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Nuclear Inst. and Methods in Physics Research, A 903 (2018) 234–240
Contents lists available at ScienceDirect
Nuclear Inst. and Methods in Physics Research, A
journal homepage:
Simulation of charge sharing in the Caliste-SO detector
J. Barylak a, *, A. Barylak a , T. Mrozek a , O. Grimm b , A. Howard b , P. Podgórski a , M. Stęślicki a
Space Research Centre, Polish Academy of Sciences, ul. Bartycka 18A, 00-716 Warsaw, Poland
Institute for Particle Physics, ETH Zurich, Schafmattstrasse 20, 8093 Zurich, Switzerland
Charge sharing
X-ray detector
X-ray spectroscopy
Solar Orbiter
Caliste-SO is CdTe X-ray pixelated detector employed in STIX telescope which is one of the instruments on-board
Solar Orbiter mission. In such type of detectors charge sharing between adjacent pixels is expected. The effect
can affect measured spectra which requires the development of dedicated method for scientific data processing.
In this article, we present simulations of the charge sharing with regard to incoming photon energy. We define
two processes causing charge sharing: fluorescence and movement of charge cloud. First type was calculated
using Geant4 toolkit to determine the response of the detector. Additionally we prepared dedicated software
written in Interactive Data Language (IDL) to calculate instrumental effects: Fano and electronic noise, charge
loss and properties of the entrance window. To calculate second type of charge sharing we calculated movement
of charge cloud in the crystal using Fick’s second law. Our simulation shows that for Caliste-SO detectors charge
sharing strongly depends on energy of incoming photon. The fraction of events classified as double counts is
nearly 6% for 150 keV photons. Furthermore, we calculated the charge sharing for the Caliste64 detector. For
this case our result is confirmed by laboratory measurements.
1. Introduction
The aim of the Solar Orbiter (SO) [1] mission planned by ESA and
NASA is to investigate the relation between the Sun and the heliosphere.
The launch is planned on February 2019. The spacecraft will perform
in-situ measurements with various types of detectors and antennas as
well as remote observations with a use of telescopes.
One of instruments on board SO is the Spectrometer/Telescope for
Imaging X-rays (STIX) [2]. It will measure solar X-ray flux in the 4–
150 keV energy range with a use of Caliste-SO detectors. The STIX’s
spatial resolution will be unprecedented, due to close approach to the
Sun at a distance of less than 0.3 AU (5 × 107 km). For imaging purpose
the instrument will use so called coded apertures [3,4] which are widely
used in high-energy observational astronomy.
The Caliste-SO is the pixelated (12) cadmium telluride (CdTe) Xray detector. Such type of detector is frequently used in recent satellite
X-ray experiments [5]. STIX will operate in a way that simultaneous
registration of counts in two separate pixels of each detector (double
count) is lost. Therefore understanding processes leading to multiple
counts is very important during scientific data analysis. Such events are
caused by three processes:
∙ two photons arrive precisely at the same time producing counts
in two pixels (this case is not investigated in this paper);
∙ one photon is absorbed close to the edge of one pixel and
escaping fluorescence photon is absorbed in neighbouring pixel
— fluorescent counts;
∙ photon is absorbed very close to the border between adjacent
pixels thus carriers cloud produced due to absorption is divided
between pixels — split counts.
These effects, if affect large fraction of counts, are severe for a quality
of scientific data, because of the loss in detection efficiency. Therefore,
the detailed simulation and comparison with laboratory measurements
is needed. This will support science output from the data collected by
the instrument.
Charge sharing problem, which is one of the primary characteristics
of pixelated Cd(Zn)Te detectors and is one of the reasons of split counts,
was studied by many authors [6–10]. Kalemci and Matteson (2002)
investigated charge sharing in CdZnTe detectors using a collimated
gamma-ray beam. They discovered that charge sharing is a function of
energy of the incoming photon and the absorption depth. The authors
found that as high as 24% of counts were split events in a case of
500 μm pixel pitch. Similar investigation using collimated X-ray beam
was performed by Allwork et al. (2012). They measured that K-shell
fluorescence X-rays increase the initial size of the charge cloud, thus
increasing charge sharing probability. Iniewski et al. (2007) proposed
Corresponding author.
E-mail address: (J. Barylak).
Received 22 December 2016; Received in revised form 26 April 2018; Accepted 26 May 2018
Available online 30 June 2018
0168-9002/© 2018 Elsevier B.V. All rights reserved.
J. Barylak et al.
Nuclear Inst. and Methods in Physics Research, A 903 (2018) 234–240
Fig. 2. The geometry of STIX. From left to right: the heat shield, the imager
with 32 subcollimators (tungsten grids), the spectrometer with 32 Caliste-SO.
Fig. 1. The measured spectrum of solar flare X-ray radiation — blue line.
The spectrum was obtained close to the maximum brightness of the X7 class
solar flare observed on January 20th, 2005. Fit to observational data was done
with two components: thermal (green line) and non-thermal (yellow line). (For
interpretation of the references to colour in this figure legend, the reader is
referred to the web version of this article.)
spectral resolution and well understanding of an instrumental effects
occurring in this critical area.
Additionally to the spectral information STIX instrument will provide
a spatial information about X-ray sources and will allow for the image
reconstruction based on different Moiré patterns generated on a different Caliste-SO detectors. Fig. 2 shows the geometry of STIX instrument.
When we look from the entrance aperture side, the first one is a heat
shield which consist of a pair of X-ray transparent beryllium windows.
Next, incoming photons go through one of many pairs of tungsten grids.
Each pair has the same pitch, but they are twisted in respect to each
other (up to 6 degrees). Their combined transmission forms a Moiré, the
location of the maximum in this pattern depends strongly on the source
location (Fig. 3). Moiré patterns are characterized by phase and intensity
which are estimated from sinusoidal function (Fig. 3, blue lines) fitted
to the X-ray distribution in the four detector stripes (Fig. 3, red lines). In
order to properly reconstruct the spatial distribution of the X-ray source,
the information from many sub-collimators is needed. Any uncertainties
and instrumental effect which affect the estimated phase and intensity
of Moiré pattern produced by the sub-collimator will affect the ability
to proper reconstruct the spatial distribution of the source.
an analytical model for estimation of the effect in CdZnTe detectors.
They reported that charge sharing apply to more than 10% of photons
of the energy of 122 keV (for the detector with 2.4 × 2.4 mm2 pixel size
and 0.1 mm pixel gap). The CdTe detectors response was investigated
by Meuris et al. (2009) who also registered more than 10% multiplepixel in a detector with smaller pixels (0.9 mm side and 0.1 mm
gap) illuminated by an 241 Am radiation source. The charge sharing
also strongly influence the energy resolution of detectors. The energy
resolution can be worsen by 6%–8% due to multiple-pixel events [9].
Additionally, in case of the STIX instrument, it will influence the image
reconstruction process based on Moiré patterns.
This paper presents results of charge sharing simulation performed
with a use of the Geant4 toolkit. We investigate the relationship between
charge sharing and the energy of incident photon. Next, we calculate
other effects, which are not implemented in the Geant4. These are:
charge loss, Fano and electronic noise, and a charge loss in the damage
layer. This allowed us to compare simulated 241 Am isotope spectrum
with the laboratory measurements.
3. Caliste-SO description
The Caliste-SO is a detector unit specially designed for STIX by
CEA/Irfu (France) and Paul Scherrer Institute (Switzerland). The detector (Fig. 4) is a hybrid module which integrates functionalities of X-ray
detection and analog front-end electronics. X-ray photons are absorbed
in the pixelated CdTe sensor with area of 10 × 10 mm2 and thickness of
1 mm. On the illuminated side, the uniform platinum cathode is located.
On the other side, aluminium–titanium–gold anode (50, 15, and 80 nm
thick, respectively) is divided into pixels. Each of them is connected to
IDeF-X HD ASIC [13,14] designed by CEA/Irfu.
The CdTe crystal with Cl compensation is slightly p-type (with
work function equal to 5.6 eV) and forms a nearly Ohmic contact with
platinum electrode (5.4 eV), passing both majority and minority carriers
easily. On the other side, aluminium layer, which is the innermost,
forms the Schottky contact (with work function equal to 4.2 eV) and
blocks the hole majority. The depletion voltage for the detector is 150 V
and the typically operated voltage is a negative 200 V at the cathode
to guarantee that the detector volume is fully sensitive and the charge
carriers are well accelerated to limit the effects of charge loss.
The IDeF-X HD is a 32 channel analog front-end with self-triggering
capability, optimized for the readout of pixelated Cd(Zn)Te sensors.
Each channel consists of charge sensitive amplifier with continuous
reset, adjustable gain stage, pole-zero cancellation stage, adjustable
shaping time low pass filter, baseline holder and peak detector with
2. Flare observation and STIX
Solar flares are observed in wide spectrum of photon energies. STIX
focuses on HXR photons which are observed from space since the
1960’s [11]. The most prominent emission mechanism producing solar
HXR is bremsstrahlung of electrons as they encounter ambient ions.
Fig. 1 shows an example of the solar flare X-ray spectrum. Electrons
which have a Maxwellian velocity distribution produce thermal component of a spectrum which dominates energies below 15–20 keV (green
line). This component allows to determine the temperature and emission
measure of the flaring plasma. The second component (yellow line) seen
at higher energies is non-thermal emission produced by electrons which
were accelerated by a release of magnetic energy during a solar flare.
The properties of non-thermal electrons can be estimated from a slope
of non-thermal component of spectrum.
The coexistence of thermal and non-thermal components and presence of the instrumental errors limit the accuracy of estimations of
a solar flare energy balance, and can significantly affect the physical
interpretation of the observed phenomena. The distinction between
these components and precise analysis of the boundary between the
areas dominated by the thermal and non-thermal emission require high
J. Barylak et al.
Nuclear Inst. and Methods in Physics Research, A 903 (2018) 234–240
Fig. 3. Top: location of a flare on the solar disk. Bottom: a Moiré pattern generated by HXR flux from flare on the detector surface. Amount of counts in four stripes
are marked by red line and fitted sinus function by blue line. (For interpretation of the references to colour in this figure legend, the reader is referred to the web
version of this article.)
Fig. 4. (a) Transparent view of Caliste-SO micro-camera taken from [12]. (b) The detector pixel pattern: One of the large pixels (no. 4) is marked by a green colour,
and one of the small pixels (no. 11) is marked by magenta. The full detector strip containing two large (no. 2, 6) and one small (no. 10) pixel is marked by an orange
colour. Blue colour indicates the guard ring. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this
discriminator. Besides that, there is common analog output buffer,
trigger output and dedicated serial interface for communication with
the ASIC and readout actions. Main parameters of the IDeF-X HD ASIC
are following:
more than 4–5 orders of magnitude in few a minutes which means that
without adjusting effective area we would get substantial dead time
effects and unacceptably high pileup.
4. Simulation method
∙ programmable gain: 50, 100, 150 or 200 mV/fC;
∙ programmable peaking time: 16 values from 0.7 to 10.7 μs
∙ low power consumption (0.8 mW/channel);
4.1. Geant4
Geant4 [15] is a toolkit enabling simulations of particles interactions
with matter and is often used for simulations of X-ray detectors response
in medical applications [16]. Recent developments in Geant4 simulation
of particle detectors operating in the energy range below 1 MeV, are
shown by Soti’s et al. [17]. Furthermore, accurate Detector Response
The expected energy resolution of Caliste-SO is equal 2.5 keV at 150 keV.
Al–Ti–Au electrode is divided into 4 ‘stripes’ (Fig. 4(b)). Each stripe
is divided into 2 large and 1 small pixel. Such scheme of pixelisation
provides redundancy and enables reduction of effective area during
intense photon fluxes in real time. Solar flares may change intensity
J. Barylak et al.
Nuclear Inst. and Methods in Physics Research, A 903 (2018) 234–240
Fig. 5. Distribution of charge in a plane of an electrode (a) and cross-section parallel to -axis in maximal point of Gaussian function over which photon was absorbed
(b). Grey line/plain is a border between two pixels. Remained cloud – charge counted in the main pixel – is marked by a green colour. Escaped cloud – charge counted
in adjacent pixel – red colour. The distance between maximal point of distribution function and border is marked by D. (For interpretation of the references to colour
in this figure legend, the reader is referred to the web version of this article.)
different volumes of the damage layer thickness. Next, we compared
features of measured and simulated spectra in energy range 4–20
keV and chose a value which recreated most accurately the observed
features. The following formula was used to take into account loss of
energy due to damage layer:
 = 0 1 − exp

Matrix (DRM) of X-ray detectors can be obtained based on Geant4
simulations [18]. Such simulations are also used as a part of complex
instrument modelling [19] including simulations of solar X-ray flux, its
interaction with the optical channel and the detector crystal.
Low energy physics list (G4EmLivermorePhysics, Geant4 ver. 10.1)
was used in the simulation, because we are interested in the 4–200 keV
energy range of Caliste-SO detectors. A deviation between the experimental library and used Geant4 model of cross-sections is below 0.2%
for all used materials [20].
The geometry model consists of the detector crystal with electrodes
and the radioactive source. Entire crystal volume has been divided into
pixels (see Fig. 4(b)). Radioactive source consisted of 241 Am sphere
(1 mm diameter) surrounded by Kevlar sheath 110 μm thick. There was
a 0.5 mm beryllium plane placed between the CdTe crystal and the
In the simulation the 241 Am spectra from LBNL Isotopes Project [21]
database had been used. Only lines with emission probability higher
than 0.1% were taken into account during the simulation.
where 0 — energy calculated using Geant4 simulation,  — photon
absorption depth,  — damage layer thickness.
The recorded energy of detector event is not equal energy of
absorbed photon due to the charge loss processes. This affects our
simulations as well as laboratory measurements. In laboratory, the
energy scale is calibrated with the use of at least two observed lines
of characteristic radiation. In our simulations we have absolute energy
scale, but we have to rescale it in the same way to achieve consistency
with laboratory measurements. Detection threshold, which is set at 4
keV for the case considered, has been also taken into account.
4.2. Detector response
4.3. Charge sharing
From the Geant4 simulation we obtain information about place
and quantity of deposited energy during absorption of photon without
influence of physical effects occurring in the detector such as noise,
charge loss, and the damage layer which can affect measured spectrum
shape and limit the energy resolution. Therefore, we prepared dedicated
software written in IDL environment.
To describe the charge loss we use analytical Hecht equation [22].
The mobility of holes and electrons is 100 cm2 V−1 s−1 and
1100 cm2 V−1 s−1 , respectively, and the hole and electron lifetimes
are 1 μs and 3 μs, respectively [23]. In a case of Caliste-SO detector the
intensity of the electric field is equal to 200 V mm−1 .
To take into account the effect of Fano noise we convolved Geant4
simulation result with the Gaussian function — corresponding to the
FWHMs calculated from the Fano equation [24]. The Fano coefficient
was assumed to be 0.1 [25] and the mean electron–hole pair energy to
be equal to 4.43 eV [5]. Similar operation was repeated for electronic
noise with constant FWHM. By comparing simulation results and real
measurements, we estimated its FWHM to be 1 keV.
In technological process of sputtering platinum layer on the CdTe
crystal the damage layer is formed [5]. In Caliste-SO detector, it is
localized just below entrance electrode and causes an additional charge
loss which depends on the distance between the cathode and the place
of energy deposition. Therefore, additional asymmetry towards the low
energy is observed. This affects mostly the low-energy lines because lowenergy photons are mainly absorbed just next to the cathode. The basic
mechanism of this effect is still not well understood, so we implemented
the semiempirical solution. We simulated spectra of 241 Am isotope with
In a pixelized detectors single photon can generate the signal in a
two neighbouring pixels by two mechanisms. The first is a fluorescence
within a crystal which was estimated on the basis of the Geant4
simulation. In the simulation the monoenergetic source of photons was
assumed to illuminate entire detector area. The event was classified as
a double count when deposited energy was higher than 4 keV threshold
in a two or more pixels. We also considered effects described in previous
chapters which can influence the recorded energy i.e. charge loss,
damage layer (See Section 4.2).
The second one (split count) is calculated geometrically. The movements of carriers is described by Fick’s second law [6]. In our simulations
initial charge cloud was assumed to be spherically symmetric and we
took into account relation between collection time and the distance
travelled by carriers (for details see [26]). The distribution of charge
on electrode was calculated (Fig. 5). When the photon is absorbed
near a border between two pixels, part of its energy is shared with the
adjacent pixel (the escaped cloud — red colour). The rest of charge is
called the remained cloud (green colour). To detect a split count, energy
measured in each pixel must be higher than the imposed threshold
(4 keV). Therefore the minimal energy of photon which can produce
split count must be higher than 8 keV. Moreover, we defined maximal
distance of split count occurrence. It is equal to a distance D (Fig. 5,
panel b) for which the escaped cloud contains charge corresponding to
4 keV. The charge distribution depends on the absorption depth (starting
point) therefore this calculation was performed for each depth.
The distribution of charge which depends also on the registered
energy was calculated using the Geant4. This energy influences the
J. Barylak et al.
Nuclear Inst. and Methods in Physics Research, A 903 (2018) 234–240
Fig. 7. The measured spectrum of a radioactive source 241 Am (red) and the
simulated spectrum (blue). Pink vertical lines mark stronger characteristic
emission lines of 241 Am. (For interpretation of the references to colour in this
figure legend, the reader is referred to the web version of this article.)
Fig. 6. Maximal distance from the boundary between pixels which circles area
where charge cloud is split.
rate of expansion of the cloud because when the energy of incident
photon grows the probability of it being absorbed deeper increases. And,
holes have a shorter distance to travel therefore split count occurrence
distance D decreases (Fig. 6). In contrary, for the lower energy photons
holes have longer distance to travel and the value of D increases.
A surface where charge cloud is split (the split count surface) can be
calculated using the geometry of pixel pattern (Fig. 4(b)) and the split
count occurrence distance D. The D value depend on depth thus, the
relationship between the number of photons absorbed at given depth for
each photon energy is needed to calculate how large portion of photons
is counted in more than one pixel.
Assuming uniform distribution of photons on the detector surface,
the number of split counts can be calculated as the split count occurrence
surface area divided by the whole crystal area. This calculation was
performed for each energy, which led to estimation of the probability
of charge sharing as function of a initial photon energy.
registrations of two ‘‘real’’ photons, but the majority of events will come
from charge sharing. This second part will change measured photon
rates in individual sections of the detector and can influence spectra
shape because the effect is strongly energy dependent. Results of our
simulation of charge sharing are shown in Fig. 8. In the left column
panels, we present complete result where charge sharing with guard
ring is included. The right column panels show charge sharing only
between pixels, when the ‘‘presence’’ of guard ring is excluded. The
charge sharing without charge loss effects (hole tailing and damage
layer) is shown in the top row plots. In the bottom row plots the charge
loss effects are included. The fluorescent counts and the split counts rates
are marked by red and blue asterisks respectively. Using black asterisks,
we show the sum of both effects. Fluorescent counts can be seen for
energies above 27 keV, because the lowest fluorescent line is Cd line at
23 keV and 4 keV threshold.
For photons with energy below 27 keV, charge sharing is caused
by splitting the charge cloud between adjacent pixels only. The lowenergy cut off for charge sharing is 8 keV. This is a consequence of the
4 keV detection threshold. With growing incident photon energy, the
relative number of split events grows also. We noticed that the maximum
probability of split events is placed around 40–50 keV because photons
with higher energy are absorbed deeper in a crystal and the split count
occurrence surface decreases with increasing absorption depth (Fig. 6).
There is an abrupt increase of absorption efficiency around 27 keV
and 31 keV connected with presence of  and  emissions lines of Cd
and Te atoms. This emission lines are also responsible for the abrupt
increase of charge sharing around 30 keV seen in Fig. 8.
Above 50 keV, number of split counts does not change with energy.
Photons with higher energy are absorbed deeper therefore, this level is
expected decrease. However, higher energy increases the size of charge
cloud and countervail the other effect.
Exclusion of guard ring decreases strongly charge sharing level as
expected. The number of photons classified as double counts is nearly
50% lower than with guard ring. Moreover, charge loss effects decrease
charge sharing and smooth its dependence from energy.
5. Results
5.1. Comparison of simulated and measured spectra
In order to verify our Monte Carlo approach, simulated and measured
spectra were normalized on the total number of counts and compared.
The result is shown in Fig. 7. The observed and modelled spectra are
in a good agreement. The simulated spectrum shows a slightly higher
number of counts in the main peak at 59.5 keV. The peak is about
5% higher in simulations than in measurements. For low energy peaks
the difference is opposite (simulations gives lower signal in peaks) and
may be as large as 10%. Furthermore, a characteristic peak asymmetry
associated with trapped holes is clearly visible for the highest peak.
Additionally, simulation shows counts deficiency in characteristic
lines at energies 14, 16 and 21 keV. And, the 16 keV line is stronger than
14 keV in measurements contrary to the model results. These differences
may be caused by the actual source geometry which is not known
with sufficient accuracy. Apparent ‘‘shelf’’ below 15 keV is caused by
the absorption in so called damage layer. The 26 and 33 keV peaks
and escape peaks are related to cadmium and tellurium emission are
modelled properly.
5.3. Comparison of the split counts model with measurements of Caliste 64
5.2. Charge sharing
We made additional Geant4 simulation of Caliste 64 detector in order
to compare it with results of detector measurements presented by Meuris
et al. [8]. Caliste 64 uses the same material, have a similar thickness
and electrodes as Caliste-SO. The only difference is a larger number of
pixels. Again, the detector was assumed to be uniformly illuminated
As a consequence of instrument operation logic double events will
not be taken into account in making the observed spectra. The exception
is simultaneous counts registered in a pixel and the guard ring. A
small fraction of double events will be a consequence of simultaneous
J. Barylak et al.
Nuclear Inst. and Methods in Physics Research, A 903 (2018) 234–240
Fig. 8. Quantity of all counts which are classified as double counts in Caliste-SO (a) - including guard ring and without charge loss effects, b) - excluding guard ring
and without charge loss effects, c) - including guard ring and with charge loss effects, d) - excluding guard ring and with charge loss effects. (For interpretation of
the references to colour in this figure legend, the reader is referred to the web version of this article.)
each point was the probability of the characteristic emission. We obtain
value of 9.5% in our simulation. This small difference can be a result of
not perfect matching between simulated and measured 241 Am spectra.
6. Summary
In this work, the method to simulate the charge sharing effect in the
Caliste-SO detector was presented. Two types of processes leading to
charge sharing were investigated: split and fluorescent counts.
Split counts occur when absorption takes place near a boundary between detector pixels. The charge cloud, which arise during absorption
of photon, divides into two adjacent pixel volumes. Fluorescent counts
occur when secondary photon emitted during absorption is recorded in
another pixel.
First type of charge sharing was calculated using equation describing
expansion of the charge cloud. The second type was simulated using
Geant4 package. All important detector effects such as the charge loss,
the Fano noise and the electronic noise were included in modelling.
Presented approach allows to calculate charge sharing function of
energy for different types of available semiconductor detectors.
It has been found that charge sharing is strongly dependent on
energy of incoming photon. We calculated that the number of split
events rapidly increases with growing photon energy up to 50 keV.
Above 50 keV, charge sharing energy dependence is flat. Moreover, the
methodology was tested on the Caliste 64 detectors. Obtained values for
double counts are similar to the laboratory measurements [8].
In the STIX experiment, double counts will not contribute to the
observed X-ray spectra by design, only the number of such ‘‘double’’
counts will be recorded. Therefore, the charge sharing will increase
observed photon flux and it will modify the spectrum shape, especially
in the very interesting in terms of solar flare science part of energy
spectrum between 8 and 50 keV where the transition between thermal
and non-thermal part of the solar flare spectra is observed. Additionally,
this effect will influence the image reconstruction, by changing the
amplitudes and in lesser degree phases of the observed Moiré patterns.
Therefore it requires the development of dedicated method for data
processing which is in progress.
Fig. 9. Quantity of all counts which are classified as double counts in Caliste 64
including guard ring and charge loss effects.
with the 241 Am source. Between the detector and the source the 500
μm thick beryllium window was placed in order to stop alpha particles.
The measurements were performed with the 2 keV photon detection
threshold. The same configuration was used in our simulations.
The result of our simulation is shown in Fig. 9. The level of charge
sharing is significantly higher than in Caliste-SO (4 times higher) due to
lower energies threshold of photon detection and higher relative area of
pixels boundaries. The charge sharing in function of energy was used to
calculate how many photons emitted by 241 Am are classified as double
There is 10.1% of double counts in the measurements of Meuris
et al. (2009). In order to compare our simulation results with this
measurements, we calculated weighted arithmetic mean of the charge
sharing value for each characteristic line energy. The contribution of
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Nuclear Inst. and Methods in Physics Research, A 903 (2018) 234–240
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