# Towards quantitative Low Energy Ion Scattering on CaSiO3 from Comparison to
Multiple-Scattering-Resolved Dynamical Binary Collision Approximation
Simulations

Johannes Brötzner  TU Wien, Institute of Applied Physics, 1040 Vienna,
Austria, EU  Lukas Kalchgruber  TU Wien, Institute of Applied Physics, 1040
Vienna, Austria, EU  Center for Electrochemical Surface Technology, 2700
Wiener Neustadt, Austria, EU  Paul S. Szabo  University of California, Space
Sciences Laboratory, Berkeley, CA 94720, United States of America  Andreas
Nenning  TU Wien, Institute of Chemical Technologies and Analytics, 1060
Vienna, Austria, EU  Andreas Mutzke  Max Planck Institute for Plasma Physics,
17491 Greifswald, Germany, EU  Hans Hofsäss  Universität Göttingen, II.
Physikalisches Institut, 37077 Göttingen, Germany, EU  Markus Valtiner  TU
Wien, Institute of Applied Physics, 1040 Vienna, Austria, EU  Center for
Electrochemical Surface Technology, 2700 Wiener Neustadt, Austria, EU  Richard
A. Wilhelm  TU Wien, Institute of Applied Physics, 1040 Vienna, Austria, EU
<EMAIL_ADDRESS>
###### Abstract

We perform Low Energy Ion Scattering with 1 keV He ions on CaSiO3 using a
commercial electrostatic detector system and determine the charge fraction of
scattered ions from comparison with Binary Collision Approximation
simulations. The simulations take dynamical surface changes due to surface
cleaning Ar sputtering into account and scattered He particles are separated
into single, dual, and multiple scattering trajectories. We find that the
charge fraction of single and dual scattered He is about 10 times higher than
the one for multiple collisions. Our results show that quantitative
concentration profiles can be inferred from this method, if the charge
fraction components are determined first.

LEIS,BCA,Charge Fraction

††preprint: PRB/LEISonCaSiO

##  I Introduction

Low Energy Ion Scattering (LEIS) is a powerful method with the ultimate
surface sensitivity among all ion beam analysis methods [1]. Used for both
structural analysis by channeling and blocking [2, 3, 4] as well as elemental
composition analysis [5] it is, however, a common misconception that LEIS
probes purely the very outermost surface layer [6]. Incoming ions can undergo
single or multiple scattering events at the surface or in deeper layers both
contributing to the final energy spectrum. One additional challenge arises
from the fact that scattered ions may have changed their charge state. Some
LEIS methods rely on the measurement of the time-of-flight of scattered ions
and are therefore not sensitive to changing ion charges [7, 8], but more
commonly, electrostatic LEIS (esaLEIS) is used. The latter has the advantage
of possibly much higher solid angles especially in commercial devices like the
ionTOF Qtac system [9], but suffers from the fact that only charged ions can
be detected. With a high solid angle, spectra can potentially be acquired in a
small amount of time even when detecting only charged scattered ions and
consequently dynamic changes in a surface due to, for example, chemical
reactions or material deposition can be monitored [10, 11].

However, in esaLEIS a quantification of the elemental composition is limited
at best, because the charge fraction of scattered ions/atoms is typically
unknown and cannot be modelled accurately with present theoretical models. As
a result, mostly qualitative analysis of dynamical surface changes are done
with esaLEIS [12].

Here we go one step further and show that with the correct simulation toolkit
one can in fact extract the charge fraction of scattered He ions even from a
multi-component target which also dynamically changes during surface
preparation by Ar ion sputtering. The determined charge fraction only has a
weak dependence on the dynamic surface changes during Ar sputtering and may
therefore serve as a reference for similar samples allowing for full
quantification [13].

In the following we use CaSiO3 as a target material, because it is an analog
material for the regolith of the Moon’s and Mercury’s surfaces where
backscattering of 1 keV/u protons from the Sun (solar wind) is used in orbital
probe missions to observe the ion-surface interaction, which significantly
alters planetary surfaces through sputtering, weathering and ion implantation
[14, 15, 16, 17].

##  II Methods

We use both, a commercial LEIS setup and two binary collision approximation
codes, to fit experimental spectra and extract the charge fraction in this
procedure. Details are described below.

###  II.1 Experimental Setup

Samples of CaSiO3 were produced by a costum-built Pulsed Laser Deposition
setup equipped with a KrF excimer laser (Coherent compex Pro) operating at 5
Hz. At the target 105 mJ per pulse arrived, which yields a fluence of $3-4$
J/cm2. The deposition was carried out at a substrate temperature of
$300^{\circ}$C in 0.04 mbar O2 and a target-substrate distance of 6 cm for 15
min. We used a natural mineral target [18] and the substrate is a standard
Si(001) wafer piece of $1\times 1$ cm2.

The CaSiO3 layer on Si(001) substrate is loaded in an ionTOF Qtac LEIS system
with a base pressure in the low $10^{-10}$ mbar range. The sample is sputtered
by Ar+ ions at 2 keV energy and $60^{\circ}$ incidence angle with respect to
the surface normal. An area of $500\times 500$ $\mu$m2 is irradiated by the Ar
ions. After each fluence step of $\Phi_{Ar}=1.67\times 10^{15}$ Ar/cm2, a LEIS
spectrum is taken. In total we apply an Ar fluence of $6.7\times 10^{16}$
Ar/cm2. Therefore, we track dynamic surface changes during the surface
preparation and cleaning procedure.

LEIS spectra are obtained with 1 keV He+ ions under normal incidence. An area
of $300\times 300$ $\mu$m2 in the middle of the Ar-sputtered area is probed by
the He beam. Scattered He ions are detected by the annular Qtac detector under
$145^{\circ}\pm 0.6^{\circ}$ scattering angle. Note, that the detector is a
toroidal electrostatic analyzer covering $360^{\circ}$ azimuthal angle, which
can only measure charged particles. Ions which neutralize in the process of
scattering are not detected. The energy analyzer is operated in constant pass
energy mode at 3 keV and has an energy resolution of $1.4\%$ of the pass
energy, i.e. 42 eV in our case.

###  II.2 Dynamical Sputtering BCA

We use SDTrimSP 6.09 to extract elemental depth profiles after each Ar sputter
fluence we applied in the experiment [19]. Therefore, we use the dynamic mode
of this binary collision approximation code [20]. For implanted Ar ions during
the sputtering process we do not restrict the Ar retention in SDTrimSP (and
reach up to $\sim 18$ at%). We checked the influence of a limited Ar retention
of 0 and 5 at% as well (see Fig. 7 in the Appendix). Note, that subsequent
diffusion or outgasing effects of near-surface implanted Ar is not taken into
account by the simulation. Since Ar and Ca have basically the same mass, He
scattering from Ca and implanted Ar cannot be distinguished in the experiment
and we have therefore no direct experimental benchmark on how much Ar is
actually implanted and with which depth distribution.

###  II.3 Multiple-Scattering-Resolved BCA

The elemental depth profiles after Ar sputtering are taken as an input for
additional BCA simulations using the IMINTDYN code [21]. IMINTDYN is a
derivative of SDTrimSP, i.e. using the same BCA description, but including
some additional features, for example, to divide particle trajectories between
single and multiple scattering. With this code we calculate the He scattering
yield for a range of $\pm 0.6^{\circ}$ around the mean scattering angle of
$145^{\circ}$ using standard ZBL potentials, and energy loss functions. Note,
that the exact form of the screened interaction potential and the electronic
energy loss model (incl. straggling) can potentially influence the LEIS
spectra [22, 23, 24, 25]. We further divide the yield into three parts, i.e.
into scattered particles which scatter once with an angle of $>90^{\circ}$
(single scattering), into scattered particles which scatter once with an angle
of $>90^{\circ}$ and once with an angle $\Theta_{2}$ of
$5^{\circ}<\Theta_{2}<90^{\circ}$ (dual scattering), and into scattered
particles with all other possible trajectories (multiple scattering). Note,
that scattering angles $<5^{\circ}$ in a single scattering event are
associated with very small energy transfers. We also want to point out that
the maximum depth from which ions can still be back-scattered with multiple
scattering amounts to $\sim 15$ nm in our simulations.

From the IMINTDYN code we do get the single, dual, and multiple scattering
parts of the LEIS spectrum also for each target element (see Fig. 2). For dual
and multiple scattering the scattered He is assigned to the element where it
obtains the largest scattering angle. However, since we cannot resolve the
LEIS signal from Ca and from implanted Ar, we will not use elemental-resolved
simulated LEIS spectra for comparison with experiment, but rather the
elemental-summed single, dual, and multiple scattering contributions.

##  III Results

Figure 1: (a) Experimental LEIS spectra using 1 keV He under normal incidence
and 145∘ scattering angle after different sputtering fluences with 2 keV Ar
ions under 60∘ incidence angle. (b) Integrated signal for the colored regions
in (a) as function of Ar sputter fluence.

We obtain LEIS spectra after each Ar sputtering step, which can be seen in
Fig. 1(a). Initially the sample is contaminated with light elements (zero Ar
fluence, dark blue). After the initial Ar sputtering step the expected
multiple scattering background for this sample can already be recovered in the
experiment (blue to cyan, multiple scattering background visible by the signal
height in between O and Si). At larger fluences (yellow to red), we see a
reduced O and Ca signal and an increasing relative contribution of Si.
Furthermore, we see a peak at about 900 eV, which would correspond to Au or Pt
and can be attributed to contaminations of the layer during the PLD growth
process.

In Fig. 1(b) the integral of the correspondingly colored regions in (a) are
shown as function of Ar fluence. One can see, that the signal intensity
increases initially due to surface cleaning. For $0.5-2.0\times 10^{16}$
Ar/cm2 a slow variation of the Ca and Si signal can be observed, which we
attribute to dynamical surface composition changes due to Ar sputtering. For
$2.0-3.0\times 10^{16}$ Ar/cm2 the signal for O, Si, and Ca remain constant,
which we assign to the region of sputtering equilibrium, i.e. no more
dynamical surface changes occur. For even larger fluences the Ca(+Ar) signal
as well as the O signal decrease and the Si signal increases, which is
understood by sputtering entirely through the PLD-deposited CaSiO3 layer on Si
wafer substrate. The Au (or Pt) contamination decreases slowly for small
fluences and somewhat faster when the layer is sputtered through. Here it
should be noted that the heavy elements are sputtered at reduced rates and are
preferentially intermixed in the layer (and the substrate) [26] which explains
the signal even when the top layer is sputtered off.

The IMINTDYN simulation provides both elemental-resolved and multiple-
scattering-resolved LEIS spectra after each Ar sputtering step. One example of
these results after $2.5\times 10^{16}$ Ar/cm2 (in the sputter equilibrium) is
shown in Fig. 2. One can see that single collisions lead to the commonly known
sharp peaks in the energy spectrum (a), while dual (b) and multiple (c)
scattering lead to increasingly broad spectral components. The sum of all
components is shown in (d), which would be the LEIS spectrum one would expect
if one did not resolve the He trajectories by element or number of scattering
events.

Figure 2: BCA simulation result of 1 keV He scattered for CaSiO3, which was
sputtered by $2.5\times 10^{16}$ Ar/cm2 under 60∘ incidence angle in a
preceding dynamic BCA simulation. The BCA simulation is decomposed into
scattered He with 1 scattering event $>90^{\circ}$ ((a) single (scattering)),
1 scattering event $>90^{\circ}$ and 1 additional scattering $>5^{\circ}$ but
$<90^{\circ}$ ((b) dual (scattering)), and all other combinations of
scattering angles and frequency ((c) multiple scattering). The sum of all
contributions is shown in (d).

##  IV Discussion

In order to compare the BCA simulated LEIS spectra with experiment, the
experimental LEIS spectra are fit by

$f_{BCA}^{fit}(E)=\xi_{s}f_{s}(E)+\xi_{d}f_{d}(E)+\xi_{m}f_{m}(E),$ (1)

through variation of $\xi_{s}$, $\xi_{d}$ and $\xi_{m}$, which are the charge
fractions for single, dual, and multiple collisions, respectively. The
$f_{s}(E)$, $f_{d}(E)$ and $f_{m}(E)$ are the partial LEIS spectra from a BCA
calculation (cf. Fig. 2(a)-(c)), which are additionally convoluted with a
Gaussian kernel to account for the finite energy resolution of 42 eV in the
experiment. An example of the fit result is shown in Fig. 3 (green solid
line). Also the non-weighted sum (cf. Fig. 2(d)) is shown, which is about 2
orders of magnitude larger than the experimental spectrum. This already
indicates that the average charge fraction is in the range of $10^{-2}$. Also
the overall shape is not in agreement with the experiment and only by applying
the fit procedure described above, the experimental spectrum can be
reproduced. Note that the experimental spectrum shows an exponential increase
below 200 eV, which is commonly attributed to the presence of charged
secondary ions in the spectrum and could be filtered from the spectrum by
using a time-of-flight analysis of the He ions through the electrostatic
analyzer [27]. The overall agreement between the BCA fit and the experiment
allows the extraction of the charge fractions for the individual scattering
events (single, dual, and multiple). Note, that there is a discrepancy between
fit and experiment for the Si signal and the Ca+Ar signal. The latter can be
partially attributed to the fact, that the Ar implantation in the BCA
elemental depth profiles does not include Ar out or in diffusion, which might
appear in the experiment. The Si signal is systematically lower in the
experiment than retrieved from the fit, which could be an indication for
charge fraction differences when the He undergoes single and dual scattering
on Si in contrast to Ca and O. However, due to the overlap of Ca and Ar, we do
not further consider elemental-sensitive charge fractionization in this work.

Figure 3: Experimental LEIS spectrum after $2.5\times 10^{16}$ Ar/cm2, i.e. in
the sputter equilibrium regime as well as a BCA simulation for the same
conditions. For the BCA simulation a weighted sum of single, dual and multiple
scattering was adjusted to fit the experimental spectrum. While the fit shows
a good agreement for the multiple scattering background (orange) at 300 eV and
the oxygen peak at 400 eV, it deviates from the experiment at higher energies.
The single collision charge fraction (red) is about 1.6 times too low for the
Ca+Ar BCA peak. The weighted BCA spectra (single, dual, and multiple) are
convoluted with a Gaussian kernel to account for the finite spectrometer
resolution in the experiment.

The fitting was done for every Ar fluence step and the extracted charge
fractions are shown in Fig. 4. For the initial Ar fluences the fitting is not
reliable, because surface contaminations are not considered in the LEIS BCA
simulation and therefore the overall spectral shapes are widely different.
However, for Ar fluences above $\sim 5.0\times 10^{15}$ Ar/cm2 the charge
fractions for the individual scattering numbers can be well extracted. From
Fig. 4 one can see that the charge fraction of multiple scattering is in the
range of $10^{-3}$, while single and dual scattering trajectories have a much
higher charge fraction of about $10^{-1}$. The charge fraction analysis is
robust against the Ar sputtering and therefore the extracted fractions remain
almost constant for the Ar fluence range from pre-equilibrium towards the
sputter equilibrium. The corresponding change in surface composition can be
extracted from the dynamic SDTrimSP simulations and is shown in Figs. 5 and 6
in the Appendix.

The large charge fraction for single and dual scattering in contrast to
multiple collisions might result from different neutralization and re-
ionization schemes active. Single and dual collision trajectories at the low
He ion energy appear close to the surface, i.e. the overall interaction time
of the ion with the material is limited at most to a few femtoseconds, so that
a substantial fraction of $\sim 10\%$ of the incoming particles remain in a
charged state. However, in these two cases relatively strong scattering (i.e.
at small interatomic distances) occurs which leads to large deflection angles.
Multiple scattering, on the other hand, is associated with a comparatively
long trajectory inside the material, whereas each scattering event could be
considered a soft scattering. The interplay and relative importance of impact
parameter dependence and interaction time in ion neutralization was recently
discussed intensively [28, 29] and remains still elusive in heavily asymmetric
ion-target combinations like it is the case here.

Figure 4: Charge fraction for single, dual and multiple scattering as function
of Ar sputter fluence. The values were deduced from the fits to experimental
data, see for example Fig. 3. The error bars indicate the uncertainty of the
fit to experiment, which results primarily from the fit offset at the Si and
Ca(+Ar) region.

##  V Conclusion

We show that LEIS spectra can be fit by BCA simulations to extract the charge
fraction of the scattered He ions using esaLEIS with multi-component oxide
target materials. The charge fraction depends on the details of the ion
trajectory in the surface. Dual and multiple scattering can have large
contributions to an observed spectrum indicating that larger depths contribute
significantly. It is therefore important to properly setup the target surface
system in a BCA simulation for LEIS and we do this by dynamically calculating
the surface atomic concentration profiles after Ar ion sputtering from
separate BCA simulations. Some effect of the chemical nature of the scattering
partner on the He charge fraction can be inferred from our data as well, while
further in-depth analysis on this effect is needed.

Since the determined charge fractions appear stable against further Ar
sputtering of the surface, we suggest that this charge fraction can be used
for similar target systems as a standard. Then, esaLEIS will allow full
quantification of unknown samples, as long as the charge fraction between
single, dual, and multiple scattering remains similar.

###### Acknowledgements.

The authors appreciate funding (WST3-F-542638/004-2021) by EFRE and the State
of Lower Austria. Funding was further provided by the Austrian FWF (Y1174-N36,
I4914-N, P36264-N).

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## Appendix

Figure 5 shows the Ar-fluence-dependent elemental depth profiles calculated
with SDTrimSP in the dynamical mode. These concentration profiles were used as
input for the multiple-scattering-resolved BCA simulations with IMINTDYN.

Figure 5: Elemental density depth distributions of Ca, Si, O, and Ar for
different 2 keV Ar fluences. Data from dynamical BCA simulations with
SDTrimSP.

Figure 6 shows the average elemental concentration for the individual elements
for increasing Ar sputtering fluence. The average is taken over 100 Å. In
comparison to the experimental signal (cf. Fig. 1(b)), the rapid dynamics
below $1\times 10^{16}$ Ar/cm2 cannot be captured, because surface
contaminations are not included in SDTrimSP. For larger fluences the SDTrimSP
simulations show a constant concentration for all elements, while the
experiment shows some gradual increase of the Ca+Ar signal. This might result
from additional implantation of Ar or rearrangement of implanted Ar, which can
also not be captured properly with BCA codes.

Figure 6: Elemental densities of Ca, Si, O, and Ar averaged over 100 Å from
the surface as function of Ar fluence from dynamical BCA simulations with
SDTrimSP.

In the SDTrimSP simulation we consider up to 20 at% Ar implantation, but we
repeated the dynamic SDTrimSP simulation and suppressed Ar retention
completely. The resulting elemental depth profiles served then as an input for
IMINTDYN and the resulting, fitted, BCA spectrum is shown in Fig. 7. In this
case the Ca peak is substantially lower than the experiment which indicates
that there is indeed a substantial implantation of Ar into surface-near
layers. However, due to uncertainties in a possibly different charge fraction
from the different surface elements, we are not able to disentangle the pure
Ar contribution to the Ca(+Ar) peak signal.

Figure 7: Same data as in Fig. 3 for comparison, but without any Ar retention
in the elemental depth profiles which serve as the basis for the BCA LEIS
simulations. The corresponding Ca(+Ar) peak is not much lower indicating, that
there is in fact a substantial amount of Ar implanted.