# The CoESCA station at BESSY: Auger electron — Photoelectron coincidences
from surfaces demonstrated for Ag MNN

T. Leitner<EMAIL_ADDRESS>A. Born  I. Bidermane  R. Ovsyannikov
F. O. L. Johansson  Y. Sassa  A. Föhlisch  A. Lindblad  F. O. Schumann  S.
Svensson  N. Mårtensson  UBjL, Uppsala-Berlin joint Laboratory  Institute for
Methods and Instrumentation in Synchrotron Radiation Research, Helmholtz-
Zentrum Berlin für Materialien und Energie, Albert-Einstein-Strasse 15, 12489
Berlin, Germany  Institut für Physik und Astronomie, Universität Potsdam,
Karl-Liebknecht-Strasse 24-25, 14476 Potsdam, Germany  Division Molecular and
Condensed Matter Physics, Department of Physics and Astronomy, Uppsala
University, Box 516, SE-751 20 Uppsala, Sweden  Max-Planck-Institut für
Mikrostrukturphysik, Weinberg 2, 06120 Halle, Germany  Materials Physics,
Chalmers University of Technology, SE-412 96 Gothenburg, Sweden

###### Abstract

In this work, we present the CoESCA station for electron-electron coincidence
spectroscopy from surfaces, built in a close collaboration between Uppsala
University and Helmholtz-Zentrum Berlin at the BESSY II synchrotron facility
in Berlin, Germany. We start with a detailed overview of previous work in the
field of electron-electron coincidences, before we describe the CoESCA setup
and its design parameters. The system is capable of recording shot-to-shot
resolved 6D coincidence datasets, i.e. the kinetic energy and the two take off
angles for both coincident electrons. The mathematics behind extracting and
analysing these multi-dimensional coincidence datasets is introduced, with a
focus on coincidence statistics, resulting in fundamental limits of the
signal-to-noise ratio and its implications for acquisition times and the size
of the raw data stream. The functionality of the CoESCA station is
demonstrated for the example of Auger electron — photoelectron coincidences
from silver surfaces for photoelectrons from the Ag 3d core levels and their
corresponding MNN Auger electrons. The Auger spectra originating from the
different core levels, $3d_{3/2}$ and $3d_{5/2}$ could be separated and
further, the two-hole state energy distributions were determined for these
Auger decay channels.

###### keywords:

Auger , Photoelectron , coincidence , spectroscopy , AES , PES , APECS ,
surface science

††journal: Journal of Electron Spectroscopy and Related Phenomena

##  1 Introduction

In 1923 Pierre Auger discovered the effect named after him. However, already
in 1922 Lise Meitner made a comment about such a phenomenon when explaining
some details in a beta radiation spectrum. For Meitner this was just a small
addition to the main processes she was studying. Auger, on the other hand,
dedicated his whole doctoral thesis to exploring this phenomenon, see for
example [1]. After core hole photoionisation, an Auger process can ocure,
where the core hole is filled by an electron from a less bound shell, while a
second electron is emitted, carrying the excess energy. A two-hole state is
produced and two electrons linked to each other leave the sample, an Auger
electron and a photoelectron. Since the initial vacancy state and the final
two-hole state have well-defined energies for each element in the periodic
table, the Auger electrons will be emitted with characteristic energies. In
this way Auger Electron Spectroscopy (AES) can be used to identify which
elements are present in a sample. Furthermore, for Auger transitions involving
shallow core-levels, the Auger energies will typically be in the range of a
few hundred eV. For such electron energies the mean free path will be
relatively short and the Auger spectral information will be surface sensitive.
For this reason AES became a very powerful and much used tool in surface
science.

One of the great successes of photoelectron spectroscopy is that one can
perform detailed chemical analysis using the chemical shift. Also Auger
transitions involving two core levels show chemical shifts. Due to the
different, and often much larger chemical shifts, AES provides additional
opportunities to distinguish different chemical species compared to
photoelectron spectroscopy. Since the chemical shifts are different for Auger
transitions and for core level photoelectrons, also the difference in kinetic
energy between these features will undergo a chemical shift. This difference,
denoted the Auger parameter, [2, 3] has also been used for analytical
purposes. The main reason for using the Auger parameter in an X-ray excited
experiment is that it does not require any calibration of the kinetic energy
scale. This is for instance an advantage for insulating samples where there
may be sample charging.

An important aspect of AES is that it provides information about the two-hole
states of a system. For this reason it is well suited for probing electron
correlation effects. In Core Valence Valence (CVV) Auger spectra from
transition metals, it can be that the two holes are delocalised, then the two-
hole spectrum is a self-convolution of the single hole valence spectrum, just
as measured by photoelectron spectroscopy. However, when electron correlation
effects become more important towards the end of a transition series,
localised final states start appearing, where the two final state holes are
localised at the same site. For late transition elements such as silver the
spectrum is completely dominated by localised two-hole states. These states
can be separated and accurately probed by coincidence spectroscopy.

There are a number of factors which often make the detailed analysis of Auger
spectra complicated. All core levels are broadened due to their finite
lifetime. The lifetime is typically in the range of a few fs and shorter. This
leads to a broadening of the spectral features in the range of a few tenths of
an eV up to a couple of eV for the transitions, which are most often used in
Auger electron studies. In addition, also the two-hole final state has a
finite lifetime. The lifetime broadening is more difficult to handle using
fitting procedures for the Auger spectra than for photoelectron spectra. The
two final state holes lead to multiplet effects and more complicated line
shapes, which makes it more difficult to accurately parametrise the spectral
profile. Often, there are also overlapping satellite transitions, due to
multiple excited initial states caused by shake-up or shake-off processes in
the creation of the initial vacancy. These multiple excited states may also be
caused by the decay of deeper core hole states. These Auger satellites usually
overlap the main spectral features, which severely complicates any detailed
analysis.

One way to avoid these complications is to measure the Auger spectra in
coincidence with the photoelectron spectra corresponding to the creation of
the initial vacancy. This technique is usually denoted Auger PhotoElectron
Coincidence Spectroscopy (APECS). In the present paper we describe the
Coincidence Electron Spectroscopy for Chemical Analysis setup (CoESCA) at the
BESSY II storage ring at HZB, Berlin. This system uses two high-resolution
wide-angle time-of-flight ArTOF spectrometers. At first, we give a short
overview of the field. Then we describe the CoESCA setup, and finally present
some initial results.

### Auger PhotoElectron Coincidence Spectroscopy - APECS

There are a number of advantages of APECS, despite the fact that it involves
quite demanding measurements. The key parameter is the ratio between true and
accidental coincidences, which very much limits the useful count rates. The
number of true coincidences will be proportional to the intensity of the
exciting radiation, $I$. The number of accidental coincidences will however
scale as $I^{2}$. This sets a limit on what intensities are practical to use.
The way to increase this ratio is to use spectrometers with the highest
possible electron acceptance angle. For this reason there are still only few
examples of successful APECS measurements.

In a pioneering paper, Haak et al.[4] used APECS to disentangle the different
components of the Cu $L_{23}M_{45}M_{45}$ Auger spectrum. They identified
satellite lines in the $L_{3}M_{45}M_{45}$ part of the spectrum, caused by the
$L_{2}M_{45}M_{45}$ Coster-Kronig (CK) process, by performing measurements in
coincidence with the 2p1/2 core electron spectrum.

In gas phase measurements, different types of satellites have been identified
[5]. For N2, the participator Auger satellites were disentangled in this way
[6]. For O2, the contributions of the O$1s$ ${}^{2}\,\Sigma$ and
${}^{4}\,\Sigma$ exchange split states to the KVV spectrum could be resolved
[7]. For CO it has furthermore been shown how one can study the Auger decay
from vibrationally resolved core hole states [5].

Thurgate and coworkers have reported a number of studies using APECS [8, 9,
10, 11]. In [8] they compare the Ni APECS spectra for Ni and an NiFe alloy and
identify changes in the Ni electronic states due to alloying. In Ref. [11]
they investigate trends in the APECS spectra in 3d transition metals from Fe
to Ga. They study the transition from bandlike final states in Fe and Co to
localized final stets in Ga. They also use the technique to study the
reduction of the $L_{2}L_{3}M_{45}$ Coster-Kronig rate going from Fe to Ga.

One important property of APECS is that it enables the distinction of Auger
spectra from different chemically shifted components of a system. The Auger
spectra are quite broad and the differently shifted components usually
overlap. However, by measuring the Auger spectrum in coincidence with
chemically shifted, distinguishable, and often narrow, core-level peaks these
spectra can be disentangled. In this way Auger spectra from different species
of Al exposed to oxygen have been identified[12]. Furthermore, the surface
core level shift for Ta(100) [12] and for the Ta4f level in TaC(111) [13] have
been used to separate the Auger spectra originating from the bulk and the
surface.

There have also been several studies of Si surfaces and their oxidation. Auger
spectra from different sites at the reconstructed Si(111)7x7 surface have been
separated by APECS [14, 15] and the different stages of oxidation of this
surface have been studied [16]. For an oxidized Si surface several oxidation
stages occur at the same time. However, these can be well distinguished in XPS
due to well-separated core level peaks. Using APECS it has thus been possible
to record a pure Auger spectrum of SiO2 [17]. It is in fact rather difficult
to record a spectrum of pure SiO2 in other ways since it may be difficult to
achieve homogenous samples. Bulk SiO2 may decompose at the surface and for
thicker samples there may also be charging effects, which will affect the
spectra.

One useful property of APECS, when studying solids, is that the coincident
spectra are more surface sensitive than the single photoelectron or Auger
electron spectra. This is due to the fact that both the photoelectron and the
Auger electron signals are attenuated due to the finite mean free path, which
implies that the coincidence signal attenuates as a product of these effects.
This increased surface sensitivity of APECS was for instance used to enhance
the Si2p signal from the outermost Si atoms for the reconstructed Si(100) 2x1
surface [18]. Using APECS it is also possible to tune the surface sensitivity
for the Auger spectra. The Auger electrons are measured in coincidence with
the photoelectrons of different kinetic energies, hence photoelectrons with
different mean free paths from different depths in the sample. Since the Auger
electrons are measured in coincidence, they stem from the same depth. This
possibility may be particularly interesting for liquids and similar systems
where there are no other ways to modify the surface sensitivity for the Auger
spectra, like for example by measuring at different takeoff angles.

The facet of the surface sensitivity was explored in another study on an Al
surface. When the 2p core level spectrum of Al(111) was measured in
coincidence with the Auger signal, a 40% decrease of the intensity of the bulk
plasmon loss signal was observed, reflecting the reduced information depth
[12]. The surface plasmon loss signal, on the other hand, was only marginally
reduced as expected. The mechanism for the increased surface sensitivity has
also been investigated for a Si(100) surface [19]. As for Al(111) the plasmon
signal decreases when the photoelectron spectrum is measured in coincidence
with the LVV Auger signal. However, the photoelectron spectrum was also
measured in coincidence with the first plasmon loss signal of the LVV Auger
spectrum. The Auger electrons, which have undergone one plasmon loss,
originated from a larger depth and hence a significantly smaller reduction of
the photoelectron plasmon loss signal could be observed. The increased surface
sensitivity has also been seen through the reduction of the Auger electron
diffraction effects for a Ge(100) surface when the measurements were performed
in coincidence with the photoelectrons [20].

APECS has also been used to study the electronic structure of the
Cu(001)-p(2x2)S adsorbate system [21]. The overlapping $L_{2}VV$ and $L_{3}VV$
spectra could be separated by measuring in coincidence with the S 2p1/2 and
2p3/2 photoelectron lines, respectively, and their intrinsic line shapes could
be determined. Overlayers of sulfur on Cu(001) and Ni(001) surfaces at
different coverages and thereby for different local environments of the S
atoms have also been studied using APECS [22]. Changes in the sulphur derived
density of states around the Fermi energy were identified when moving from a
copper to a nickel substrate.

When measuring Auger spectra in coincidence with the photoelectron spectra the
uncertainty due to the finite lifetime can be removed. In such a case, an
energy loss $-\Delta E$ for the photoelectron will by the conservation of
energy lead to energy gain $\Delta E$ for the corresponding Auger electron.
The only remaining lifetime broadening in the APECS spectra will hence be
caused by the finite lifetime of the final states. This implies that one can
study Auger processes and Auger two-hole final states which are not broadened
by the lifetime of the core hole state, under the assumption that the two-hole
state decay times are much longer than decay times of the selected initial
core hole state, so that the selected initial state can decay independently
[23]. One advantage of this is that one is not restricted to using the
narrowest core levels in order to achieve high resolution.

This narrowing effect was demonstrated for Cu where the 3p3/2 line was
measured in coincidence with the $M_{3}M_{45}M_{45}$ Auger spectrum [24]. The
33/2 line has a width of 2.2 eV, while the $M_{45}M_{45}{}^{1}G$ final state
has a width of only 1 eV. When the 3p3/2 spectrum was measured in coincidence
with a fixed and narrow energy window for the Auger spectrum they measured a
photoelectron peak, which was narrower than the 2.2 eV expected from its
lifetime. The intrinsic lifetime of the 3p3/2 level was instead manifested as
a shift within this 2.2 eV span as the energy of the Auger window was moved.
The line narrowing effects were also clearly demonstrated in an investigation
of Xe [25].

In this connection the $N_{23}N_{45}N_{45}$ spectra in the 4d transition
elements and the following elements up to Xe constitute a particularly
interesting case. The Super Coster-Kronig character of the
$N_{23}N_{45}N_{45}$ decay makes it very rapid and a one-step description of
the excitation-deexcitation process becomes absolutely crucial. The
distinction between the photoelectron and the Auger electron becomes less
relevant and the shapes of the individual spectra may be heavily distorted
[26]. However, by determining the sum of the energies of the emitted electrons
with APECS, one can still accurately probe the energy spectrum of the
$N_{45}N_{45}$ double-hole states, as demonstrated for Pd [27] and Ag [28].
For Pd, the 4p photoelectron peaks are broad with a Lorentzian width of 4.7
eV, but except for the additional Lorentzian broadening their line shapes are
the same as for the narrower 3d lines [29]. In these works it was demonstrated
that a correlation map can reveal the nature of the Auger decay. In the case
of the 4p decay of Pd and Ag surfaces it was found that the Auger decay is
described best by a 1-step process, while the 3d decay proceeded in a two-step
manner. Such a behaviour can also be expected for the elements following Ag in
the periodic table on the basis of their heavily distorted 4p line shape. The
concept of first creating a 4p hole, which then decays, completely breaks
down. In fact, it is no longer relevant to talk about $4p_{1/2}$ and
$4p_{3/2}$ single hole states. However, using the sum spectra, the
$N_{45}N_{45}$ double hole states can also in this case be accurately probed,
and the spectra show a similar shape as when determined using the
$M_{45}N_{45}N_{45}$ Auger decay [28].

At ELETTRA in Trieste, the coincidence setup (ALOISA) incorporates several
spectrometers, which allows angle resolved coincidence measurements [30]. The
angular capabilities have allowed the establishment of the technique denoted
Dichroic Effects in Angle Resolved APECS (DEAR-APECS). This has for instance
been used to separate the different multiplet terms in the $M_{3}M_{45}M_{45}$
Auger spectrum from Cu(111) [31]. This technique has also been used to study
antiferromagnetism in the NiO/Ag(001) [32]. Furthermore, in thin films of Fe
on Cu(001) the dichroic effects have been used to identify spectral features
where the holes are created either in the minority or in the majority bands
[33]. It was then found that there were particularly strong correlation
effects when the holes were created in the majority band.

One has also used coincidence techniques to probe the angular and energy
correlation of a pair of electrons emitted from a surface upon impact of an
electron of specific momentum [34] or excited by a beam of monochromatic
photons [35]: In this way one has derived information on the exchange-
correlation hole in solids. The two-hole emission spectrum has also been
studied in direct double photoionization processes and at energies where Cu 3p
holes can be created, showing similar energy sharing effects in both cases
[36].

##  2 Experimental Setup

Figure 1: Schematic of the CoESCA measurement setup. The X-rays enter the
experiment from the right side in the figure and hit the sample in front of
the spectrometers. The sample is not shown in this illustration. It is mounted
on a 5-axis manipulator installed at the top flange of the analysis chamber.

The Coincidence Electron Spectroscopy for Chemical Analysis (CoESCA) end-
station is built at the BESSY UE52-PGM beamline which is a conventional soft
X-ray plane-grating monochromator beamline, installed at an elliptical APPLE-
II-type undulator, with a combination of a cylindrical and spherical mirror to
provide a small horizontal focus of about 100 $\mu$m near the monochromator
exit slit. The available photon energy is in the range from 120 eV up to 1600
eV and linear or elliptical polarisation can be set. The beamline offers a
photon flux in the order of 1012 ph/s/100mA and a resolving power of more than
10000 at 400 eV photon energy [37, 38].

The CoESCA end-station is designed for electron-electron coincidence
measurements on either in-situ or ex-situ prepared samples. It consists of an
analysis chamber, equipped with two angle resolved time of flight (ArTOF)
spectrometers [39], Fig. 1. The two ArTOFs are of different types reflecting
the evolution of this type of spectrometers. One is an ArTOF 10k (actually the
prototype) with an acceptance angle of $\pm$14∘and the other instrument is an
ArTOF 2 EW type with a wide acceptance angle of $\pm$24∘. Both spectrometers
are positioned at a 54.6∘angle with respect to the incoming photon beam.

The sample is placed on a 5-axis manipulator (xyz-position, polar- and
azimuthal rotations) with active sample heating or cooling in a temperature
range from 30 K up to 900 K. A radial sample transfer system connects the
analysis chamber with a load lock for sample introduction, a sample storage
and a sample preparation chamber. The preparation chamber is equipped with a
4-axis manipulator with resistive heating, direct current heating or electron
bombardment options (up to 1200 K) and provides sample current and
temperature, a sputter gun and a quartz balance. There are a number of free
ports for further equipment like evaporators or gas dosing systems. Another
utility chamber (not shown in Fig. 1) is situated on top of the analysis
chamber, and is equipped with mass spectrometer, sputter gun and extra flanges
for more user equipment. In addition, there are free access ports to our
sample transfer system for accommodating user provided chambers to carry out
specific sample preparations.

The ArTOF electron spectrometers use advanced electron lenses in combination
with measuring the time-of-flight of the electron and its impact position on
the detector at the end of the flight tube. From this, the exact particle
trajectory through the lens system can be calculated including the take-off
angle of the electron providing for full 3d electron distributions in "one
shot", i.e. for one set of parameters for electron analyser, beamline and
sample position. The kinetic energy is determined from the time-of-flight and
the precisely known length of the flight path [39]. The instruments can, of
course, be operated in non-coincidence mode for advanced studies of materials
where, for example, two different core level regions can be monitored
simultaneously while scanning an experimental parameter, such as the sample
temperature.

ArTOF spectrometers demand a pulsed light source with a minimum time
separation between the pulses, which depends on the chosen electrostatic lens
mode and the kinetic energy of the electrons under investigation. For ArTOF
measurements at the UE52-PGM beamline, the pulse-picking-by-resonant-
excitation (PPRE) mode of BESSY II is used, providing quasi single bunch
pulses separated by 800 ns (repetition rate of 1.25 MHz) [40]. However, recent
developments on the BESSY machine side give rise to higher pulse repetition
rates in the future. They are developing a TRIBs mode of operation for the
storage ring [41, 42], where a selected number of the electron bunches is
pushed to an alternative orbit. The light pulses originating from the
different orbits can be separated in the beamlines. The experimentalist can
set the beamline to the light from either orbit, enabling to effectively offer
two pulse fill patterns at once. One fill pattern can be optimised for one or
a few experiments without effecting the larger majority of running
experiments. For the CoESCA station, at least up to 5 MHz pulses repetition
rate, i.e. 4 times the present value, can be processed, yielding 4 times
shorter acquisition times for the same data quality.

##  3 Measuring Coincidences

In our setup an event is stored as a coincidence, if one electron is detected
in each spectrometer after excitation by the same photon pulse. The data is
7-dimensional: 3D for each electron (x,y-hit coordinates and arrival time
coordinate t) stored together with a trigger timestamp:

$\text{Event}=\\{x_{1},y_{1},t_{1},x_{2},y_{2},t_{2},\text{\emph{trig}}\\}.$
(1)

True coincidences are pairs of electrons which are created by absorption of
one photon. However, there is also a background of accidental coincidences. In
this case, the two detected electrons have been excited by the same photon
pulse, but they originate from two different photons, hence different sites in
the sample. The aim is to measure the true coincidence distribution as
accurately as possible and in the shortest possible time. There is no way
experimentally to directly distinguish true from accidental coincidences.
However, one can instead separately determine the distribution of only
accidental coincidences and subtract them to derive the distribution of true
coincidences from the data. It is then essential that the distribution of
accidental coincidences is measured in exactly the same way as the full
coincidence distribution.

Our setup is ideally suited for achieving this. During the experiment, a
database is written containing each event in each detector together with a
timestamp, which serves as a unique photon pulse ID. In post-processing, true
& accidental coincidences measured from the same pulse (all coincidences) are
extracted from the data, for events where an electron was detected in both
detectors for the same pulse. Accidental coincidences are extracted for cases,
where one electron is recorded in each spectrometer, but for events from two
different photon pulses (accidental coincidences).

The data lists are sorted into multi-dimensional histogram distribution
matrices $M$. The distribution for coincidences from one photon and one site
in the sample, the true coincidences dataset $M_{t}$, is derived in post-
processing by a simple subtraction of the accidental distribution $M_{a}$ from
the all coincidences distribution $M_{c}$:

$M_{t}=M_{c}-M_{a}$ (2)

with

$M_{a}=\tfrac{1}{\gamma}\,M_{\gamma},$ (3)

where $\gamma$ is the number of virtual pulses per real pulse, which are
analysed for accidental coincidences to get the measured distribution of
accidentals Mγ. In our case, the accidental data is created from comparing
detector A, pulse N with detector B, pulse N-1 and, vice versa, from comparing
detector A, pulse N-1 with detector B, pulse N. Hence, it is created from
twice as many virtual pulses than the all coincidences map and therefore
$\gamma=2$.

The full 6D coordinates can be used to analyse the data. In most cases one
looks at 2D maps of $E_{1}$ vs. $E_{2}$ (see Fig. 4 and Fig. 5), but any other
combination of coordinates can be used, for example one can additionally
discriminate by the angles of the electrons and look at coincidences resolved
in energy- and k-space.

All events are stored in a list-like database together with a timestamp. This
enables a variety of possibilities for post treatment and analysis of the
data. One may for instance detect, that there have been some changes of the
sample during the measurements due to contamination or radiation damage and
that therefore only a subset of the collected data is usable. This can be
based on a careful analysis of the singles spectra, extracted from the data
base. The singles spectra are calculated by evaluating the signals for each
ArTOF independently, without looking for coincidences. This yields the same
spectra as in a classic non-coincident setup. These spectra are very useful,
since they usually have two to three orders of magnitude higher count rates
than the coincidence data. If a subset is identified in the singles data,
where the changes can be neglected, one knows that the corresponding subset
can be used also for the coincidence data. Furthermore, when using only part
of the coincidence data this can always be connected to the corresponding
determination of the accidental coincidences. All these spectra have in this
case been recorded under exactly identical conditions.

The fact that the events are stored together with a timestamp, makes the
experiment well adapted to studies of time-dependent phenomena. One can study
slow processes, where the theoretical time resolution is set by the separation
of the x-ray pulses, which in the case of BESSY II in the single bunch mode is
800 ns. In praxis, this time resolution is much slower and governed by the
data statistics, since the low count rates make it necessary to integrate over
many x-ray pulses before enough useful information can be found in the data
set. For studies of more rapid processes one could use a femto- to picosecond
pump laser pulse, with a tuneable delay to the x-ray pulse. In this case the
time resolution is set by the length of the x-ray pulse, typically 40 ps at
present. However, for now the CoESCA station is not equipped with such a pump
laser system.

An Auger spectrum provides information on the energies of two-hole states of a
system. Usually, the two-hole energies are determined from an Auger spectrum
by subtracting the core level binding energy from the Auger energies. By doing
so, the Auger spectrum is plotted on an energy scale which corresponds to the
binding energy for the two-hole final states. If, for a metallic solid, the
core level binding energy and the Auger energies are referenced to the Fermi
level, also the two-hole energy scale will be referenced to the Fermi level.
This is a widely used method to obtain the two-hole spectrum, which is valid
in regions, where there are no overlapping Auger transitions due to the decay
of other core levels. However, one has to accept, that the spectrum will be
influenced by any broadening effect connected to the core ionisation. In
particular, the life time broadening of the core level will be seen as a
corresponding broadening of the Auger spectrum and hence of the corresponding
two-hole spectrum.

However, in a coincidence measurement it is possible to derive directly the
binding energy of the two-hole final state. Since, for each coincident event,
the energies of the photoelectron and the Auger electron are both measured,
also the sum of these energies can be determined. The two-hole energy is then
obtained by subtracting this energy sum from the photon energy. In our set-up
it is straight-forward to extract the two-hole energy spectrum. The two-hole
spectrum can be derived directly from the true coincidence map by summing the
kinetic energies for each point in the map. Alternatively, one can treat the
data in the same way as when deriving the true coincidence map, only that one
for each event is calculating the sum of the kinetic energies, for the
coincidence recording as well as for the recording of the accidental
coincidences.

The two-hole spectrum, derived in this way, is not broadened by the core-hole
life time. In coincidence spectra recorded at high resolution this allows
improved resolution for the two-hole spectra. The count rate, however, is
lower for the coincidence data so in each case one has to judge which type of
evaluation of the data provides the most accurate results. Furthermore, the
direct derivation of the two-hole spectrum makes it possible to use also
rather broad core levels in Auger spectroscopy. This is a great advantage
since it extends the range of core levels which can be used for detailed
measurements.

### Effective coincidence count rate and limitations

The true and accidental coincidence count rates are small compared to the
primary particle pulse repetition rate. For example, at CoESCA we typically
see an order of $10^{-6}$ coincidence counts per photon pulse. The measured
signals from different pulses are pair-wise independent and do not influence
each other. Therefore, we can describe the behaviour of the probability of $k$
events detected for the same pulse for an average rate of events per pulse
$\lambda$ with a Poisson distribution:

$P_{\lambda}(k)=\frac{\lambda^{k}}{k!}\text{e}^{-\lambda}\overset{(\lambda\ll
1)}{\;\approx\;}\ \frac{\lambda^{k}}{k!}$ (4)

$\lambda$ scales linearly with the incident flux, i.e. the number of primary
particles per pulse (e.g. photons). In [12], Jensen et al. provide a detailed
analysis of the link between electron count rates and experimental parameters,
such as primary particle flux, total detection volume, detection efficiencies
and cross-sections for electron pair creation.

For a true coincidence, one primary particle is absorbed ($k=1$), which
creates one electron pair, leading to one coincidence event in the detectors.
An accidental coincidence occurs, when two primary particles are absorbed in
the sample ($k=2$), and two electrons, which are recorded by the detectors,
are created at two different sites. Events for more than two absorbed primary
particles can be neglected, since the probability drops very fast with
$(\lambda^{k}/k!)$. The probabilities for detecting a true ($k=1$) or
accidental ($k=2$) coincidence read as:

$\displaystyle P_{\lambda}(1)$ $\displaystyle\approx\lambda,$ (5)
$\displaystyle P_{\lambda}(2)$ $\displaystyle\approx\frac{1}{2}\lambda^{2}.$

The probability of finding any number of events for a single pulse is the sum
over $P_{\lambda}(k)$ for all $k$. And the probabilities for any two distinct
pulses $A$ & $B$ are linearly independent. Thus, the probability to record an
accidental coincidence from these two pulses is the product of the
probabilities of measuring one or more events from each pulse independently:

$\displaystyle P^{A\&B}_{\lambda}$
$\displaystyle=P^{A}_{\lambda}\;P^{B}_{\lambda}=\left[\sum_{k>0}P_{\lambda}(k)\right]^{2}$
(6)
$\displaystyle\approx\left[P_{\lambda}(1)\right]^{2}=\lambda^{2}=2\;P_{\lambda}(2)$

The equation above states, that the accidental coincidence signal, which is
derived from comparing pairs of different pulses is twice as intense as the
accidental contribution to the coincidences signal derived from single pulses
only. This is accounted for in Eq. (3) by the scaling factor
$\tfrac{1}{\gamma}$.

The true and accidental count rates are defined as counts per time. They are
linearly proportional to the respective $P_{\lambda}(k)$. However, the
proportionality constants are different for measuring true or accidental
coincidences, since the detection volume for accidental coincidences is larger
than for true coincidences, and since there is a contribution to the
accidental coincidences arising from competing events against which one is
trying to discriminate, like for example inelastic scattering of higher energy
electrons [12]. In order to respect these proportionalities, constants are
introduced, which connect the count rates $\nu_{t}$, $\nu_{a}$ with the
respective probabilites $P_{\lambda}(k)$:

$\displaystyle\nu_{t}$
$\displaystyle=\sigma_{t}\,\,P_{\lambda}(1)\propto\lambda,$ (7)
$\displaystyle\nu_{a}$
$\displaystyle=\sigma_{a}\,P_{\lambda}(2)\propto\lambda^{2}.$

The rate of all coincidence counts per time, measured from single pulses is
given by the sum of the true and accidental coincidence count rates:

$\nu_{c}=\nu_{t}+\nu_{a}.$ (8)

For a given acquisition time $\tau$, the number of all coincidence counts
measured in an experiment is $N_{c}=\nu_{c}\,\tau$ and the number of
accidental counts in this signal is $N_{a}=\nu_{a}\,\tau$. The ratio of these
counts can be expressed as:

$R=\frac{N_{c}}{N_{a}}=\frac{\nu_{t}+\nu_{a}}{\nu_{a}}\propto\lambda^{-1}+1$
(9)

and it approaches $R=1$ for an infinite flux of primary particles $\lambda$.

In order to validate the assumptions and approximations in Eq. (4)-(9) for our
setup, we performed short coincidence runs for three different light
intensities and determined $N_{c}$ and $N_{a}$ for each run. Fig. 2 shows the
ratios $R$ from these runs versus the inverse flux, which was deduced from the
singles count rates. A linear fit extrapolates $R_{0}=1.038\pm 0.001$ for
$\lambda^{-1}=0$, which is in good agreement with the theoretical value of 1
and validates our assumptions.

Figure 2:  Ratio R of coincidence counts from one pulse $N_{coin}$ and
coincidence counts from two pulses $N_{acc}$ versus the inverse flux. The
fitted line extrapolates to $R_{0}=1.038\pm 0.001$ for an inverse flux of 0,
which confirms the validity of our assumptions in Eq. (4)-(9).

The ratio of accidental to true counts for events recorded from single pulses
is an important parameter for coincidence experiments. From Eq. (7) we see
that this ratio is given by:

$\nu_{a}/\nu_{t}\propto\lambda\propto\text{flux}.$ (10)

The higher the flux, the higher the relative accidental background, therefore
simply increasing the flux is not beneficial for a coincidence experiment. On
the other hand, simply lowering the intensity in order to remove almost all
accidental coincidences leads to low count rates and therefore long
acquisition times. In order to judge the flux and the acquisition time needed
to achieve a dataset of acceptable quality, it is useful to look at the
behaviour of the ratio of the derived true coincidences signal and its
statistical error, i.e. the signal-to-noise ratio $S$ of the true coincidences
dataset as calculated from the measured data:

$S=M_{t}/\Delta M_{t}$ (11)

This ratio can be interpreted as the amount of useful information, which is
added to the data for a given acquisition time. In [12], the authors discuss
the conditions for reaching a certain value of this ratio in a coincidence
measurement, starting from very basic assumptions. In their considerations,
the contributions to the statistical noise, which originate from the
subtraction for calculating the true coincidences in Eq. (2) are approximated
as negligible. They find, that the signal-to-noise ratio approaches an
asymptote, when the flux of primary particles becomes too high. Here, we
present a calculation of $S$, which is adapted to our data acquisition system
and includes all contributions to the statistical error of the derived true
coincidences dataset, which arise from the measurements of all coincidences
from single pulses, $M_{c}$, and the determination of the accidental
coincidences $M_{a}$ from comparing pairs of different pulses. These two
datasets and their statistical noise can be defined in terms of the count
rates $\nu_{t}$ and $\nu_{a}$ and the acquisition time $\tau$. Please note,
that the following considerations, about the statistical quality of the counts
in our multidimensional data matrices $M_{x}$ apply to each single point
within the matrices. Therefore, they also apply to the sum of a subset of
these matrices, when binning the data. The total count rates
$N_{x}=\sum{M_{x}}$ are the extreme case of binning to one single point per
dataset.

The coincidences originating from single pulses, $M_{c}$, are measured
directly and can be described as:

$\displaystyle M_{c}$ $\displaystyle=(\nu_{t}+\nu_{a})\tau$ (12)
$\displaystyle\Delta M_{c}$
$\displaystyle=\sqrt{M_{c}}=\sqrt{(\nu_{t}+\nu_{a})\tau}$

The accidental dataset $M_{a}$ is derived from $M_{\gamma}$, which was
measured with a statistical error of $\Delta M_{\gamma}=\sqrt{M_{\gamma}}$, we
get:

$\displaystyle M_{a}$ $\displaystyle=\tfrac{1}{\gamma}M_{\gamma}=\nu_{a}\tau$
(13) $\displaystyle\Delta M_{a}$ $\displaystyle=\tfrac{\partial
M_{a}}{\partial M_{\gamma}}\;\Delta
M_{\gamma}=\tfrac{1}{\gamma}\sqrt{M_{\gamma}}=\sqrt{{\nu_{a}\tau}/{\gamma}}$

The true dataset $M_{t}$ and its statistical error can be written as:

$\displaystyle M_{t}$ $\displaystyle=M_{c}-M_{a}=\nu_{t}\tau$ (14)
$\displaystyle\Delta M_{t}$ $\displaystyle=\sqrt{(\Delta M_{c})^{2}+(\Delta
M_{a})^{2}}$
$\displaystyle=\sqrt{\left(\nu_{t}+(1+\tfrac{1}{\gamma})\nu_{a}\right)\tau}.$

Hence, we get:

$\displaystyle S$
$\displaystyle=\sqrt{\frac{\tau}{\nu_{t}^{-1}+(1+\tfrac{1}{\gamma})\nu_{a}\nu_{t}^{-2}}}$
(15)
$\displaystyle\propto\sqrt{\frac{\tau}{\lambda^{-1}+1+{\tfrac{1}{\gamma}}}}$

with $\nu_{t}\propto\lambda$ and $\nu_{a}\propto\lambda^{2}$, see Eq. (7).

For infinite flux, $\lambda=\infty$, $S$ approaches an upper limit:

$\displaystyle S_{0}=\lim\limits_{\lambda\to\infty}S$
$\displaystyle=\sqrt{\frac{\tau}{(1+{\tfrac{1}{\gamma}})\nu_{a}\nu_{t}^{-2}}}$
(16) $\displaystyle\propto\sqrt{\frac{\tau}{1+{\tfrac{1}{\gamma}}}}$

Figure 3: Effective signal-to-noise ratio $S/S_{0}$ versus photon flux in
units of $\nu_{a}/\nu_{t}$. The dashed lines mark $\nu_{a}/\nu_{t}=1$. See
text for more details.

Fig. 3 plots the effective signal-to-noise ratio $S/S_{0}$ versus the photon
flux in units of $\nu_{a}/\nu_{t}$ for $\gamma=2$, which means that twice as
many virtual pulses are used for the determination of the accidental dataset
than real pulses have hit the sample. Note, that the values for $S/S_{0}$ are
only qualitative, since we neglected the proportionality constants for
$\nu_{t}$ and $\nu_{a}$ in this representation. However, we see that $S/S_{0}$
approaches its asymptote very fast and the gain in signal quality decreases
rapidly already for increasing the flux above a level corresponding to an
accidental to true ratio of $\nu_{a}/\nu_{t}=1$. Hence, the acquisition time,
which is necessary to achieve a desired statistical quality of the true
coincidence data does not substantially decrease anymore for going to higher
fluxes. On the other hand, a further increase of the flux quadratically
increases the number of recorded events and hence the amount of data to be
stored. For example, at $\nu_{A}/\nu_{T}=10$, depending on the sample, the
CoESCA station can easily produce more than 500 GB of coincidence data for a
typical measurement week of $6\times 12$-hour shifts. This corresponds to two
or three coincidence maps, i.e. combinations of Auger and Photoelectron energy
window settings of the detectors.

In order to increase $S/S_{0}$, a data analysis scheme for working with
$\gamma>2$ is currently being developed for the CoESCA station. The
accidentals dataset $M_{\gamma}$ will be created by adding up the accidentals
analysis results from pulse pairs (N,N-1), (N,N-2), …, (N,N-K), with
$K=\gamma/2$. The theoretical limit of $S$ for ${\gamma\to\infty}$ corresponds
to the intrinsic signal-to-noise ratio arising from the measurement of the
coincidence signal only and equals to $M_{t}/\Delta M_{c}$.

The best way to strongly reduce acquisition times, while remaining at an
acceptable data rate is to increase the number of experiments per time, hence
the pulse repetition rate. In this experiment, the pulse repetition rate from
the storage ring was fixed to 1.25 MHz. The earlier mentioned development of
the TRIBs mode operation of the storage ring [41, 42] could enable up to 5 MHz
pulse repetition rate in the near future.

##  4 Results & Discussion

Arena et al. have previously reported Ag 3d-M45NN APECS measurements [43] and
shown how coincidence spectroscopy can be used to determine the intrinsic
shapes of overlapping spectral lines. In their experiment, they measured the
coincidences with two cylindrical mirror electron analysers (CMA) of 1 eV
instrumental resolution. One CMA was set to a fixed energy in the Auger
region, while the second CMA scanned the core level spectrum and, vice versa,
one CMA was set to a fixed core level energy region, while the other CMA
scanned the Auger spectrum.

In contrast to their setup, like many other coincidence setups nowadays, the
CoESCA station can record a coincidence map and a corresponding map of
accidental coincidences in one run, without changing the analyser settings or
any other experimental parameter. The best guess of the true coincidences
dataset is derived in post-processing by a simple subtraction, see Eq. (2).
For electron-electron coincidences from surfaces, the successful subtraction
of the accidental coincidences contribution from the coincidence dataset has
previously been demonstrated in [44].

For the measurements presented in this paper, we chose a photon energy of 700
eV and operated the beamline at a resolution of 100 meV. The ArTOF 10k
spectrometer was set to record the Auger spectrum in the range of $335-359$ eV
kinetic energy, while the ArTOF 2 EW spectrometer was set to record the
photoelectron spectra in the range of $318-330$ eV kinetic energy. The total
experimental resolution was around 0.6 eV, determined from fitting the PES
lines. The position of the Fermi edge was used to calibrate the energy axis
for both spectrometers in post-processing. The silver single crystal sample,
Ag(111) (99.999%, MaTeK GmbH), was cleaned by repeated $Ar^{+}$ sputtering and
annealing cycles until no signs of contamination of the Ag surface by other
materials, especially carbon, nitrogen and oxygen were visible in the
photoelectron spectra.

The photon flux was adjusted via the exit slit of the beamline to achieve
singles count rates of $0.8\text{\times}{10}^{3}$ $s^{-1}$ for the Auger
region and $1.0\text{\times}{10}^{3}$ $s^{-1}$ for the core level region. The
total acquisition time was 24h, which yielded 106124 coincidence counts from
single pulses and 101504 accidental coincidence counts from cross-comparing
two consecutive pulses, resulting in 55372 true coincident counts. This
corresponds to a measured coincidence rate of $\nu_{c}=1.2\;s^{-1}$, composed
of $\nu_{t}=0.64\;s^{-1}$ true and $\nu_{a}=0.59\;s^{-1}$ accidental
coincidences and and accidental-to-true ratio of $\nu_{a}/\nu_{t}=0.92$. The
photon pulse repetition rate was 1.25 MHz.

(a)

(b)

Figure 4: Raw data maps (2D-histograms): _(top)_ All coincidences acquired
from single pulses. _(bottom)_ Accidentals recorded for two consecutive
pulses. The energy of the Auger electron is plotted on the x-axis and the
binding energy of the photoelectron is shown on the y-axis. Figure 5: True
coincidence map derived from the raw data shown in Fig. 4, see text for more
details on how the true map is obtained. Colored frames in the map indicate
the integration regions for the Auger spectra in coincidence with the M4
(3d3/2, orange) or the M5 (3d5/2, blue), respectively. On the left are the
integrated photoelectron spectra and the Auger spectra are plotted on top of
the map. In addition, the sum of the true map (black) and the non-coincident
singles spectra (grey, dashed) derived from the accidentals map are shown. The
M5NN Auger spectrum is a intrinsic spectrum already, while the M4NN spectrum
still contains up to 6% of true coincident background originating from
scattered M5 photoelectrons. See text and Fig. 6 for a description of the
origin of this background and an estimated intrinsic M4NN Auger spectrum.

We were operating the ArTOF 2 EW analyser at its design limits and therefore,
the transmission function along its energy window was not constant. For the
present analysis, it is sufficient to account for this in post-processing by
correcting the spectral intensities with a linear transmission function such,
that for the singles photoelectron spectra (PES) the ratio of M5 peak area
over M4 peak area would match the literature value of 0.67 [29]. In a recent
study, the potential to operate angular resolved time of flight spectrometers
beyond the standard limits and extending the time of flight range which can be
analysed has been shown [45]. The ArTOF 10k detector, used for measuring the
Auger spectra, was operated well within its specifications, with a constant
transmission function.

The data maps as acquired are shown in Fig. 4. Fig. 5 shows the true
coincidence map.

The coloured frames in the map mark the integration regions, used for
extracting the Auger spectra obtained in coincidence with the 3d3/2 (orange)
and 3d5/2 (blue) photoelectron peaks, respectively. These are plotted on top
together with the full sum of the coincidence map. Also the singles spectrum
is shown. It is clearly seen that the singles spectrum has a much larger
background. This reduction of background is another advantage of recording the
Auger spectrum in coincidence with the appropriate photoelectron region. The
PES spectra are plotted on the right. The PES peaks have two equivalent
denotations: 3d3/2 or M4 for the peak at $E_{b}=373.8$ eV and 3d5/2 or M5 for
the peak at $E_{b}=367.8$ eV.

The spectrum obtained in coincidence with the 3d5/2 photoelectron line is a
pure M5NN Auger spectrum. For the spectrum in coincidence with the 3d3/2
photoelectron line the situation is, however, slightly different. The orange
region in the coincidence map contains not only 3d3/2 photoelectrons. There is
also a contribution from 3d5/2 photoelectrons, which have lost energy due to
shake-up or inelastic loss processes. n the case of silver these additional
excitations will be delocalised and will not significantly modify the 3d5/2
decay spectrum. For this reason the spectrum obtained by integration of the
orange region will contain a contribution which is identical to the M5NN Auger
spectrum. In order to estimate the intensity of this contribution we have made
a numerical fit of the 3d photoelectron peaks. As a model for the inelastic
tail of the spectra we have used a Shirley background. From the fit we can
then determine the intensity of the tail of the 3d5/2 spectrum in the
integration region of the 3d3/2 peak. We find that, for our experiment, this
contribution amounts to about 6% of the M4 peak intensity and we use this as
an upper limit for the M5NN contribution to the M4NN spectrum. Note, that the
amount of this type of true coincident noise depends on the amount of
inelastic scattered signal in the recorded true coincident spectrum and thus
on the full width of the detection window in energy space. Therefore our value
of 6% is true only for this experiment. Another source for such a contribution
to the coincidence background could be due to a Coster-Kronig (CK) type decay.
For silver, however, only M4M5O CK are energetically allowed, and the cross-
sections for those are negligibly small.

The M4NN spectrum is shown in the top panel of Fig. 6 before and after
correction for the M5NN contribution. It is clearly seen that the M5NN
contribution background is present on the low kinetic energy side of the main
peak. The main M4NN peak is therefore unaffected by the M5 contribution, as a
result of the good resolution of the CoESCA setup. The correction is also very
small and changes the appearance of the spectrum very little. Also the
fraction of M5 contribution depends on the resolution of the setup. If
measured with lower resolution the relative amount of the M5 contribution
would be larger.

The bottom panel of Fig. 6 shows the measured and intrinsic M4 and M5 two-hole
spectra. These were obtained by summing the kinetic energies for the true
coincidences, as described in the previous section. The data was then sorted
in a histogram with equidistant bins of 500 meV.

Figure 6:  _(top)_ Measured M4VV coincidence spectrum (orange), scaled M5NN
coincidence spectrum (blue) and their difference as best guess for the
intrinsic M4NN spectrum (green, see text for details). _(bottom)_ Two-hole
binding energy spectra: Comparison of M5NN (blue), M4NN as measured (orange)
and derived intrinsic M4NN (green). The markers in both plots are the measured
data. The solid lines are the data smoothed with a Savitzky-Golay filter [46]
as guide for the eye.

##  5 Summary & Outlook

The APECS technique has been introduced and a detailed overview of previous
experiments on this topic was given. The experimental end station for APECS at
the BESSY II synchrotron facility, the CoESCA station, has been described
together with important basic considerations on the data acquisition and
treatment procedure in an electron-electron coincidence experiment.
Fundamental limits on acquisition times and Signal-to-Noise ratio have been
derived. We have presented the first APECS results using the CoESCA station on
a clean Ag(111) single crystal for measuring coincidences between the Ag 3d
core levels (M4 and M5) and the corresponding Auger electrons from M45NN Auger
decays. The acquired true coincidence spectrum for the M5NN Auger decay is
already intrinsic. The acquired M4NN Auger spectrum, however, still contains
contributions from the M5NN decay. We have explained the origin of these
contributions and presented a method to obtain an estimate of the clean,
intrinsic M4NN spectrum. Furthermore, we extracted two-hole binding energy
spectra for each Auger decay, M4NN and M5NN, respectively, from the true
coincidences map. These spectra can be determined only from coincidence
measurements and show the distribution of the total energy needed to create a
coincident Auger electron – Photoelectron pair, leaving two holes in the
sample’s electronic system.

Further recent results from the CoESCA station on Auger- and Photoelectron
coincindences of molecular O2 adsorbed on Ag(111) [47] and quantifying Ni L2,3
core-hole relaxation pathways [48] have been submitted for publication.

##  6 Acknowledgements

This work has been supported by the European Research Council
(FP7/2007-2013)/ERC grant agreement no. [321319], the Swedish Research Council
and Carl Tryggers Foundation for Scientific research (CTS).

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