a)
indicate different cuts through the surface. Molecules/alkali ions on identical
lines belong to the same slice as shown in (b).
46
LUMO-derived Band
Intensity (arb. units)
a) Normal Emission
B
S2
S1
b) Grazing Emission
S2
B
S1
1.2
1.0
0.8 0.6 0.4 0.2
Binding Energy (eV)
0.0
Figure 5.4: Simulation of the LUMO-derived band of K3 C60 . Experimental data are
shown for two emission angles. The energy separation and intensity ratio
of the components are obtained from the core-level, taking the electron multiplicity of the surface electronic structure discussed into account. The simulation consisting of contribution from bulk (B) and the two surface sites
(S1),(S2) resemble the experimental data for both emission angles.
Figure 5.5: Illustration of the surface electronic structure. The configurations (a)-(c)
are energetically equivalent. Paths for electron hopping are indicated. See
Tab. 5.1 for more information.
47
C Monolayer on Al(110)
60
Topic of this chapter is the interaction between the C60 molecule and the Al(110) surface.
The knowledge about the degree of modification of molecular structure upon adsorption is
of particular importance for the development of nanoscopic devices. The photoemission
lineshape of C60 adsorption systems [35, 37, 84, 36, 103, 104, 105] is broad throughout
the complete valence region. In literature it is speculated that the origin of the splitting and
broadening of the C60 bands is due to the symmetry-reducing substrate interaction and to
a hybridization with the electronic states of the substrate. Angle-dependent photoemission
shows that the lineshapes of the band components change relatively to each other. The
analysis of the angular distribution (AD) enables a more detailed understanding of the
adsorbate–substrate interaction.
Variation of Angular Photoelectron Distribution with Excitation Energy
HOMO-b
(d)
3000
2000
1000
-40
0
hν = 27 eV hν = 32 eV hν = 35 eV
1000
0
2000
0
(f)
6000
4000
2000
0
(g)
6000
4000
2000
0
6000
(h)
hν = 24 eV
(c)
2000
0
4000
hν = 45 eV
1000
HOMO-b
(e)
Intensity (arb. units)
(b)
2000
0
HOMO-a
hν = 50 eV hν = 110 eV
HOMO-a
(a)
hν = 40 eV
Intensity (arb. units)
1000
800
600
400
200
0
4000
2000
0
40 -40
0
40
Emission Angle (o)
-40
0
40 -40
0
Emission Angle (o)
40
Figure 6.1: Cross section effects in the AD of C60 /Al(110) for the two HOMO-derived
components. The light polarization is at 25◦ . All angles are given with respect
to the sample normal. The structure of the AD varies with the photon energy,
see the text for more details.
For the present work an Al(110) surface has been chosen as substrate for the following
reasons: (a) Al is a simple metal with very little structure in the spectral region of interest,
(b) a procedure to grow exactly one single layer C60 is well established [35], (c) no surface
48
reconstruction has been observed for Al(110) upon C60 deposition [35].
Legend
A
A'
B
Intensity
Molecular Angle-Dependence
Experimental
Data
HOMO-a
HOMO-b
-40
Calculation
-20
0
20
40
Emission Angle (o)
Calculation
(f) edge
(a) 6-6 bond
5
5
(b) 6-6 bond
(g) 6-ring a
5
5
6
6
5
5
(h) 6 ring b
5
6 6
(d) 5-6 bond
(i) 5 ring
(e) edge
(j) 5 ring
Emission plane
-40
-20
0
20
40
Emission Angle (o)
Intensity
Intensity
(c) 5-6 bond
Emission plane
-40
-20
0
20
40
Emission Angle (o)
Figure 6.2: Schematics of the molecular orientation and corresponding calculated photoelectron angular distributions for emission in the experimental emission
plane. The part of the molecule closest to the surface is shown, with the bond
or atom ”touching” the Al surface indicated by a thick line or a filled circle.
The curves are calculated for emission in a vertical plane with an orientation
as defined by the arrows. The experimental AD is given in the top graph. The
AD from density functional theory (DFT) calculations [106] is shown for the
indicated molecular orientations. The contributions of the calculation to the
emission intensity are marked according to the overlap of the wave functions
with the substrate: A = significant, B = non-significant overlap. In some cases
all components have significant overlap, marked with A and A’. See the text
for more details.
Due to the strong interaction with the substrate the molecules are in a fixed orientation.
No charge transfer from the Al substrate to the C60 LUMO has been observed suggesting
an interaction of predominantely covalent nature [35, 107]. The raw data have been introduced in Fig. 4.6. The labeling of the spectral features and the fitting of the data using
empirical lineshapes is described in Sect. 4.2.2. The angular dependence of the HOMO-a
and HOMO-b is shown in Fig. 6.1. The AD distribution consists of several peaks with
a strong dependence on the excitation energy. For solid C60 the AD was found to be a
49
(b)
(a)
Adsorption Geometry
Molecular Wave Functions in the Plane of Emission
HOMO-a
n
HOMO-b
C atom
C-C bond
n
[001]
[1-10]
Al
Al
Figure 6.3: (a) Suggested molecular orientation of C60 /Al(110). Only the carbon atoms
closest to the surface are shown explicitly. The C-C bond closest to the substrate is indicated by a thick solid line. The adsorption site depicted is arbitrary. The emission plane is indicated by arrows across the molecules. (b)
Contour plot of the wave functions of the HOMO-derived components. Portions with positive (negative) phase are shown as solid (dashed) lines, and the
nodal lines as dash-dotted lines. Circles show C atom positions, while the
squares indicate the intersection between the emission plane and C-C bonds.
The substrate and the surface normal are indicated. Only two out of the five
HOMO-components are shown, since the emission plane is a nodal plane for
three of the HOMO-derived components in this geometry.
smooth distribution with a maximum mainly determined by the angle of light polarization, see Fig. 4.3. This is observed at hν = 110 eV for the monolayer system, as shown
in Fig. 6.1(a). The AD has a maximum close to the direction of light polarization for both
components, HOMO-a and HOMO-b. For all other cases the ADs for the HOMO-a and
HOMO-b are more different. In particular for the HOMO-b another peak appears with
decreasing excitation energy at negative emission angles. New structures appear in the
AD of the HOMO-a for energies of about hν = 35 eV. For both components a AD rather
symmetric to normal emission is found for hν = 32 eV. This seems to be an energy at
which the influence of the light polarization is minimized. The hν = 32 eV AD will be
investigated further to determine the orientation of the molecules on the substrate.
The C60 molecule has three rotational axes, a threefold axes through the 6-ring, a fivefold axes through the 5-ring and a twofold axes through the 6-6 bond [108]. Furthermore
there are local two-fold symmetry axes at the 5-6 bond and the edge atom. These high
symmetry orientations are sketched in Fig. 6.2. Calculated ADs from DFT are shown for
all orientations. In cases (a), (c), (e), (h) and (i) three out of the five HOMO components
have a nodal plane in the plane of photoelectron emission, leaving only two contributions
to the photoemission signal in the emission plane. This matches the visual impression of
two components in the raw data. In all other cases the HOMO components have to be
arranged in two groups. Since the strength of the hybridization depends on the overlap of
the molecular wave function with the substrate the MOs are arranged into ”little overlap”
50
(B) and ”significant overlap” (A).
In order to determine the adsorption orientation the calculated ADs are discussed and
compared to the experimental data. The calculated AD in cases (a),(b) and (f) predict high
intensity at greater emission angles, whereas the experimental AD decreases at greater
emission angles. Geometry (d) does not fit since the component distribution with significant intensity at normal emission has only weak structures at very high emission angles, in
contrast to the observation for HOMO-a. Case (e) shows rather uniform distributions, and
therefore has no counterpart in experiment. There is no local maximum for the ADs in (g),
(h), (i) and (j). The remaining orientation (c) has one component with significant intensity at normal emission, and both components show the structures observed for HOMO-a
and HOMO-b. The relative placement of those structures is in quite good agreement with
experiment. A compression of the calculated AD towards smaller angles is expected in
parallel to the results for solid C60 as shown in Paper I. Thus the orientation with a 5-6
bond in contact with the surface and aligned to the [001] direction is the only reasonable
case. The orientation of the molecules on the surface is illustrated in Fig. 6.3(a).
A summary of the adsorption orientations of C60 on different substrates is given in
Tab. 6.1. In all stable monolayer cases C60 adapts its orientation to the substrate symmetry. The result of the present work is in excellent agreement with the orientations for C60
on the similarly structured surfaces Cu(110) [109, 110] and Pd(110) [111] determined by
XPD.
Table 6.1: Summary of C60 primary orientation for different stable monolayer systems
determined with X-ray photoelectron diffraction.
Sample
Contact to substrate
C60 /Al(111) [109]
6 ring
C60 /Cu(111) [112]
6 ring
C60 /Cu(100) [113]
edge atom
C60 /Ag(001) [114]
edge atom, 6-6 bond
C60 /Al(001) [112]
edge atom
C60 /Ni(001) [112]
6-6 bond
C60 /Cu(110) [109][110]
5-6 bond
C60 /Pd(110) [111]
5-6 bond
present work
C60 /Al(110)
5-6 bond
51
6.0.3
Splitting of the HOMO-band
As shown in Fig. 4.10 there is a splitting of 0.5 eV between the HOMO-a and HOMO-b.
The countour plots of the electronic wave functions in Fig. 6.3(b) show that the HOMO-a
has a significant overlap with the substrate, whereas the overlap of the HOMO-b is only
minor. It can be concluded that the HOMO-a is the component that is mainly involved in
the bonding. This assumption is reinforced by the observation that the low energy component is greatly broadened for increasing interaction with the substrate for the different
C60 /Al systems [35].
The HOMO-a has a higher probability to pick up electrons from the substrate after
photoionization and the screening of the final state is enhanced for the HOMO-a. A a photohole created by photoionization from the HOMO-b will be localized on the molecule.
The better screening places the HOMO-a at lower binding lower binding energy in PES
compared to the HOMO-b.
(a)
Screening of the photohole
in HOMO-derived components
HOMO-a
HOMO-b
+
Al
-
Al
Image Screening
"Metallic" Screening
(b) Determination of the Correlation Energy
one-hole states
two-hole state
Figure 6.4: (a)Illustration of the screening of a photohole in the HOMO-a and HOMOb. The photohole is localized at the HOMO-b and is screened by an image
charge in the substrate. At HOMO-a the the photohole is delocalized into over
the system consisting of molecule and substrate.(b) Experimental determination of the correlation energy Ucorr by comparing a two-hole state (Auger
spectrum) with two one-hole states (convoluted PES).
Assuming the extreme case of complete localization or complete delocalization, this
leaves the molecule with local charges of +1 and 0, as illustrated in Fig. 6.4(a) The difference in energy cost, i.e., the splitting of the levels, can be estimated to be the self-energy
of a single charge on an adsorbed fullerene. The aim in what follows is to relate the self
energy of a single hole to the measured quantity correlation energy U
.
In the following a system is assumed consisting of point charges qi = Q located at
positions distributed on the C60 shell. The self energy of the charges in the presence of a
potential can be written as [73]:
52
UΦ
1
q i Φi ,
2 i
=
(6.1)
where Φi is the potential of the field created by all other
charges, at the position of charge
qi . The potential can be written in terms of the charges qj = e
Φi
qj
.
Rij
j
=
(6.2)
Expressing the potential in terms of charges gives the self energy:
Σ1
1 qi qj
2
Rij
=
(6.3)
i=j
The correlation energy of two like charges localized on the molecule is [44]
qi qj
Ucorr =
Rij
(6.4)
i=j
The correlation energy Ucorr between two holes in C60 is measured from a the comparison of a two-hole state (Auger spectrum) with two one-hole states (convoluted PES)
[25, 45], as illustrated in Fig. 6.4(b). In order to see the contribution of the single charge
self energies inthis comparison the double hole situation is expressed in terms of the
double charge i 2qi = 2Q self energy
Σ2
=
1 2qi 2qj
2
Rij
(6.5)
1 qi qj
2
Rij
(6.6)
2Σ1 + Ucorr .
(6.7)
i=j
=
4
i=j
=
The double charge self energy can be split into the correlation energy and two single
charge self energies Σ1 . The energy comparison the two-holes state vs the two-one hole
state gives as difference Ucorr . This means that in both cases the single charge self energy
is identical, and a single hole localized on a molecule involves the single charge self
energy Σ. This is the energy splitting observed in the present case. A comparison of
Eqn. 6.3 and 6.4 gives
Σ1 =
1
Σcorr .
2
(6.8)
With help of Eqn. 6.8 the observed splitting can be related to the correlation energy measured for the monolayer. For C60/Ag(111) [46] the correlation energy was found to be
0.6 eV. Assuming a similar value for the present case gives a self energy of 0.3 eV. This
approach provides an estimation of the splitting and comes close to the observed value of
0.5 eV.
53
Rigid Energy Shift in Core-Level and Valence
Photoemission
Tab. 7.1 provides an overview over results in literature, supporting the idea that the energy spacing between core-level and valence-level is mainly a constant throughout many
systems studied so far. That C 1s and valence levels shift rigidly together is discussed on
some detail for ML systems[35, 46, 98, 115]. Tjeng et al.[98] discuss that Coulomb interactions do not cause considerable changes in the molecular orbital structure as a function
of doping is understood.
The parallel shift of core level and valence PES can be understood from the fact that
both electronic levels are rather insensitive to local potential variations. Valence orbitals
on the one hand due to their wave function delocalized the molecules. The core-levels are
insensitivity to local potential variations for the C 1s line due to the efficient polarization
screening[116] for pure C60 . The good screening is reflected in the narrow C 1s lines
observed for solid C60 and it can be surmised to hold for more complex cases such as C60
adsorbed on surfaces [32, 35]. All available data on bulk fullerides is consistent with the
presented model of a rigid shift of all levels in C60 upon charge transfer, as a function of
charge state. The shift holds as well for most monolayer systems. This table shows that
for all system, where the HOMO consists of a narrow line, or where components in the
HOMO could be identified, the difference to the core-level binding energy is 282.7 eV
within an interval of 100 meV. This is found for ionic and covalent systems.
The split in HOMO components is in the range 0.4 eV - 5.5 eV. This is in the order
of the single hole self-energy for a monolayer. Recall that for charge transfer systems the
energy difference between the HOMO and EF is close to the fundamental gap[25, 46] of
1.6 eV in all cases.
54
Table 7.1: C 1s and HOMO-derived binding energies for the indicated samples, illustrating the rigid-band-like relationship in cases of charge transfer bonding.
Sample
C 1s (eV)
HOMO (eV)
∆E (eV)
interaction
solid C60 [62](i)
289.6
6.9
282.7
vdW
K4 C60 [79]
285
2.3(m)
282.7
ionic
(m)
(c)
K6 C60 [45]
285.1
2.3
282.8
ionic
K3 C60 [79]
285
2.3(m)
282.7
ionic
K3 C60 (p)
285
2.3(m)
282.7
ionic
(m)
C60 /Cu(111)[34]
284.2
1.65
282.55
ionic/cov.
C60 /Ag(111)[103]
284.5
1.9
282.6
ionic/cov.
C60 /Ag(110)c(4x4)[33]
–
1.9(m) 1.5(t)
–
ionic/cov.
282.55
ionic/cov.
282.8
ionic/cov.
282.85
ionic/cov.
–
covalent
(m)
C60 /Ag(110)[117]
284.35
1.8
C60 /Au(110)[32]
284.4
1.6
C60 /Au(111)[118]
284.45
1.6(a) ,1.9(b)
(a)
(b)
C60 /Ge(111)[37]
–
1.5
C60 /Pt(111)[103]
284.2
2.1(m)
282.1
covalent
C60 /Ni(111)[103]
284.4
2(m)
,2
282.4
covalent
(m)
282.7
covalent
C60 /Si(111)(7x7)[84]
284.8
2.1
C60 /InPt(100)[105]
284.5
2.2(m)
282.2
covalent
C60 /Si(111)[36](f )
284.9
2.0(a) ,2.4(b)
282.9
covalent
C60 /Al(110)(p)
√
√
C60 Al(111)(2 3x2 3)[35]
283.93[35]
1.25(a) , 1.8(b)
282.68
covalent
284.05
1.25(a)
282.80
covalent
C60 /Al(111)(6x6)[35]
283.90
1.25(a)
282.65
covalent
(f) Reference to EF of a substrate in electrical contact with sample
(a) Low binding energy component of HOMO-a, (b) High binding energy component of HOMO-b
(c) Private communication
(i) Ionization potential, referenced to vacuum level
(m) Maximum of broad structure (p) Present work
Multi-Walled Nanotubes (MWNT)
8.1
Sample Characterization
On a micrometer scale the surface area of the MWNT is an evenly flat black material, with
some crater like spots dispersed over the sample area. The scanning electron microscopy
(SEM) image in Fig. 8.1 shows such a crack in the sample material. At the side walls
of the crack the aligned tubes are seen emerging from the substrate to the surface of the
film. From SEM images the length of the tubes is estimated to be more then 60 µm. No
large array graphite like flake structures are seen. The sample looks uniform and consists
almost entirely of MWNT’s. At higher magnification spots of a few nanometer size are
found dispersed on the sample. This structure is most probably due to amorphous carbon.
Prior to the spectroscopy experiments the sample was annealed at 600 K for 30 min in the
vacuum in order to drive adsorbates out of the sample.
Figure 8.1: SEM of the investigated MWNT sample at a spot showing a crack in the flat
surface area. At the side walls of the crack the macroscopic alignment of the
nanotubes perpendicular to the substrate surface is seen.
8.2
Orientation of MWNT on Nanoscopic Scale
In this section the quality of alignment on a nanoscopic scale is investigated. By employing angle-dependent XAS the intensity of the π ∗ - and σ ∗ - resonances is compared. This
ratio gives a measure of the average degree of alignment. A particular problem for XAS at
56
the carbon K-edge is encountered by intensity variations of the light beam, as illustrated in
Fig. 3.6. In order to quantify peaks in XAS these variations have to be measured by taking
a reference spectrum. Such a reference spectrum (the beamline ”throughput” spectrum)
can be measured on, e.g., a carbon-free substrate or a gold mesh typically placed before
the analysis chamber. A beamline throughput in the energy range of the carbon K-edge
is expected to show a double-loss structure due to carbon contamination at the optical
elements, often called carbon dips. However, most of the beamline throughputs taken
during the experiments of the present work show three structures, i.e. an extra structures
at 288 eV. The origin of this structure is not discussed in literature, in spite of the fact that
it has quite substantial contribution in the transmission function of many beamlines. A
throughput spectrum taken over a wide energy range shows another double-loss feature
at about 576 eV and 585 eV. This structure is due to photon absorption by chromium,
which is a common material for mirror coatings. However, in second-order light the Cr
double-loss show up in the carbon region with significant influence on the spectrum, see
paper VII for more details.
Suggested Throughput Correction
orption
tal Abs
rys
Clean C
Intensity
2
ted
Correc
1
ghput
Throu
Cr Structure
0
285
290
295
Photon Energy (eV)
Figure 8.2: Illustration of the throughput correction applied in the present study. Three
dips are seen in the clean crystal absorption (TY). The same region taken at
high retardation voltage, Vret = −340 V, shows Cr-induced structures in the
C 1s region. After scaling the Cr absorption spectrum to match with the clean
crystal absorption spectrum in the region about 288 eV a difference spectrum
is taken. The Cr-induced structures are removed in the differences spectrum,
the ”corrected throughput”. This spectrum is used in the analysis of the raw
data.
Correcting the throughput
As a first step the throughput has to be corrected for higher-order contributions. The
higher-order contribution can be measured by recording a spectrum at a retardation voltage Vret large enough to block the electrons excited by first-order light. As an illustration
spectra taken in TY and PY are shown in Fig. 8.2. The TY spectrum shows a triple loss,
whereas in the PY spectrum the loss at low photonenergies has disappeared. In order
57
to subtract the second-order contribution the PY spectrum is scaled so that the losses
match the corresponding losses in the TY throughput. The difference spectrum reveals
the ”pure” first-order structure reference spectrum. In the discussion above the contributions due to third- or higher-order light have been neglected so far. This is justified since
the intensity is decreasing fast with higher orders.
Correction of the Raw Data for Cr Contribution
(a)
Corrected Throughput
100
80
30
60
20
40
Raw Data
10
20
Cr
0
(b)
Intensity (arb. units)
Intensity (arb. units)
40
0
Raw Data divided by Throughput
Intensity
not Cr corrected
Cr corrected
282
284
286
288
290
292
Photon Energy (eV
294
Figure 8.3: Illustration of the XAS throughput correction in the raw data. (a) The corrected (first-order) throughput and the ”Cr”-spectrum (higher order) spectra
from Fig. 8.2 together with the PY MWNT raw data. The ”Cr” spectrum is
scaled to the maximum value judged by possible structure in the region of the
lower energy structure at 288.5 eV. Arrows indicate to which axes the data
refer to. (b) The raw data are divided by the throughput shown in (a) after
subtracting the maximal ”Cr” contribution as shown in (a). The spectra are
rescaled after subtraction for better comparison. The dashed lines are for the
ease of comparison.
Correction of the raw data
In cases where the substrate consists of a thick carbon film, as the sample investigated in
paper VIII the majority of the collected electrons will be carbon Auger electrons and the
58
first-order contribution will be dominating the raw data. However, for a carbon monolayer
a large second-order contribution is observed in the raw-data and a dominating structure
is seen in the raw data, as discussed in Paper VII. For the monolayer system the Auger
electrons and direct photoemission from the TiO2 sample excited by second-order light
have a significant contribution as compared to the monolayer signal. Similar to the correction of the beamline throughput the raw data are corrected for the contribution due to
second-order light. This is illustrated for the MWNT sample in Fig. 8.3. The raw data
show very little structure in the region 288.5 eV. The ”Cr” spectrum is scaled to approximate a maximum contribution in raw data. In Fig. 8.3(b) two spectra are shown, the
first one reflects the raw data simply divided by the corrected throughput, whereas for the
other spectrum the maximum ”Cr” spectrum was subtracted prior to the division by the
corrected throughput. The two spectra in Fig. 8.3(b) shows minor differences. The ”Cr”
corrected raw data the background between the main resonances is essentially flat.
Intensity
Determination of the π* to σ* ratio
MWNT
HOPG
π* Background
Simulation
upper limit
lower limit
π ∗-bac
kgrou
280
285
290
295
Photon Energy (eV)
nd
300
Figure 8.4: PY (Vret =-210 V) MWNT spectrum taken at normal incidence. Determination of the σ ∗ and π ∗ ratio in HOPG (taken at 45◦ ) and MWNT from Spot
A.
In paper VIII the orientation of nanotubes at the sample surface is investigated. As
described in Sec. 3.2, the XAS cross section strongly depends on the orientation of the
molecular orbitals with respect to the light polarization and can be used to map the spatial
orientation of a system. For the planar system graphite, the σ ∗ and π ∗ cross sections can
be zero for a particular orientation of sample and light orientation, see e.g. Ref. [119].
Angle-dependent XAS of the present sample did not show any significant change in σ ∗
to π ∗ cross section, suggesting a more disordered structure at the surface. In order to
quantify the average degree of alignment from the intensity of the σ ∗ and π ∗ resonances
in the XAS spectrum a ratio is derived from geometrical considerations, which can be
found in the appendix of paper VIII. As a result an intensity ratio of the π ∗ and σ ∗
59
excitations I CN T for isotropically oriented MWNT is expected to be
T
IπCN
∗
CN
Iσ∗ T
isotropic
=
Iπ0∗
.
3Iσ0∗
This ratio is given relative to the atomic cross sections I 0 for the respective excitations
of carbon atoms. In order to apply this result to the MWNT measurement the atomic
cross-sections are needed. Assuming that the cross sections are similar in graphite and
MWNT they can be estimated from a comparison to graphite XAS. In a graphite spectrum
taken at 45◦ incidence the π ∗ and σ ∗ resonances are excited with equal geometric factors.
Therefore, the atomic value I 0 in the derivation above are related to the experimental cross
sections of graphite I G by
G
Iπ0∗
Iπ∗
=
.
G
Iσ0∗
Iσ∗ 450
The intensities of the resonance in graphite and MWNT XAS are compared in Fig. 8.4.
The graphite spectrum is broadened with a Gaussian to make the area of the π ∗ resonance
equal for both spectra. A linear background, motivated by the spectrum of HOPG[120], is
used to separate the π ∗ and σ ∗ regions in the spectra. The background is subtracted from
the HOPG spectrum giving the ”pure” σ ∗ contribution in the region at higher photon
energies. The difference spectrum is scaled and added onto the π ∗ background of the
MWNT in order to match the σ ∗ region of the MWNT sample.
This estimation relies on the choice of the π ∗ backgrounds. In order to give an error margin on the presented procedure different backgrounds were employed in the data
analysis. The result for extreme values is shown by the solid lines in Fig. 8.4, giving a
conservative error margin of ±0.2 for the scaling factor. The scaling factors of the best
fit is 2, giving a geometrical ratio π ∗ /σ ∗ of 0.50±0.06. This value has to be compared
to the value of 0.33 derived above for an isotropic distribution. The value of 0.5 is larger
then the isotropic value. The higher experimental value suggests that in spite of the good
macroscopic alignment the tubes tend to lie parallel to the sample surface. This finding
can be rationalized considering the way the sample is grown. The carbon tubes start growing from nucleation sites on the substrate. Neighboring tubes sustain each other during
growth, which is the origin of the good macroscopic alignment. As soon as neighboring
tubes stop growing, the sustain is missing for the still growing tubes and these will bend
parallel to the surface.
60
8.3
Electronic Structure
PES of MWNT
(a)
Spot A)
(b)
Spot A)
Intensity
Spot B)
Spot B)
Spot C)
Spot C)
Spot D)
Spot D)
287
286
285
284
Binding Energy (eV)
20
15
10
5
Binding Energy (eV)
0
Figure 8.5: (a) Core-level and (b) valence-level PES of a MWNT sample taken at representative sample positions. Core-level spectra are taken at hν = 350 eV
and valence-level at hν = 110 eV excitation energy. The Shirley background
is shown in the core-level data. The lineshapes are changing with sample
position.
PES spectra were taken at different positions on the sample. The spectra shown in
Fig. 8.5(a) are representative for the spectral variations found by mapping the sample. All
core-level spectra show one peak of a broad and asymmetric lineshape, the C 1s spectra,
however, differ in peak position and width. As discussed in Paper VIII spectrum A consists a state-of-the-art spectrum. The smallest width observed in the sample is a FWHM of
0.63 eV. Due to similarities in (local) geometric structure it is natural to compare the spectrum to graphite. Graphite core-level lineshape has a FWHM of 0.36 eV[121] consisting
of (1) Lorentzian broadening due to the core-hole lifetime of ΓL ≤ 160 meV[122, 123],
(2) vibrational broadening of Γvib ≤ 100 meV[122, 123], and (3) a broadening due to the
surface screening shift (surface core-level shift, SCLS) of approximately 120 meV[123].
Related carbon systems with a stronger curvature than graphite have contributions of
similar magnitude, e.g., C60 (1) ΓL ≤ 150 meV[116], (2) vibrational broadening of
Γvib ≤ 320 meV[116], and (3) (SCLS) of approximately 100 meV[116]. Thus there is no
physical motivation to assume that theses principle values are changed significantly for
MWNT and can be the origin of this broadening. This suggests that the origin of the broad
lineshapes could to be some defect structure in the sample. In order to test this assumption
61
the core-level spectra are compared to the valence spectra for the respective sample spots.
To enable a comparison the excitation energies in both kinds of spectra were chosen so
that the kinetic energies of the photoelectrons were approximately the same, resulting in
comparable probing depth.
All valence spectra for the selected sample spots are show in Fig. 8.5(b). The same
gross structure, in particular the peaks at 7.5 eV and 13 eV and the kink at 3.3 eV, is
observed for all sample spots. A general observation is that the tail at the higher binding
energy side is varying in parallel for core-level and valence-level PES. Related to a high
background is a structure at 5.5 eV in the valence spectrum. Whereas the core-level
spectra show strong variations in peak position and width, the general structure of the
valence lineshape is constant. This can be understood from the fact that the valence
electrons are delocalized Bloch waves in the periodic potential[61] of the carbon atoms.
This makes valence PES less sensitive to local defects in contrast to core electrons, which
constitues a very local probe, sensitive to chemical shifts.
Compared to other core-level data in the literature spectrum A reflects the state-ofthe-art of present MWNT samples, see discussion in paper VIII. In Fig. 8.6 the MWNT
valence spectrum is displayed together with a graphite valence PES and a graphite bandstructure calculation[124]. A strong correlation between the structures seen in the MWNT
spectrum and regions of a high DOS in the graphite band structure is found. Dashed lines
connect critical points,e.g., regions with high density of levels of the band structure with
peaks and shoulders in the spectrum. To reinforce this correlation the data are compared
with the (broadened) total DOS of graphite in Fig. 8.6.
As discussed above the surface of the sample investigated consists of large diameter
MWNTs oriented on average parallel to the sample surface. Due to the intrinsic curvature
of the tubes together with a set of tube orientations at the sample surface this makes the
spectrum integrated over all emission angles and thus reflecting the total DOS.
To summarize, the variety of sample quality is found to be quite high. As discussed in
paper VIII this variation in lineshape is consistent with an interpretation of disorder and
structural defects. However, selected spots show very little defect structure with valence
spectra being in excellent agreement with graphite DOS. This is in agreement with the
general consensus that photoemission of carbon nanotubes should approach the electronic
structure of graphite.
62
Binding Energy (eV)
20
Intensity
H)
15
10
5
0
HOPG
MWNT
total DOS
DOS broadened
A)
K
Graphite Bandstructure
Γ
M
K
Figure 8.6: (a)Valence PES of MWNTs and HOPG[121] taken at hν =110 eV. Also
shown the total DOS of graphite[124]. (b) Graphite band structure calculation
from Ref. [124]. Critical points in the bandstructure are connected by dashed
lines with features in the MWNT spectrum. There is an excellent qualitative
agreement between the graphite total DOS and the MWNT spectrum.
63
Acknowledgments
Many people have contributed to the work presented in this thesis.
First of all, I would like to thank my supervisor Paul Brühwiler, from whom I have learnt
most of what I know about the fullerenes. He has not only been my supervisor, but also a
good friend.
I would like to thank Joseph Nordgren and Nils Mårtensson for giving me the opportunity
to do my PhD at Physics II and Physics V. Svante Svensson has been in charge of the
program during most of the time I have spent here, and I am grateful for his support.
It has been a fantastic privilege to work with my colleagues in the Kluster-Lab: Achim,
Carla, James, Lissy, John, Katharina, Barbara, Annika.
There are many present and former members of the group making Fysikum into the pleasant place it is: Anders H., Andreas, Arantxa, Cecilia, Dennis, Emma, Florre, Gunnar,
Henrik, Ingela, Karo, Lars-Åke, Li Min, Magnus, Marcus, Raimund, Tanel, Thorsten,
Charlie, Dimitri, Olle, Ruben, Annika, Birgit, Gunnel, Loa, Bo, Janne, Leif and Ulrik.
Thank you.
The experimental work done in Uppsala and in Lund would not have been possible without the profound knowledge of our engineers, the instrument makers at the mechanical
workshop and the staff at MAX-lab.
Petra, Ingrid and Thomas it was always great fun to have beamtimes and discussions
together with you.
During the last years I have had the pleasure to work with Pietro and Mauro from Trieste,
thank you for your excellent calculations and many fruitful discussions.
My most sincere gratitude goes to my parents for their everlasting support.
Last, but not least, I would like to thank my beloved wife Mirjam and daughter Annamaria. They are continually supporting me and have accepted many weeks of absence,
which is nothing as compared to being with them.
Thank you all!
Joachim Schiessling, Uppsala 2003
64
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Acta Universitatis Upsaliensis
Comprehensive Summaries of Uppsala Dissertations
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