ELECTRON SPECTROSCOPY OF SURFACES
Characterization of Solid Surfaces and Thin Films by
Photoelectron and Auger Electron Spectroscopy
F-Praktikum in den Masterstudiengängen Physik
Versuch Nr. 35
Lehrstuhl E20, Raum 229
Betreuer: Francesco Allegretti
1
Introduction
Electrons are well suited probes for the investigation of the electronic and geometric properties of clean and adsorbate-covered surfaces. Consequently, the use of electrons is the
basis of a plethora of experimental techniques commonly employed in surface science.
This experiment focuses on two techniques, Photoelectron Spectroscopy (PES) and
the photon induced Auger Electron Spectroscopy (AES), which both entail the detection of ejected electrons and are well-suited for investigation of the electronic properties
of atoms, molecules and solids and for elemental and chemical analysis of surfaces.
One of the main reasons for the widespread use of electrons as probes in surface science
is their short inelastic mean free path (λe ) in solids (Fig. 1). This quantity describes the
average distance that an electron can travel through the material without suffering energy
losses by inelastic scattering; it therefore provides an indication of the electron escape
depth. For electrons with kinetic energy in the range between 10 and 1000 eV, λe can
vary between 5 and 30 Å depending on the material and thus amounts to only a few atomic
layers. This ensures that in a typical experiment based on electron emission only electrons
emitted from a narrow region at the solid-vacuum interface can reach the detector without
energy loss. As a result, the PES and AES methods are highly surface sensitive.
During the experiment, the students will become familiar with the fundamental principles, the basic operation and methodology of PES and AES and will get an insight into the
underlying physics. The potential of the techniques and the range of information that can
be gained will be illustrated by considering a prototypical application, the condensation
of a magnesium film onto a tungsten surface and its subsequent oxidation. It will also be
shown that these nondestructive techniques are of relevance for a vast range of systems
not only in condensed matter physics, chemistry, and materials science, but also in applied
physics and even biophysics. The technical basis of the experiment encompasses:
• basics of ultra-high vacuum (UHV) technology
• generation of X-ray radiation
• analysis in energy and detection of electrons
• sample preparation: deposition of a Mg film by evaporation in UHV and subsequent
oxidation by molecular oxygen
Figure 1: Inelastic mean free path of electrons as a function of kinetic energy for various elements.
• computer control of the measurements; acquisition of a comprehensive data set
Gaining insight into the analysis and interpretation of the data and drafting a short scientific report (in German or English) are further achievements of this FOPRA experiment.
2
2.1
Photoelectron Spectroscopy
Basic principles
PES is based on the photoelectric effect, which was first observed experimentally by Hertz
and Hallwachs in 1887-1888 and explained theoretically by Einstein in 1905 [1]. Although
the effect has been well known for a long time, it took more than six decades of experimental developments before Siegbahn and coworkers succeeded in establishing PES as a
standard analytical tool in atomic, molecular, and solid state physics. The basic process is
illustrated in Fig. 2a: an incident photon of energy ~ω is absorbed by an electron system
(e.g., by a solid surface), promoting an electron from an occupied electronic level into
an unoccupied state. If this unoccupied state lies above the vacuum level, the electron
can escape into the vacuum and be detected by an energy sensitive analyzer. The energy
balance is the following:
~ω + Ei (sys) = Ekin + Ef (sys)
(1)
where Ei (sys) and Ef (sys) are the total energies of the system (atom, molecule, cluster,
or solid) before and after photon absorption, respectively, and Ekin is the kinetic energy of
the emitted photoelectron. In a simplified one electron picture (i.e., neglecting the energy
of mutual electron-electron interactions) the difference Ef (sys) − Ei (sys) can be simply
regarded as the binding energy of the ejected electron:
Eb = Ef (sys) − Ei (sys) = ~ω − Ekin
(2)
For a solid surface (Fig. 2b), binding energies are conventionally measured with respect to
the Fermi level rather than to the vacuum level, and the previous relationship is written
in the form:
Eb = ~ω − Ekin − Φw
(3)
where Φw represents the work function of the material.
2
z
photon
e-
hω
in vacuum final state
photoelectron
θp
Ekin
Φw
θe
y
φp
Eb
vacuum level
Fermi level
hω ω
φe
initial state
sample
x
(a)
(b)
Figure 2: Schematic view of the photoemission process: (a) a photon of energy ~ω impinges on a
solid surface, and after absorption of the photon an electron is ejected in a given direction (θe , φe )
with respect to the reference system; (b) corresponding energy balance within the framework of
the single particle (or one electron) picture. The work function is the minimum energy required
to remove an electron from the solid; it can be seen as the energy barrier that electrons have to
overcome in order to escape from the surface into the vacuum.
For a given photon energy, recording the number of photoelectrons as a function of their
kinetic energy yields a spectrum of distinct lines, which reflects - in the first approximation
- the energy distribution of occupied orbitals of the electron system under investigation.
Since the binding energies of the occupied orbitals and their sequence are different for
(and therefore characteristic of) each chemical element, photoemission spectra can serve
as “fingerprints” of the respective elements (Fig. 3). This renders PES a very useful
analytical tool, making it possible - for instance - to determine the composition of an
unknown sample and to assess the degree of cleanliness of solid surfaces.
Depending on the photon energy we discriminate core level PES (electrons excited
from inner shells → Eb ≥∼ 40 eV) and valence electron PES (electrons excited from
outer shells → 0 ≤ Eb ≤∼ 40 eV). The latter is named UPS (Ultraviolet Photoelectron
Spectroscopy) because UV photons from gas discharge sources or UV synchrotron beamlines are commonly used. PES with soft X-rays (~ω below 2-3 keV), which can excite
core level electrons, is labeled XPS (X-ray Photoelectron Spectroscopy). Typical light
sources are X-ray tubes with or without an additional monochromator, and soft X-ray
synchrotron beamlines. In the present experiment, XPS measurements will be performed
Figure 3: Photoemission spectra of the 1s core levels of the second row elements (taken from
Ref. [2]).
3
using the characteristic X-ray radiation from an aluminium anode (the Al Kα line at ~ω
= 1486.6 eV).
2.2
2.2.1
Spectral features and quantitative aspects of core level PES
Binding energy and the chemical shift
When comparing the binding energies of core electrons of a distinct atom in different
systems (i.e., in different molecules, compounds or solids), one finds that the exact value of
the binding energy depends on the chemical environment of the atom and that energy shifts
may occur when inequivalent atoms of the same elemental species are present (Fig. 4).
These energy shifts are termed chemical shifts. By comparison with data from wellknown “standard” substances the values of these shifts can be used in many cases for
the determination of oxidation states and of the nature of the chemical bond formed by
the atoms. This application of XPS, which is denoted by the alternative name ESCA
(Electron Spectroscopy for Chemical Analysis), is an important application of core level
PES in chemistry, surface physics and materials research.
(a)
(b)
Figure 4: (a) Chemical shifts in isolated molecules (C 1s and N 1s levels); (b) 4f7/2 core level shift
for a W(111) surface. In (b) the surface component at lower binding energy is clearly discerned,
whereas the component arising from the first sub-surface layer can only be detected by means of
a more sophisticated analysis. This special type of chemical shift originates from the different
coordination (→ different chemical environment) of surface atoms relative to bulk atoms: it is
usually referred to as surface core level shift. Panels (a) and (b) are both taken from Ref. [2].
4
2.2.2
Initial and final state effects in photoemission
In the analysis of the energy shifts in core level photoemission one can separate different
energetic contributions arising from distinct effects and different physical processes. These
effects can be classified depending on the fact that they act, respectively, on the initial state
of the system under study or on the final state reached after the photoelectron ejection [3].
Initial state effects
• Ground state effects:
Ground state effects are those contributions to the observed energy shifts that are
due to variations of the distribution of valence electrons depending on the chemical
environment, i.e. that are due to the electronic part of the potential. Experimentally
observed chemical shifts are only partly due to ground state effects. So-called final
state effects (see below) can also contribute to chemical shifts, and although their
contribution is often assumed not to be dominant, it cannot be neglected a priori.
• Reference level effects:
Shifts of the reference level for the kinetic energy scale may also contribute to experimentally obtained initial state shifts. In order to be able to compare Eb values, all
photoemission spectra have to be calibrated against identical reference levels. This
can be difficult for atoms in different environments. For gas phase measurements Eb
values are commonly referenced to the vacuum level, while - as noted before - for
solid state investigations the Fermi level is the commonly adopted zero point of the
binding energy scale. Therefore, if gas phase and solid state data are compared one
has to know the energy separation between the vacuum and the Fermi level ( = the
work function Φw , see Fig. 2b).
Final state effects
• Relaxation shift:
A very important final state effect is the relaxation of the electron system in response
to the creation of a core hole (= the vacancy in the inner shell) upon photoemission.
The core hole represents a positive charge acting on the remaining electrons, which
therefore rearrange themselves to shield the electron vacancy and to minimize the
total energy of the ionized atom. The screening of the core hole typically comprises
an intra-atomic and an extra-atomic contribution. The intra-atomic part is due to
the relaxation of the electrons (essentially, the outer shell electrons) of the excited
atom itself. For isolated atoms this is the only contribution. For atoms bound in
molecules or solids the electrons of the neighboring atoms are also polarized by the
creation of the core hole, although to a lesser extent, thus giving rise to the extraatomic component of the relaxation. Due to the energy conservation the relaxation
of the electron system reduces the apparent binding energy Eb measured for the
photoelectron. The energy balance before and after photoemission is, in fact:
~ω + Ei (N ) = Ekin + Ef (N − 1) =⇒ Eb = Ef (N − 1) − Ei (N )
where Ei (N ) is the energy of the ground state of the atom with N electrons and
Ef (N − 1) the energy of the final state of the ionized atom. If relaxation takes
place, the minimization of Ef (N − 1) leads to a decrease of the expected binding
5
energy. Because the screening of the core hole depends on the electronic environment1 , relaxations shifts differ from system to system for a specific core level line.
This difference, in combination with the initial state effects (see above), contributes
to the chemical shift.
• Multiplet splitting:
Removal of a core electron may create different final state configurations with different spin and orbital angular momentum, and therefore different binding energies in
PES (= different lines in the spectrum). In particular, multiplet splitting occurs if
the initial state of the photoionized atom contains unpaired electrons. For instance,
in the N 1s photoionization of an isolated NO molecule two lines are obtained, which
correspond to parallel or anti-parallel orientation of the spin of the residual 1s electron with respect to the unpaired electron in the molecular 2π orbital (triplet and
singlet final states, respectively).
Another example is given by some transition metal ions, such as Mn2+ [3]. Mn2+
has a high spin configuration, S = 5/2, in which all five 3d electrons in the outer
shell are unpaired and with parallel spins. If a photoelectron is ejected from the 3s
level, the exchange interaction between the spin of the remaining 3s electron and
the total 3d spin produces different binding energies for the two possible final states
S ± 12 = 3, 2. As a consequence, the 3s photemission line is split into a doublet,
where the 7 : 5 intensity ratio of the two components stems from the ratio of the
respective mS degeneracies.
• Spin-orbit coupling in the final state:
In the photoemission from p, d and f inner subshells the spectral lines are split into
two-component peaks (Fig. 5a). This splitting arises from spin-orbit coupling effects
in the final state [4, 5]. While in the initial state the inner subshells are completely
filled (for example, the configuration of the inner shells in gold is: (1s)2 (2s)2 (2p)6
... (4f )14 ... ), in the final state one electron has been removed and an unpaired spin
is left behind. The spin can be oriented up or down, and if the core hole belongs
to an orbital with non-zero orbital angular momentum (l > 0) there will be a coupling between the unpaired spin and the orbital angular momentum: the two states
j+ = l + 1/2 and j− = l − 1/2 are not degenerate and a spin-orbit split doublet is
observed in the photoelectron spectrum.
The intensity ratio of the two spin-orbit components is dictated by the ratio of the
respective multiplicities: (2j+ + 1)/(2j− + 1) = (2l + 2)/2l (Fig. 5b), which determines the relative probability of transition to the two states upon photoionization.
Generally, in the photoemission spectrum from a given subshell the core level subpeak with maximum j is detected at lower binding energy. Obviously, no spin-orbit
splitting occurs in the photoemission from s core levels.
• Multi-electron excitations and satellites:
The reorganization of the electrons upon creation of the core hole can lead to electronically excited final states. Because of energy conservation this excitation energy
is missing in the kinetic energy of the photoelectron: the corresponding satellite lines
1
For example, the screening ensured by electron rearrangement is typically more effective in metals than
in ionic solids, thanks to the availability of valence electrons (called conduction electrons) that are free to
move inside the material. Accordingly, the magnitude of the binding energy reduction due to relaxation is
more pronounced in metals than in ionic materials.
6
(a)
(b)
Au 4f 7/2
Subshell
Au 4f 5/2
Total angular
momentum j
components
Counts
s
Ratio of the
degeneracies
(g = 2j +1)
1/2
-
p
3/2, 1/2
4/2
d
5/2, 3/2
6/4
f
7/2, 5/2
8/6
Binding Energy (eV)
Figure 5: (a) Spin-orbit coupling leads to a splitting of the 4f photoemission line of gold into a
doublet [2]. (b) Table listing spin-orbit split components and intensity ratios for different subshells.
The notation n[l-subshell]j is commonly used (e.g., 4f7/2 ).
are therefore shifted to higher binding energy relative to the main core level line2 .
Different processes can be identified. Shake-up satellites occur when an additional
electron is promoted from an occupied energy level into a bound unoccupied state,
whereas shake-off satellites when the additionally excited electron is promoted into
a state in the continuum above the vacuum level (Fig. 6). Other possible satellites
are related to plasmon excitations. Plasmons are quasi-particles arising from the
quantization of plasma oscillation, i.e. of the collective oscillation of the free electron gas density with respect to the positively charged ion cores. Plasmon satellites
appear displaced to higher binding energy from the “elastic” line by amounts n(~ωp )
+ m(~ωs ), where n and m are integers and ~ωp and ~ωs are the energy of a bulk and
a surface plasmon, respectively. Finally, interband satellites in solids correspond to
transitions of additional electrons into unoccupied states above the Fermi level and
to the creation of electron-hole pairs. They may show up as discrete lines in some
cases, but commonly they give rise to an asymmetric broadening of the high binding
energy side of the photoemission peaks.
(a)
shake-up
(b)
shake-off
shake-up structure
CuO
Cu 2p1/2
Cu 2p3/2
970
960
950
940
930
binding energy (eV)
Figure 6: (a) Schematic of the shake-up and shake-off transitions; (b) Shake-up loss structure in
the Cu 2p spectrum of copper (II) oxide (CuO), adapted from Ref. [6].
2
Additional satellites in PE spectra occur when the photon source is not monochromatic (see §5.2).
7
2.2.3
Surface sensitivity and collection geometry
As noted in section 1, the surface sensitivity of photoelectron spectroscopy stems from the
short inelastic mean free path of electrons. While X-rays interact only weakly with matter
and consequently can penetrate deeply into a solid (1000 nm or more at ~ω ∼ 1 keV),
electrons with energy in the range 5-1500 eV readily lose energy by inelastic scattering.
XPS experiments are mainly concerned with the intensity of emitted photoelectrons that
have suffered no energy losses: therefore, the XPS sampling depth refers to a characteristic length over which electrons can travel without undergoing inelastic scattering events.
This quantity is the inelastic mean free path λe plotted in Fig. 1, which is defined as
the average distance that an electron of given kinetic energy Ekin travels between two
successive inelastic collisions [4]. In other terms, the probability for an electron to cover a
distance z in the solid without losing energy can be written as an exponential decay:
z
−
P (z) ∝ e λe
Z
=⇒
< z >=
zP (z)dz = λe
If an electron experiences energy losses, but still has enough energy to escape from the
surface into the vacuum, it will not contribute to the main photoemission line but rather
to a background signal on its low kinetic energy side. For the correct determination of
peak areas, peak positions and peak widths this background is always substracted3 .
If one considers for simplicity the electrons emitted in the direction perpendicular to
a solid surface, the previous considerations imply that a small element of thickness dz at
a distance z from the surface (z = 0 denotes the surface plane) gives a contribution dI to
the measured intensity:
z
−
λ
dI ∝ e e dz
(4)
For the total intensity I coming from a thin film of thickness t right underneath the surface
this yields (i.e., by integrating Eq. (4) between 0 and t):
I = I0 [1 − e−t/λe ]
(5)
The sampling depth of the XPS experiment is often defined as 3λe , which means that 95%
of the photoemission intensity of the core level line comes from the corresponding region
(3λe thick) below the surface [4].
When detecting photoelectrons emitted at an angle θe away from the surface normal
(see Fig. 2a), one has to consider the effective path z/cosθe of the electrons in the solid,
and Eq. (4) becomes:
z
dI ∝ exp[−
] · dz
(6)
λe · cosθe
Hence, in grazing emission geometry the sampling depth of XPS is reduced to 3λe · cosθe
and the surface sensitivity is strongly enhanced (e.g., θe ∼ 80◦ =⇒ cosθe ∼ 0.17).
2.2.4
Quantitation
From the previous discussion it is clear that an extended X-ray photoelectron spectrum
contains peaks that appear superimposed on a smooth background and can be associated
with the different elements (except H and He) present in the outer ∼50 Å or less of the
sample. Determination of the peak areas (appropriately corrected to take into account
3
Particularly at low kinetic energies (< 100 eV) the inelastic electron background is large due to the
increasing number of secondary electrons emitted in “cascade” processes.
8
instrumental factors) allows, in principle, an estimate of the elemental ratios, such that
the composition of the sample can be determined semi-quantitatively. To this purpose,
the absolute intensity I of the photoemission line i from an element A is usually expressed
as [4]4 :
ZZZ
z
] dx dy dz (7)
Ii,A = K · J0 · σi,A (~ω) · T (EA ) · Li,A (γ) ·
nA (z) exp[−
λe (EA ) · cosθe
Here, K is an instrumental constant; J0 is the incident photon flux, which is assumed for
simplicity to be independent of the (x, y, z) position inside the sample; σi,A (~ω) represents
the photoionization cross-section of peak i from the element A, related to the probability
of creating a photoelectron in the orbital i of A at the photon energy ~ω; T is the transmission function of the electron analyzer; Li,A (γ) describes the angular dependence of the
photoemission process (γ = angle between the incident X-ray beam and the direction of
the ejected electrons); nA (z) is the density of atoms A at a distance z below the surface
(neglecting lateral variations, i.e. parallel to the surface plane), and λe (EA ) is the inelastic
mean free path of electrons of energy EA in the material.
In most cases, calibration of absolute intensities based on Eq. (7) is not possible, since
instrumental factors may be difficult to determine. However, measurements of relative
intensities are valuable in practical experiments where elemental ratios are important,
such as - for instance - for the detection of relative surface coverages of adsorbates and
contaminants or for the determination of the stoichiometry of a compound.
2.2.5
Peak width of core level lines
The observed line shape of a given photoemission peak results from the convolution of
different contributions. These are related: i) to the equipment used in the experiment
(instrumental resolution); and ii) to the photoemission process itself (lifetime of the core
hole, presence of satellite features). To i) contribute primarily the linewidth and lineshape
of the photon source used for the excitation, and the energy resolution of the electron
energy analyzer employed to analyze in energy the distribution of photoelectrons. An
essential contribution to ii) is the peak broadening due to the finite lifetime of the core
hole; broadening by coupling to the nuclear motion (intra-molecular vibrations including
rapidly dissociating antibonding states, and phonons) and due to the presence of shake-up
satellites, electron-hole pair excitation and multiple splitting effects may be in many cases
non-negligible.
The spectral lineshape due to the core hole lifetime τ is Lorentzian [7]:
I(E) = I(Ec )
Γ2
(E − Ec )2 + Γ2
(8)
where I(E) is the intensity at the energy E, and Ec is the center of the Lorentzian peak
(when the spectrum is plotted in the binding energy scale, Ec is the binding energy Eb
of the “main line” satisfying the energy conservation law with the relaxation shift taken
into account). The energy broadening is therefore quantified by the the full-width at halfmaximum (FWHM) of the line, 2Γ, which is called intrinsic or natural linewidth and is
related to the lifetime through the following expression [8]:
2Γ =
~
6.58 × 10−16 eV · sec
=
τ
τ [sec]
4
(9)
Photoelectron diffraction effects arising from coherent scattering of the photoelectron wavefield by
neighbouring atoms are neglected in formula (7). This is correct, for example, in amorphous or polycrystalline samples and for angle-integrated mesurements.
9
2Γ is typically larger for inner shell orbitals, because these can be filled rapidly by electrons
from the outer shells. Therefore, for a given element 2Γ tends to increase with increasing
binding energy (for example: the natural broadening increases in the order 4f < 4d <
4p < 4s in gold). In a similar way, for a given core level orbital (e.g. 1s) 2Γ increases
as the atomic number Z increases, due to the higher valence electron density in heavier
atoms.
At variance with the Lorentzian broadening produced by the core hole lifetime, instrumental effects and vibrational broadening yield Gaussian lineshapes. In metals electronhole excitations at the Fermi edge can cause additional asymmetric line broadening, with
an asymmetric tail on the low kinetic energy side of the photoemission peak. Multiple
splitting and shake-up satellites also contribute with asymmetric broadening: depending
on their binding energy and the instrumental resolution they may or may not be resolvable
from the main photoemission peak.
The contributions of intrinsic and instrumental effects to the experimentally observed
linewidth can be combined to a first approximation into a quadratic sum [4]:
2
2
F W HMtot
= (2Γ)2 + F W HMX
+ F W HMA2
(10)
with the second and third term on the right side due to the X-ray source and analyzer
resolution, respectively.
3
3.1
Auger Electron Spectroscopy
Decay of a core hole
Photoionization of inner shell levels creates electronically excited states. These excited
states can decay via two different de-excitation routes:
(a) The hole in the inner shell X is filled by an electron from an outer shell Y , and
a photon is emitted. This is the well-known X-ray emission process or fluorescent
decay. The energy balance is:
~ω = Ei (X) − Ef (Y )
(11)
where ~ω is the energy of the fluorescence photon, and Ei (X) and Ef (Y ) are the
total energies of the system with holes in the shells X and Y , respectively.
(b) The hole in the inner shell X is filled by an electron from an outer shell Y as in the
previous case, but the excess energy is transferred to a third electron from an outer
shell Z, which is emitted. The process, called Auger decay, involves three electrons:
the electron knocked out in the initial ionization (photoelectron), the electron that
decays to fill the inner shell vacancy, and the emitted electron from the outer shell
(Auger electron). As a consequence, the final state is a doubly ionized state. Since
the energy is conserved during the transition, the kinetic energy of the emitted Auger
electron, measured with respect to the Fermi level EF , is:
Ekin,F = Ei (X) − Ef (Y, Z)
(12)
Here, Ei (X) and Ef (Y, Z) represent the total energies of the system with one hole
in shell X, and two holes in shells Y and Z, respectively. The non-radiative decay is,
of course, only permitted for Ekin,F > 0; this condition limits the number of possible
X,Y ,Z combinations.
The branching ratio of processes (a) and (b) is governed by the respective decay crosssections. For the binding energy range below 1.5 keV, as in the present experiment, and
especially for the lighter elements, the non-radiative decay by far prevails.
10
3.2
Important aspects of AES
In most cases, core ionization and core hole decay can be treated as independent (twostep process). Besides via photoionization, the primary core hole can be also created
by inelastic electron scattering. One can thus distinguish between XAES (X-ray induced
Auger Electron Spectroscopy) and EAES (Electron induced Auger Electron Spectroscopy),
depending on whether the primary hole has been created by photoionization or by electron
scattering. Excitation by electrons is very popular in conventional laboratories, because
electron sources are much cheaper than photon sources and the experimental set-up can
be relatively simple [9]. Moreover, electron guns can have very small beam spots enabling
element-specific Auger electron microscopy. Photon induced core ionization, on the other
hand, has the advantage that the concomitant rate of valence excitations is lower than in
the EAES case. Valence excitations are the main sources of irradiation damage, therefore
XAES is a less destructive tool. Because of this, XAES is an important technique for
investigation of radiation sensitive layers on surfaces.
As in the PES case, discrete, element-specific lines associated with Auger transitions
appears in AES spectra (see Fig. 7 for a survey of the different processes in photoexcited
electron spectra). Similarly to PES, therefore, Auger spectra can be used for elemental
analysis. Moreover, chemical specificity is ensured by the occurrence of chemical shifts
caused by shifts in the inner shell energy levels due to changes in the bonding. It should
also be noted that the emitted Auger electrons carry a well-defined kinetic energy, which
directly reflects the sequence of energy levels involved in the Auger transition and does
not depend on the energy of the photons/electrons used to create the primary hole in
the inner shell. At variance with core level peaks in PES, which are characterized by a
constant binding energy (→ the kinetic energy increases linearly with the photon energy),
Auger lines are better identified by their distinctive kinetic energy and AES spectra are
therefore commonly plotted on the kinetic energy scale.
The nomenclature of Auger transitions follows the electron shells contributing to the
Figure 7: Features of photoexcited electron spectra. From right (high kinetic energy) to left
(low kinetic energy): d) photoionization of valence band levels; c) Auger transitions; b) core level
excitation; a) inelastic loss processes.
11
Figure 8: Explanation of different types of Auger decay processes based on the energy level
diagrams: a) KLL decay; b) LM M decay; c) Coster-Kronig transition; d) Auger decay involving
valence band levels of a solid. Figure taken from Ref. [10].
decay. An Auger line labeled XY Z corresponds to a primary hole in the X shell that
decays into final holes in the Y and the Z shells (see Fig. 8). Commonly, the X-ray
nomenclature is used for identification of the holes: the K shell denotes 1s electrons, while
L1 , L2 , L3 indicates 2s, 2p1/2 , and 2p3/2 electrons, respectively, etc. The decay crosssection is maximum if one of the two final holes has the same principal quantum number
(i.e., is from the same shell) as the primary hole. These XXZ processes are called CosterKronig transitions. For super Coster-Kronig decays all participating holes have identical
principal quantum numbers (e.g., N4 N6 N6 and N5 N7 N7 for tungsten). When the atom
in which the Auger process takes place is bound in a solid, extended electronic bands can
be involved in the decay and the label V is used. For example, a L3 V V transition occurs
when an electron from the valence band de-excites into the L3 core hole, with the excess
energy being transferred to another valence band electron. Because strong redistribution
of valence electrons may occurr upon formation of new chemical bonds, valence band
Auger transitions supply chemical information.
Similarly to PES, satellite lines occur in AES. Multiplet features are even richer for
AES in comparison to PES because of the doubly ionized final state, i.e. there are at least
two holes which interact with each other. Depending on the atomic number Z, L − S (for
low Z) or j − j coupling (for large Z) prevails. Possible final states of KLL transitions are
presented in Fig. 9. Decay satellites, such as shake-up or shake-off processes triggered upon
decay, can render the situation even more complicated. Characteristic energy losses due to
excitation of plasmons and asymmetric peak broadening caused by interband transitions
are also frequently observed in solids. For all these reasons, Auger lines appear - in general
- broader than typical core level photoemission peaks, and they may also exhibit a more
complex shape.
Calculation of the kinetic energies of Auger electrons according to Eq. (12) can be difficult for electron systems larger than isolated atoms. Hence, approximations are required.
One possibility is to take the binding energy for the energy level X of the primary hole,
remove from it the binding energy of the decay electron from shell Y in order to quantify
the de-excitation energy, and finally subtract the binding energy of the level Z from which
the Auger electron is ejected [11]. Inserting an additional term Uh−h that accounts for the
12
Figure 9: Relative KLL Auger energies from theory (lines) and experiments (points) as a function
of the atomic number Z. Light elements (left side): L − S coupling, heavy elements (right side):
j − j coupling; intermediate coupling case in between. The doubly ionized electronic configurations
are indicated in brackets, preceded by the spectroscopic notation (1 S0 , 1 P1 , etc.). See Ref. [9].
interaction of the two holes in the final state, one can write:5
Ekin,F = EbP ES (X) − EbP ES (Y ) − EbP ES (Z) − Uh−h
(13)
By neglecting Uh−h , one obtains the approximate kinetic energy range of the Auger transition. Uh−h can be determined experimentally by comparison with the measured Ekin,F ,
thus providing important information about the interaction energy of the two holes.
4
Adsorption on surfaces
The term “adsorption” indicates the process of trapping and binding of foreign species
(atoms or molecules) onto a surface by condensation from the gas phase. The energy
released in this process is called energy of adsorption Uads or also binding energy (not
to be confused with the binding energy in PES). The term “substrate” refers to the solid
surface onto which adsorption occurs, while “adsorbate” is used to indicate the species that
are adsorbed onto the substrate. Adsorption can be associative (if a particle or molecule
is adsorbed as a single unit) or dissociative (if the particle or molecule is dissociated upon
adsorption), and moreover adsorption processes may be reversible or irreversible.
The reverse process, the removal of adsorbed species from the surface, is called “desorption”. Desorption may be stimulated by heat (thermal desorption), by electrons (electron
stimulated desorption), or by photons or ions (photon or ion stimulated desorption).
4.1
Types of adsorption
Physisorption:
Physical adsorption (= physisorption) is governed by weak Van der Waals interactions with
the surface. The adsorption energy Uads is small, typically < 30 kJ/mol or 0.3 eV/particle.
Formation of multilayers (condensates) is possible at sufficiently low temperatures.
Example: He on noble metal surfaces at cryogenic temperatures.
5
sample
To express Ekin,vacuum
the work function has to be substracted from Ekin,F in Eq. (13).
13
Chemisorption:
Chemical adsorption (= chemisorption) involves the formation of a chemical bond between
the adsorbate and the surface, e.g. transfer of electrons and/or formation of covalent bonds
(hybrid molecular orbitals). In most cases the adsorption energy is much larger than 30
kJ/mol, ≥ 100 kJ/mol or 1 eV/particle. Chemisorption is often dissociative and may be
irreversible; activation barriers are possible, and chemisorbates form typically only a single layer (= direct contact of surface atoms and the chemisorbate is required). Moreover,
specific binding sites may be favoured because of the highly corrugated surface potential.
Examples: CO and oxygen chemisorption on transition metals at room temperature.
4.2
Adsorption order
First order adsorption:
One particle from the gas phase yields one particle of the adsorbate, i.e., the impinging
particles are molecules that do not dissociate upon adsorption. The reverse process is first
order desorption.
Examples: CO/nickel (CO chemisorbs on Ni surfaces molecularly with Uads ∼ 120 kJ/mole);
Ar/Ruthenium (Ar physisorbs on Ru with Uads ∼ 10 kJ/mol).
Second order adsorption:
A molecule dissociates upon adsorption. One particle in the gas phase yields two particles
on the surface. The reverse process is associative desorption or second order desorption.
Example: H2 /Nickel (H2 dissociates into two H atoms on Ni, Uads ∼ 90 kJ/mole).
4.3
Nomenclature
Other concepts that are common in adsorption studies in the realm of surface science:
Nads
• Surface (relative) coverage Θ:
Θ≡
Nsub
with Nads = number of adsorbate particles per unit area; Nsub = number of particles
per unit area in the substrate surface layer(s). Θ is typically expressed in monolayers
or as a fraction of a monolayer (ML), 1 ML corresponding to an adsorbate surface
density equal to the surface density of substrate atoms.
• Collision rate ν:
it is defined as the number of particles hitting a surface per unit time and unit area.
The Hertz-Knudsen equation following from the gas kinetic theory states that:
p
ν=√
[particles · s−1 · m−2 ]
2πM kB T
with P = pressure [N· m−2 = Pa]; M = particle mass [Kg]; T = temperature [K];
kB = Boltzmann constant.
• Sticking coefficient s:
dNads
s=
dt
dNcoll
dt
0≤s≤1
probability that a particle colliding with the surface is adsorbed and stays on it.
• Exposure:
measure of the amount of gas that a surface has been exposed to; more specifically, the product of the gas pressure and the time of exposure. Normal unit is the
Langmuir, where 1L = 10−6 Torr ·s (1 Torr = 133.3 Pa = 1.333 mbar).
14
5
Experimental set-up
The experimental set-up, schematically depicted in Fig. 10, consists of an ultra-high vacuum (UHV) chamber on which the PES apparatus and the equipment for sample insertion,
preparation and manipulation are mounted.
5.1
Vacuum system
The UHV chamber is maintained at a base pressure lower than 1 × 10−9 mbar (1 × 10−7
Pa). The pressure is measured by an ion gauge (hot filament ionization gauge) mounted
inside the chamber. Pressure in the UHV regime is required in order to permit electron
detection (avoiding scattering of the photoelectrons between the sample surface and the
detector) and to ensure that atomically clean surfaces can be prepared and maintained
free of contaminants during the experiment. The chamber is pumped by an ion getter
pump directly mounted inside the chamber. Auxiliary pumping by a titanium sublimation pump is possible. In addition, an external turbomolecular pump (with attached a
backing roughing pump) can be connected to the UHV chamber through a gate valve.
This turbomolecular pump is also used to pump the load-lock system adjacent to the
main chamber. The UHV regime can only be reached after baking out the chamber for
about 24 hours (or longer) at temperatures exceeding 160-180◦ C. This procedure allows to
eliminate residual molecules (predominantly water) adsorbed on the stainless steel walls of
the chamber, which otherwise would be released at a low rate thus increasing the pressure.
A brief introduction to the UHV technology, instrumentation and related protocols can
be found in Refs. [12, 13].
hemispherical
electron energy
analyzer (HSA)
detector
UHV chamber
pressure gauge
e-
leak
valve
holder
X-ray source
O2 line
W sample
load
Mg evaporator
gate valve
titanium
sublimation
pump
lock
syst
em
turbomolecular
pump
+
roughing pump
ion pump
Figure 10: Scheme of the UHV chamber with the PES apparatus and ancillary equipment.
15
5.2
X-ray source
energy
A conventional X-ray laboratory source provides characteristic Al Kα radiation. The
source consists of a cathode filament, which emits electrons upon heating by direct current (typical emission current: 20-22 mA), and an anode, onto which the electrons are
accelerated by applying a high voltage (typically, 11-12 kV). Water cooling is required
during continuous duty operation of the X-ray source, in order to prevent melting of the
anode target. Here, the anode is an Al film - some 10 µm thick - supported on a copper
rod. During operation, the electrons from the cathode collide with the atoms of the Al
target, causing vacancies in inner electron shells. The subsequent de-excitation by fluorescence decay (see §3.1) produces X-ray radiation of characteristic energy.
L3
L2
2p3/2
2p1/2
L1
2s
K α1
K α2
K
Al K α1,2
ħω = 1486.6 eV
FWHM = 0.78 eV
1s
(a)
(b)
Figure 11: Characteristic radiation from an Al anode source: (a) schematic energy level diagram
explaining the production of the individual Kα1 and Kα2 lines; (b) emission spectrum showing
the convolution of the Kα1 and Kα2 lines into a composite Kα1,2 line centered at 1486.6 eV with
0.78 eV FWHM. Adapted from Ref. [12].
As illustrated in Fig. 11, the Kα1 and Kα2 lines are generated, corresponding to L3 → K
and L2 → K transitions, respectively, where L3 , L2 and K denote the 2p3/2 , 2p1/2 and 1s
levels. The L2,3 subshell is split due to spin-orbit coupling, such that the relative intensity
of the two lines reflects the L3 to L2 population ratio of 2 : 1. As a consequence, the Kα1,2
line is in principle a doublet with an energy splitting of 0.43 eV. However, since each line
has a natural width of 0.47 eV caused by lifetime broadening, the doublet is not resolved
and the resulting composite line has a linewidth of 0.78 eV (FWHM) and is centered at
~ω = 1486.6 eV. In addition, a Kα3,4 satellite is also produced, attributed to emission
from doubly ionized atoms [12]. This satellite line is centered at about 1496 eV and its
intensity is ∼ 10% of that of the main Kα1,2 emission.
Additional emission lines can arise from contamination (e.g., the O Kα line centered
at ~ω = 524.9 eV if the anode material is partly oxidized) or other modifications of
the anode (e.g., when the Al film becomes too thin, the Cu Lα line from the copper rod
beneath may be excited, ~ω = 929.7 eV).
5.3
Electron energy analyzer
An electrostatic 180◦ hemispherical analyzer (HSA) is used to analyze in energy the electrons emitted from the sample. This electrostatic device consists of two metallic hemispheres, concentrically arranged as in Fig.12, and enables to “disperse” the electrons as a
function of their kinetic energy similarly to a prism that disperses light depending on its
wavelength. For this purpose, a potential difference ∆V is applied between the inner and
outer hemispheres, so that the trajectory of the incoming electrons is bent into a curve6 .
6
To prevent perturbation of the electron trajectories by stray magnetic fields, the analyzer region is
shielded by a µ-metal shield inside the vacuum vessel.
16
V(R2) = - V2
electron
optics
V(R1) = - V1
detector
∆V = V(R1) - V(R2)
Figure 12: Schematic of a concentric hemispherical analyzer. Both hemispheres are at negative
potential, with V (R2 ) < V (R1 ) (→ V2 > V1 ). Adapted from Ref. [14].
An electrostatic lens between the sample and the entrance slit S of the analyzer focuses
the photoelectrons from the sample onto S. At a given ∆V , ideally only the electrons
with a well-defined kinetic energy Ep are able to complete their path along the median
trajectory of radius R0 = (R1 +R2 )/2 (R1 and R2 radii of the inner and outer hemisphere)
and emerge at the exit slit F . Ep is called pass energy and its typical values range between
5 and 50 eV for XPS measurements.
An important concept is that of energy resolution of the analyzer. This is a measure
of the ability of the analyzer to distinguish and separate (→ resolve) peaks that differ in
energy by only small amounts. As discussed in §2.2, the energy resolution of the analyzer
contributes to the overall FWHM of a core level peak (Eq. (10)). For the HSA, the energy
resolution can be expressed by the formula [12, 13]:
∆E/Ep =
WS + WF
α2
+
4R0
2
(14)
in which ∆E is the FWHM, WS and WF are the widths of the entrance and exit slit,
respectively, and α is the angular spread of the electron beam. The analyzer is operated
at constant pass energy to yield a constant absolute resolution ∆E. The lower the pass
energy, the better the energy resolution.
In order to enable scans over arbitrary kinetic energy ranges, the electrons are retarded
(or accelerated) to the kinetic energy Ep by a potential difference R inside the lens system
situated between the sample and the entrance slit. A channel-type electron multiplier
(channeltron) is located behind the exit slit of the analyzer, where the emerging electrons
are counted. Therefore, by scanning R a spectrum of the photoelectron intensity as a
function of the kinetic energy is recorded, the measured kinetic energy being simply R+Ep .
When R = 0, the Fermi levels of sample and analyzer are aligned (in practice, both
objects are grounded), whereas they are separated by R when the retarding voltage is
applied. However, due to the different values of the work function, the vacuum levels
of sample and analyzer do not coincide even for R = 0. From the energy level diagram
illustrated in Fig. 13 it then follows:
analyzer
Eb = ~ω − (Ep − Φanalyzer − R) = ~ω − Ekin,
vacuum − Φanalyzer
17
(15)
e-
Ep
Ekin,F
E vacuum,analyzer
hω
Φanalyzer
E F,analzyer
E vacuum,sample
R
Φw
E F,sample
Ekin,F = R + Ep + Φanalyzer
analyzer
(measured)
Ekin,vacuum = R + Ep
Eb
sample
Ekin,vacuum = R + Ep + (Φanalyzer - Φw )
Core Levels
Sample
Analyzer
Figure 13: Photoelectron detection by an electron energy analyzer: schematic diagram of relevant
energy levels and voltages.
Eq. (15) shows that the work function of the analyzer, rather than the work function of
the sample, needs to be taken into account. Φanalyzer enters the equation because in the
experiment the kinetic energy scale is referenced to the vacuum level of the analyzer. To
keep Φanalyzer constant, all electrodes are covered with a chemically inert material (gold
or graphite; in the present case graphite).
5.4
Samples
Three samples will be investigated during the experiment. A tungsten (W) ribbon will be
studied initially. It can be heated up to 2500 K by direct current flow in order to remove
contamination from the surface. The W ribbon is mounted on a four-degree-of-freedom
manipulator enabling translational motion along three orthogonal directions and rotation
around the axis of the manipulator. In this way, the polar angle θe defined in Fig. 2a can
be changed, thus varying - when needed - the surface sensitivity of the PES measurements.
Further, the W ribbon will serve as substrate for the growth of a Mg film that will
be deposited in-situ under UHV conditions. The subsequent oxidation of magnesium
will provide a clear illustration of the concept of chemical shift; moreover, measurements
with different surface sensitivity will provide structural information on the depth of the
oxidation process.
Finally, a third sample to be analyzed will be introduced through the custom-made
load-lock system, which allows fast insertion of ex-situ prepared samples without breaking
the vacuum of the main chamber. An UHV compatible sample chosen by the students
will be inserted into the chamber and characterized by PES. Possible examples: a metal
substrate covered by an organic sulphur-containing self-assembled monolayer (SAM); a
coin; a (cheap!) piece of jewellery; the crown cork of a bottle; a fragment taken from a
broken DVD, CD or hard disk; a piece of special glass, etc.
18
5.5
Magnesium evaporator
The evaporator consists of a small high-melting-point crucible containing Mg grains. The
crucible is heated by passing current through a conducting wire coiled around it. Prior
to evaporation, the Mg grains need to be outgassed repeatedly, in order to ensure that a
clean Mg film is deposited on the tungsten ribbon during the experiment.
5.6
Gas handling line
A gas line filled with molecular oxygen is connected to the main chamber through a highprecision leak valve. In this way O2 can be admitted into the chamber in a controllable
fashion during the experiment.
6
Concepts to be understood before the experiment
• Fundamental principles of PES and AES: the photoemission process, Auger transitions. Core level lines, valence band excitation. Binding energy. Work function.
Satellite lines. Spin-orbit splitting. Chemical shifts.
• Surface sensitivity of PES and AES. Importance of the electron detection geometry:
normal emission vs. grazing emission.
• Generation of characteristic X-rays by fluorescent decay. Working principle of the
Al anode X-ray source.
• Hemispherical electron energy analyzer. Pass energy. Retarding voltage. Instrumental resolution.
• Ultra-high vacuum. Adsorption of foreign species. Dissociative adsorption.
7
Instruction for the experimental session
The goal of the experiment is to characterize by core level PES the tungsten ribbon
mounted inside the chamber, and to study by PES and AES the modifications introduced
by the deposition of a Mg film. The effect of the oxidation of the Mg film is also part of
the investigation. In addition, insight into the performance of the hemispherical analyzer
will be gained, in particular as to the dependence of the core level intensity and energy
resolution on the pass energy. In order to stimulate the scientific curiosity of the students,
in the final part of the experiment the possibility of studying an additional sample at choice
is offered. In this way, the experiment provides an overview on the main information that
can be obtained from the two experimental techniques, on some technical aspects and on
typical issues faced in adsorption studies and surface science.
Proceed according to the following steps:
A. Performance of the analyzer and characterization of the W sample
1. Get an introduction to the experiment and to the equipments by your advisor.
2. Clean the W ribbon following the advisor’s instructions. After setting the pass
energy to Ep = 50 eV, record a survey spectrum7 with 100 eV ≤ Ekin ≤ 1500 eV.
In this broad scan you are not interested in the fine details of the core level lines,
7
Unless otherwise stated, photoemission spectra will be taken at an electron emission angle of 45◦ ,
which corresponds to an incidence angle of 45◦ of the photon beam relative to the surface normal.
19
so you can use a large energy step (1 eV). Try to assign all maxima to known core
level and Auger peaks: this may be easier if you plot the spectrum in the binding
energy scale, using the appropriate computer software.
3. Zoom-in into the W 4f doublet using an energy step of 0.1 eV and record a sequence
of spectra with different values of Ep (e.g., 7.5, 10, 15, 20, and 50 eV). In order to have
good statistics, at each value of the pass energy select appropriately the integration
time per energy point.
4. Zoom-in into the C 1s and O1s core level regions at Ep =50 eV. Is the surface
completely free of contaminants?
5. At Ep = 20 eV record a photoemission spectrum of the W valence band (see Fig. 7).
Determine Φanalyzer from the position of the Fermi edge.
B. Cleanliness of the Al anode of the X-ray source
6. Using Ep = 50 eV, acquire a PES spectrum for 200 eV ≤ Ekin ≤ 530 eV with the
X-ray source operated at reduced anode voltage of 1.4 kV and an emission current
of 6 mA (consult the advisor to change the operation conditions). Now that the Al
Kα emission is suppressed, what is the origin of the spectral features observed?
C. Deposition of a Mg metal film
7. The advisor will now deposit a Mg film on the W sample: record a survey spectrum
from 50 to 1500 eV (Ep = 50 eV, ∆Estep = 1 eV). Assign all the features of this
spectrum and assess qualitatively the cleanliness and thickness of the film. Can you
see any signal from the W substrate?
8. Record the Mg KLL Auger spectrum in the kinetic energy range from 1060 eV to
1200 eV (Ep = 20 eV, ∆Estep ∼ 0.3 eV) for:
(1) nearly normal electron exit (θe = 10◦ );
(2) nearly grazing electron exit (θe = 80◦ ).
Keeping in mind the different probing depth of the two geometries, can you conclude
that the (electronic) structure of the metallic film is uniform across its thickness?
9. Zoom-in into the Mg 1s region (Ep = 10 eV). Write down the kinetic energy of the
main line. Record a photoemission spectrum (Ep = 10 eV) from the O 1s region.
Any feature?
D. Oxidation of the Mg film at room temperature
10. After the Mg overlayer has been oxidized by dosing ∼45 L O2 at room temperature
(PO2 = 2 × 10−7 mbar), repeat step 9. Any changes? Explain the results in the light
of what you have learnt about the chemical shift.
11. Repeat step 8. Which conclusions can be drawn based on the different surface
sensitivity of the two collection geometries? Is the film uniformly oxidized and
structurally homogeneous across its thickness?
20
E. Elemental analysis of a sample at your choice
12. Help the advisor to insert the ex-situ prepared sample you have chosen into the loadlock chamber. Follow instructions to start pumping. After a good pressure has been
reached, open the gate valve to the main chamber and bring the sample into the
measurement position in front of the X-ray source. Take all XPS spectra you deem
are necessary for characterizing the sample in terms of its elemental composition.
8
Writing up your report
Write up a short report of your experiment. After a concise introduction on the PES and
AES techniques, discuss the experimental results addressing all issues listed below:
• Assign all spectral features in 7.2. Calibrate the binding energy scale by making use
of 7.5. As an alternative method to determine the analyzer work function, search
for the literature value of the W 4f7/2 binding energy of metallic W (if possible, for
a polycrystalline W foil) and use Eq. (3) together with the results of 7.3. Comment
on the surface cleanliness (see 7.4).
• Focus your attention on the W 4f doublet (from 7.3). Discuss the spin-orbit splitting
and the intensity ratio of the components. Determine the W 4f intensities after
background subtraction and plot them as a function of Ep , commenting on the
observed dependence.
• Plot the experimentally obtained FWHMs for the two constituents of the 4f doublet
as a function of Ep . How does the trend compare to Eq. (14)? Referring to Eqs. (9
and (10), set a lower limit for the core hole lifetime using - for instance - the data
at Ep = 10 eV.
• Rationalize the results of 7.6. Consider X-ray emission from contaminants on the Al
anode.
• Assign all spectral features from 7.7. Comment on the thickness of the metallic film
and, using 7.8, make conclusions on its uniformity.
• Explain all details of 7.8 and identify the main Auger transitions (KL2,3 L2,3 , KL1 L1
etc.) by consulting available literature. You can also check the reliability of the
work function value determined above by comparing the tabulated and experimental
values for the KL2,3 L2,3 (1 D) line8 .
• Consider the progression of plasmon losses in the Auger KLL spectrum: determine
the plasmon energy and compare your estimate with the expected value (see also
exercise 3 below).
• In the Auger KLL spectrum select a transition of your choice and calculate the
hole-hole interaction energy Uh−h from Eq. (13).
• Compare the Mg 1s and O 1s data from 7.9 and 7.10. Describe the effect of the
oxidation (structural and chemical evolution).
• Compare and interpret the results of 7.8 and 7.11. Is the Mg film uniformly oxidized
through its thickness or can you infer differences between the surface layer(s) and
the region underneath?
• Briefly describe the results of the elemental analysis of 7.12.
8
Note that tabulated values are often given with the kinetic energy measured relative to the Fermi level.
21
9
Exercises
One of these exercises, at your choice, will be asked during the final colloquium:
1. Determine after which time interval an originally clean metal surface (e.g., Mg) will be
covered with one monolayer of O atoms at a pressure of 2 × 10−7 mbar (= 2 × 10−5 Pa)
of molecular oxygen O2 .
[Hint: make use of the Hertz-Knudsen equation (see §4.3) to determine the impingement rate
of O2 onto the surface; assume s = 1 for the sticking coefficient; give an estimate of the surface
density of Mg atoms, e.g. on a Mg(0001) surface for which the size and area of the primitive cell
are known; remember that the adsorption of O2 is dissociative.]
2. Assume a hemisherical analyzer with radii R1 (inner) and R2 (outer). What is the
potential difference ∆V that has to be applied to the hemispheres in order to bend the
trajectory of electrons of kinetic energy Ep into a circular orbit of radius R0 = (R1 +R2 )/2?
Numerical values: R1 = 9.5 cm, R2 = 10.5 and Ep = 5 eV.
[Hint: the centripetal force bending the electron’s trajectory must equate the force exerted by
the electric field; make use of the Gauss’s law.]
3. Determine the bulk plasmon energy (in eV) of magnesium metal in the jellium model,
using the formula: ~ωp = [n~2 e2 /me 0 ]1/2 , with me electron mass and n number density
of free electrons for Mg metal)
[Hint: n can be determined from the mass density and the atomic weight of Mg, assuming that
two conduction electrons per atom are made available.]
10
Useful tables
• Electron binding energies for all elements:
http://xdb.lbl.gov/Section1/Table 1-1.pdf
• Energies of the X-ray emission lines for all elements:
http://xdb.lbl.gov/Section1/Table 1-2.pdf
• Subshell photoionization cross-sections:
http://xdb.lbl.gov/Section1/Sec 1-5.pdf
• Energies of the main Auger lines
http://xdb.lbl.gov/Section1/Sec 1-4.html
22
References
[1] H.P. Bonzel and Ch. Kleint, On the History of Photoemission, Progress in Surface
Science 49, 107 (1995); doi:10.1016/0079-6816(95)00035-W.
[2] S. Hüfner, Photelectron Spectroscopy — Principles and Applications, Springer-Verlag,
Berlin, 2003.
[3] For a thorough discussion of these effects see for example:
C.S. Fadley, Basic Concepts of X-ray Photoelectron Spectroscopy (chapter 1), in:
Electron Spectroscopy: Theory, Techniques, and Applications (Vol. 2), edited by:
C.R. Brundle and A.D. Baker, Academic Press, London, 1978.
[4] B.D. Ratner and D.G. Castner, Electron Spectroscopy for Chemical Analysis (chapter
4), in: Surface Analysis — The Principal Techniques, edited by J.C. Vickerman, J.
Wiley & Sons Ltd., 1997.
[5] D. Briggs, XPS: Basic Principles, Spectral Features and Qualitative Analysis (chapter
2), in: SURFACE ANALYSIS by Auger and X-ray Photoelectron Spectroscopy, edited
by D. Briggs and J.T. Grant, IM Publications and SurfaceSpectra Limited, 2003.
[6] M.C. Biesinger et al., Resolving Surface Chemical States in XPS Analysis of First Row
Transition Metals, Oxides and Hydroxides: Sc, Ti, V, Cu and Zn, Applied Surface
Science 257, 887 (2010); doi:10.1016/j.apsusc.2010.07.086.
[7] J.C. Fuggle and S.F. Alvarado, Core Level Lifetimes as determined by X-ray
Photoelectron Spectroscopy Measurements, Physical Review A 22, 1615 (1980);
doi:10.1103/PhysRevA.22.1615.
[8] J.J. Sakurai, Modern Quantum Mechanics, Addison-Wesley Publishing Company,
Reading - Massachusetts, 1995. See pp. 341-345.
[9] C.C. Chang, Auger Electron Spectroscopy, Surface Science 25, 53 (1971);
doi:10.1016/0039-6028(71)90210-X.
[10] H. Lüth, Solid Surfaces, Interfaces and Thin Films, Springer-Verlag, Berlin, 2001.
[11] J.T. Grant, AES: Basic Principles, Spectral Features and Qualitative Analysis (chapter 3), in: SURFACE ANALYSIS by Auger and X-ray Photoelectron Spectroscopy,
edited by D. Briggs and J.T. Grant, IM Publications and SurfaceSpectra Limited,
2003.
[12] I.W. Drummond, XPS: Instrumentation and Performance (chapter 5), in: SURFACE
ANALYSIS by Auger and X-ray Photoelectron Spectroscopy, edited by D. Briggs and
J.T. Grant, IM Publications and SurfaceSpectra Limited, 2003.
[13] J.C. Rivière, Instrumentation (chapter 1), in: PRACTICAL SURFACE ANALYSIS,
Vol. 1: Auger and X-ray Photoelectron Spectroscopy, edited by D. Briggs and M.P.
Seah, J. Wiley & Sons Ltd., 1990.
[14] P. Willmott, An Introduction to Synchrotron Radiation — Techniques and Applications, J. Wiley & Sons Ltd., 2011.
23
Appendix A:
Theory of core level photoemission
The interaction of electromagnetic radiation with an electron system is described by the
Hamiltonian:
1 e ~ 2
H=
+ eΦ + V = Ho + H 0
(A.1)
p~ + A
2m
c
with
p~2
Ho =
+V
(A.2)
2m
being the unperturbed Hamiltonian of the electron (e.g., in a solid in the absence of the
electromagnetic field), and
H0 =
2
e
~2
~+A
~ · p~) + eΦ + e A
(~
p·A
2mc
2mc2
(A.3)
~ By assuming source free
the perturbation due to the photon field with vector potential A.
~
space, adopting appropriate gauge transformations (Coulomb gauge: Φ=0, divA=0)
and
~ (i.e., the term A
~ · A,
~ which represents two photon processes)
neglecting higher orders of A
one obtains:
e ~
H0 =
A · p~
(A.4)
mc
~ of the electromagnetic radiation defines the direction of
Here, the vector potential A
polarization, while p~ is the momentum operator. Assuming a small perturbation H 0 , in
the first order perturbation theory the Fermi’s Golden Rule provides the transition rate
Pi→f (transition probability per unit time) for the excitation from the initial N -electron
state Ψi of energy Ei to the final N -electron state Ψf of energy Ef :
Pi→f =
2π
|hΨf | H 0 |Ψi i|2 δ(Ef − Ei − ~ω)
~
(A.5)
The angle-integrated cross-section will be therefore:
X
dσ
∼
|Mi→f |2 δ(Ef − Ei − ~ω)
dEf
(A.6)
~ · p~ |Ψi i, and the sum is performed
where the transition matrix element is Mi→f = hΨf | A
over all initial and final states that are allowed by energy conservation (= for which the
argument of the delta function is zero).
If one separates the wavefunction of the photoelectron from that of the other N − 1
“passive” electrons, the previous equation can be expressed as [2]:
X
X
dσ
~ · p~ |φi,k i|2
∝
|hφf,Ekin | A
|cs |2 δ(Ef,kin + Es (N − 1) − E0 (N ) − ~ω)
dEf
s
(A.7)
f,i,k
P
where the cs coefficients denote N − 1 overlap integrals and the
s is calculated by
summing over all possible excited final states of energy Es (N − 1); E0 (N ) is the energy
of the initial N -electron state (ground state energy) and Ef,kin represents the kinetic
energy of the photoelectron, which has been excited from the inner orbital φi,k to the
final state of wavefunction φf,Ekin . Eq. (A.7) thus contains the main ingredients of a core
level photoemission spectrum that have been discussed in section 2, namely a “main line”
accompanied by a number of satellites which reflect the excitation spectrum of the electron
system with the core hole.
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