# Energy deposition and formation of nanostructures in the interaction of
highly charged xenon ions with gold nanolayers

I. Stabrawa  D. Banaś<EMAIL_ADDRESS>A. Kubala-Kukuś  Ł. Jabłoński  P.
Jagodziński  D. Sobota  K. Szary  M. Pajek  K. Skrzypiec  E. Mendyk  M.
Borysiewicz  M. D. Majkić  N. N. Nedeljković  Institute of Physics, Jan
Kochanowski University, Uniwersytecka 7, 25-406 Kielce, Poland  Departament of
Chemistry, Maria Curie-Skłodowska University, Plac M. Curie-Skłodowskiej 3,
20-031 Lublin, Poland  Institute of Electron Technology, aleja Lotników 32/46,
02-668 Warszawa, Poland  Faculty of Technical Sciences, University of Priština
in Kosovska Mitrovica, Knjaza Miloša 7, 38220 Kosovska Mitrovica, Serbia
Faculty of Physics, University of Belgrade, P.O. Box 368, 11001 Belgrade,
Serbia

###### Abstract

The effect of the deposition of kinetic energy and neutralization energy of
slow highly charged xenon ions on the process of the nanostructures creation
at the surface of gold nanolayers is investigated. The nanolayers of thickness
of 100 nm were prepared by e-beam evaporation of gold on crystalline silicon
Si(100) substrate. The samples were irradiated at the Kielce EBIS facility of
the Jan Kochanowski University (Kielce, Poland), under high vacuum conditions.
The irradiations were performed for constant kinetic energy 280 keV and
different ions charge states (Xeq+, q = 25, 30, 35, 36 and 40) and for
constant charge state Xe35+ and different kinetic energies: 280 keV, 360 keV,
420 keV and 480 keV. The fluence of the ions was on the level of 1010
ions/cm2. Before and after irradiation the nanolayer surfaces were
investigated using the atomic force microscope.

As the result, well pronounced modifications of the nanolayer surfaces in the
form of craters have been observed. A systematic analysis of the crater sizes
(diameter on the surface and depth) allowed us to determine the influence of
the deposited kinetic and the neutralization energy on the size of the
obtained nanostructures. The results are theoretically interpreted within the
micro-staircase model based on the quantum two-state vector model of the ionic
Rydberg states population. The charge dependent ion-atom interaction potential
inside the solid is used for the calculation of the nuclear stopping power.
According to the model the formation of the nanostructures is governed by the
processes of the ionic neutralization in front of the surface and the kinetic
energy loss inside the solid. The interplay of these two types of processes in
the surface structure creation is described by the critical velocity. Using
the proposed theoretical model, the neutralization energy, deposited kinetic
energy and critical velocities were calculated and compared qualitatively with
the experimental results. The results are consistent (after normalization)
with previous experimental data and molecular dynamics simulations for single
ionized Xe and crystalline gold surface.

††journal: Vacuum

##  1 Introduction

Modification of metal, semiconductor and insulator surfaces by the ion
irradiation is of great importance for developing new technologies for
manufacturing a small functional electronics systems with nanometer
dimensions, and has the potential to introduce novel nanostructures and
material properties not achievable by any other material processing methods
[1]. Modification of materials by swift (high kinetic energy) heavy ion (SHI)
irradiation is already used in many industrial processes, such as: the
generation of nanopores in polymers [2], controlled drug delivery in
biomedicine [3], precise band gaps modification [4, 5], modification of high
temperature superconductors [6], and others [7, 8]. It has also been
demonstrated that with SHI beams regular patterns (usually in amorphic form
[9]) of lateral dimensions in the order of several tens of nanometers can be
created.

One of the promising alternatives for creation of surface nanostructures is
modification of surface by an impact of a single (i.e. each ion creates
nanostructure) low-energy (slow) highly charged ions (HCI). The term slow HCI
usually refers to impact velocities $v\ll$ 1 a.u., corresponding to 25 keV/amu
(nuclear stopping power regime). HCI are characterized by an additional (to
the kinetic energy) high potential energy, resulting from the removal of many
of the electrons from the neutral atom. For example, for Xe50+ ion the
potential energy is around 100 keV, i.e. 8400 times higher than that of a
single charged xenon Xe+ ion. The neutralization energy of the HCI in the
interaction with solid surface is also large for very slow ions (in keV energy
range). As a consequence, the interaction of slow single HCI with a surface is
also governed by the potential (neutralization) energy of the ion [10, 11,
12]. This energy is deposited on a small surface area along the first few
nanometers below the target surface [13]. Recent research on 2D materials
shows [14], that potential energy deposition of highly charged ion (Xe38+) is
limited to only up to two layers within multilayer MoS2 (on graphene). For
very low ionic velocities (down to $v=0.03$ a.u.) the deposited potential
energy (close to the ionic neutralization energy) can lead [15] to creation of
various surface nanostructures, so far mainly observed on insulators such as
alkali and alkaline earth halides, oxides and polymers, but also on highly
oriented pyrolytic graphite (HOPG), sapphire and gold crystals, and silicon
semiconductor [16]. On the other hand, for moderate ionic velocities
($v\approx 0.25$ a.u.) both the neutralization and the deposited kinetic
energy participate in the surface modification [10, 12]. Nanostructures
created using HCI can have a form of hillocks, craters (called also pits) or
caldera-like structures, with diameter of about 5-20 nm and a few nanometers
vertical extension [15, 16, 11]. It is known from experiments, that different
parameters of ion beams, type of irradiated materials and processing
conditions lead to different characteristic of the modifications obtained on a
material surface, including defect production, sputtering of material and
changes in material surface topology.

The recent studies of nanostructures formation on surfaces by HCI concentrate
mainly on the basic characterization of nanostructures and fundamental
understanding of the mechanisms responsible for the surface modifications [15,
10, 12]. Moreover, most of the experimental observations were performed for
insulator while for semiconductors (pure Si) and metals (Ti, Au) only single
experiments were carried out, which due to the lack of the systematic studies
did not allow for a detailed examination of the mechanism of nanostructures
production on such surfaces [16]. The reason for the small interest in this
type of studies were the earlier experiments with swift heavy ions (SHI),
which suggested that in the interaction of such ions with materials of high
thermal conductivity, the production of nanostructures is unlikely due to the
rapid outflow of energy from the area of impact. However, the results of
experiments performed by Pomeroy et al. [17] and our recent results [18]
showed that different nanostructures can be produced by slow single HCI also
on metallic surfaces. Unfortunately in both of these experiments potential and
kinetic energies of the ions were simultaneously changed, which made it
difficult to separate their influence on the produced nanostructures.

Systematic experimental studies of the interaction mechanism are very
important also from the theoretical point of view because there is still no
unified picture of the nanostructure creation process. Up to now, the proposed
theoretical models of the nanostructure production by slow single HCI,
including Coulomb explosion [19, 20, 21], molecular dynamics simulations [22,
23], inelastic thermal spike model [24, 25], and plasma model [26, 27]
describe the mechanism only in a qualitative manner and agree quantitatively
only with the results of selected experiments, mainly for insulators. For the
metallic surface modifications, the micro-staircase model of the HCI
neutralization accompanied by the charge dependent model of the kinetic energy
loss has been proposed [28, 12].

The aim of the present study is the systematic experimental and theoretical
investigation of the mechanism of energy deposition and nanostructures
creation in collisions of a single HCI with metallic surfaces. We consider the
moderate ionic velocity region, characterized by the interplay of the
neutralization energy and the deposited kinetic energy. We performed the
experiment with Xeq+ ions (q = 25, 30, 35, 36 and 40) impinging upon a gold
nanolayer at kinetic energy 280-290 keV and with Xe35+ ions at kinetic
energies: 280 keV, 360 keV, 420 keV and 480 keV. As the results, we obtained
the well pronounced modification of the surface in the form of craters. In the
present paper, the results are interpreted within the prediction of the micro-
staircase model [28, 12] and molecular dynamics simulations for single ionized
xenon hitting crystalline gold surface [29]. According to the micro-staircase
model, simultaneously with the ion cascade neutralization above the surface,
the neutralization energy deposits into the solid inducing the first
destabilization of the target as a consequence of the high free electron
density characteristic for conducting surfaces. Below the surface, the kinetic
energy loss is governed by the elastic collisions between the ion (carrying
the information about the ionic initial charge and velocity) and target atoms.

This article is organized as follows. In Section 2 we discuss the energy
deposition process during the interaction of HCI with surface and current
status of the experimental and theoretical studies for single and highly
ionized xenon atoms interacting with metallic (gold) surface. In this section
we also introduce the micro-staircase model of the HCI-metal interaction.
Section 3 is devoted to the present experiment. We characterize samples,
describe the experimental conditions and the atomic force microscope (AFM)
system used for the sample imaging. In Section 4 we present examples of the
AFM images and extracted diameters and depths of the observed craters. In
Section 5 we discuss the results and compare them with theoretical predictions
and available experimental data for single ionized xenon [30]. The concluding
remarks are given in Section 6.

##  2 HCI - surface interaction

###  2.1 Overview of the HCI interaction with metallic surfaces

Up to now, nanometer-sized structures produced by individual HCI impact on
conductive surfaces were reported for a crystalline Au(111) by Pomeroy et al.
[17]. In this experiment, the samples were irradiated with 200 keV Xe25+ and
350 keV Xe44+ ions, which have significantly different potential energies, 8
keV and 51 keV, respectively. After irradiation the samples were analyzed in
situ with scanning tunneling microscope (STM). The STM images showed many
different features on the gold surface, such as isolated hexagons, hexagonal
rings with craters in the center and hexagonal islands with pits, with the
features density approximately equal to the ions fluence. It is worth to note
that previous sputtering measurements [31] with gold did not report a
measurable increase in sputter yield with increasing of the HCI charge and
thus probability for a nanostructure formation on gold was assumed to be
negligible. Finally, Pomeroy et al. concluded that the primary formation
mechanism of the features they observed on Au(111), is related to the kinetic
energy (nuclear energy loss) and seems weakly dependent on the potential
energy of the HCI, they emphasized the simultaneous change in the potential
and kinetic energy of the ions used in the experiment, which complicated to
isolate their contribution to the created nanostructures. Subsequent attempt
to repeat Pomeroy et al. experiment using 440 keV Xe44+ ions has failed,
probably due to too high surface roughness [32].

Figure 1: Schematic description of the micro-staircase model of the cascade
neutralization with intermediate Rydberg state population followed by rapid
deexcitation (both presented by dashed curves) and the nanocrater formation
processes during the interaction of HCI with solid surface [12].

A similar experiment, but at lower velocities, was also carried out by our
group [18]. In this experiment, nanolayers of gold and titanium, were
irradiated with low-energy (50-120 keV) highly charged xenon ions. The samples
were prepared at Institute of Electronic Materials Technology, Warsaw, Poland,
by sputtering of gold (50 nm) and titanium (75 nm) nanolayers on polished
crystalline quartz SiO2(100) 4-inch diameter wafers, and titanium (25 nm - 75
nm) nanolayers on crystalline silicon Si (100) wafers. The samples were
irradiated at the Kielce EBIS facility (Institute of Physics, Jan Kochanowski
University, Kielce, Poland) [33]. As a result of irradiation, we were able to
create nanohillocks on both titanium and gold surfaces and perform statistical
analysis of their heights and volumes using AFM images [18]. In this
experiment the kinetic energy of the ions have been charge dependent (because
of the ion source configuration) and thus it was difficult to extract
separately the potential or the kinetic energy influence.

A systematic analysis of the Xeq+ ion interaction with gold nanolayers at
moderate velocities (craters formation) will be presented in Section 3.

###  2.2 Overview of the single charged ions interactions with metallic
surfaces

A many of scientists have discovered small craters on metallic surfaces
bombarded with single ionized high-energy heavy ions which they attribute to
the effect of spikes. The concept of thermal spikes resulting from single ion
impacts was discussed for the first time in the literature in the 1950s by
researchers such as Brinkmann [34], Seeger [35], and Seitz and Koehler [36,
37]. In particular, Merkle and Jäger used transmission electron microscopy
(TEM) to examine Au surfaces irradiated with single ionized Bi and Au ions, in
the energy range of 10-500 keV and discovered craters on the irradiated
surfaces for the ion energies above 50 keV with fewer than 1% of collisions
causing the crater formation [38]. Average crater sizes were typically about 5
nm. Although the authors conclude that spike effects were responsible for the
crater formation they attribute the effect mainly to sublimation of surface
atoms from the surface [38]. Following this experiment, Birtcher and Donelly
irradiated Au(110) films with Xe+ ions at energies of 50 keV, 200 keV or 400
keV. They found, using in situ TEM, that single xenon ion impacting on gold
forms crater with size as large as 12 nm and that approximately 2-5% of
impinging ions produce craters [39, 30]. Authors concluded that crater
formation results from ion-induced sudden melting (and volume expansion) of
the material associated with localized energy deposition (surface energy
spikes) and explosive outflow of material from the hot molten core. The later
experiments of Donelly and Birtcher on surfaces of Ag, In, and Pb led them to
the same conclusions [40].

The results of Donelly and Birtcher experiment [30] were examined using
classical molecular-dynamics (MD) simulations by Bringa et al. [29]. They
performed simulations of crater formation during 0.4-100 keV single charged
Xe+ bombardment of Au target. The simulations confirmed that the craters are
built by liquid flow of atoms from the interaction zone. They also found that
energy density needed for crater production strongly depends on the heat spike
lifetime and that for xenon energies higher than 50 keV cratering can results
from lower energy densities due to long lifetime of the heat spike. MD
simulated cratering probability was always higher than 50% in the studied
energy range [29].

###  2.3 Nanostructure formation on metallic surface: micro-staircase model

Recently, in the article [12] we discussed the nanohillocks formation by the
impact of Xeq+ ions on titanium and gold nanolayers [18] using the micro-
staircase model for the cascade neutralization based on the quantum two-state
vector model (TVM). The model takes into account both the ionic neutralization
energy and the kinetic energy deposition inside the solid [28, 12]. The
similar model can be used for the analysis od the craters formation.

According to the model, the process of the cascade neutralization of the ion,
$Q=q\to q-1\to...Q(R)\to...q_{fin}$, is mainly localized in front of the
surface (see Fig. 1). At ion-surface distance $R$, the electron is captured
from the metal into the intermediate high-$n$ (Rydberg) state of the ion
almost in a ground state. The population of each macro step consists of
several micro-steps (population of the low-$l$ Rydberg states $n_{Q}$ with the
probabilities $P_{n_{Q}}$). For example, considering the Xe25+ ion impinging
upon the metal surface at moderate velocity $v=0.25$ a.u. we have the
following populate scheme [28]: at ion-surface distances $R$, in the range
from $R=28$ a.u. to $R=10$ a.u., the Rydberg states corresponding to $n=23$ to
$n=15$ of the ion with charge $Q=q-1=24$ (core charge $25$) are populated with
probabilities $P_{n_{25}}=0.01\to 0.2$, $\sum P_{n_{25}}=1$. After the first
macro-step is finished at $R=10$ a.u, the population of the ion of the charge
$Q=q-2$ with core charge $24$ begins in the range from $R=9$ a.u. to $R=6$
a.u. The states $n=14$ to $n=12$ are populated with probabilities
$P_{n_{24}}=0.3\to 0.35$, $\sum P_{n_{24}}=1$, and so on. In Fig. 1) we
present the final stages of the macrosteps $Q=q$, $Q=q-1$, … $Q=q_{fin}$. At
each macro step, the rapid deexcitation could be via radiative process and
closer to the surface via Auger type processes with secondary electron
emission in interplay with the described population process [28]. The
neutralization cascade finishes when the HCI arrives into the interaction
region at minimal ion-surface distance $R=R_{min}$ [12] with the final charge
$q_{fin}$ ($R_{min}$ is the distance from the jellium edge [41]). The
corresponding neutralization energy $W^{(q,nMV)}$ within the nanolayer-metal-
vacuum (nMV) system is deposited into the first nanometers of the surface [42]
very fast (few fs for metal targets [11, 17]), increasing the energy density
in the impact region [43] and inducing the destabilization of the surface
[12].

The neutralization energy $W^{(q,nMV)}$ is defined as a difference between the
potential energy $E_{p}\equiv W_{q,pot}$ (which describes the state of the ion
before the beginning of the neutralization) and the potential energy in front
of the solid surface $W_{q_{fin}^{nMV},pot}$ [41, 44, 12]:

$W^{(q,nMV)}=W_{q,pot}-W_{q_{fin}^{nMV},pot}.$ (1)

The energy $W^{(q,nMV)}$ can be calculated using the results valid for the
metal-vacuum MV-system [12], which is supported by the experimental fact that
the lattice structure of the nanolayer is very similar to the bulk material
for the layers thickness [45] considered in the present article.

Although many elementary charge exchange processes are possible at solid
surface, we assume that the ion with $Q=q_{fin}$ penetrates the surface.
Within the framework of the model, we also assume that neutralization inside
the solid in the process of the nanostructure formation can be neglected (has
negligible influence on the total deposited energy). The last assumption is
based on the fact that the nanocraters are formed in the narrow region of the
depth $\Delta x$ smaller compared to the penetration depth necessary for the
ionic charge to be significantly changed [12]. Therefore, we use $Q\approx
q_{fin}$ as the ionic charge for the analysis of the ionic motion and the
corresponding processes inside the target (see Fig.2). For more accurate
description of the overall neutralization process, the analysis of the
neutralization below the surface can be added to our model.

Below the surface, the ions constantly lose their kinetic energy due to the
elastic collisions with the target nuclei (nuclear stopping power $dE_{n}/dx$)
[11, 46, 47] and the inelastic interaction with the target electrons
(electronic stopping power $dE_{e}/dx$). Simultaneously, the damage of the
local atomic structure and the surface modification due to the ionic kinetic
energy loss take place. On the overall ionic trajectory the ionic kinetic
energy is deposited into the solid. However, analyzing the experimentally
obtained surface nanostructures, relevant is only the near surface region of
the length $\Delta x$ [12], so that

$E_{k,dep}=(dE/dx)\cdot\Delta x.$ (2)

For low to moderate ionic velocities electronic stopping power can be
neglected, i.e., $dE/dx=dE_{n}/dx=NS_{n}$, where $N$ is the atomic density of
the target. The corresponding nuclear stopping cross section $S_{n}$ we
calculate using the classical scattering theory with charge dependent ion-
target atom interaction potential [48, 12]:

$V_{int}(r)=\frac{(Z_{1}-Q)Z_{2}}{r}\varphi(\frac{r}{a_{u}})+\frac{QZ_{2}}{r}\varphi(\frac{r}{a_{s}}),$
(3)

where $Z_{1}$ and $Z_{2}$ are the nuclear charges of the projectile and the
target atom, respectively. Other quantities are explicitly given in [12]. We
note that, the charge dependence of the energy loss has been firstly
theoretically introduced by Biersack [49]. Further, the charge dependent
kinetic energy transfer for HCI interacting with C nanomembrane and C foil
target was elaborated in [50]. The time-dependent interatomic potential energy
was used to get the more accurate model for the calculation of the kinetic
energy loss in [51].

##  3 Experiment

The studies presented in this paper are continuation of our research [18, 52]
related to the nanostructure formation in interactions of highly charged xenon
ions with metallic surfaces. The aim of the experiments carried out for the
purposes of current work is to separate, as far as it is possible, the
influence of kinetic and potential energies of the HCI xenon ions on the
produced surface nanostructures. In the measurements we use gold nanolayers of
the thickness of 100 nm deposited on Si (110) wafers. The structure and
properties of such nanolayers were expected to be similar to the bulk metal,
but with possible lower density due to nanolayer structure [45] and an
influence of the substrate cannot be completely excluded [10].

###  3.1 Samples

The 100 nm Au nanolayers used in this experiment were prepared at Institute of
Electron Technology (Warsaw, Poland) using high vacuum (13$\cdot$10-8 hPa)
e-beam evaporation VST TFDS-462U deposition system. The metallic nanolayers
were evaporated on Topsil (Warsaw, Poland) Si (110) polished prime wafers type
N 4-inch diameter. The thickness of the silicon wafer was 0.635 mm $\pm$ 0.015
mm. The deposition rate was 0.4 nm/s. The thickness of the gold was set and
controlled by a crystal oscillator. Just after preparing, the wafers were cut
into rectangles of dimensions of 0.5 cm x 1 cm. The roughness of the samples
surface was checked by AFM technique. Root-mean-squared (RMS) roughness
determined by the AFM technique (UMCS, Lublin, Poland) for a few randomly
selected (1 $\mu$m x 1 $\mu$m) areas of the gold nanolayers using NanoScope
Analysis ver.1.40 (Veeco, USA) program were on the level of $0.45\pm 0.1$
nanometers. The crystalline structure of the substrate was confirmed based on
the measurements carried out using the XRD technique. Using the GIXRD
technique, it was determined that the 100 nm gold nanolayers have a
polycrystalline structure homogeneous in depth. Additionally using the XRR
technique, the thickness and density of the nanolayers were measured.
Thickness turned to be consistent with the declared one (100 nm), but the
density was slightly lower (but within the uncertainties) than the bulk
density. The XRR, XRD and GIXRD measurements were performed with X’Pert Pro
MPD reflectometer/diffractometer (for details see [53, 54]), placed at
Institute of Physics of UJK (Kielce, Poland). The 100 nm Au nanolayers were
irradiated at the Kielce EBIS facility of the Jan Kochanowski University
(Kielce, Poland) [33], under high vacuum conditions. After irradiation the
samples were again checked with AFM technique (UMCS, Lublin).

Figure 2: Topographic AFM 3D images of Au 100 nm nanolayer deposited on Si
surface before and after irradiation with HCI Xeq+. Top row: images of the
nanolayers before irradiation (left panel) and after irradiation with 280-290
keV Xe30+, Xe35+, Xe40+. Bottom row: images of the nanolayers after
irradiation with Xe35+ of different kinetic energies. The images were analysed
using the software NanoScope Analysis ver. 1.40 (Veeco, USA).

###  3.2 Kielce EBIS facility

The Kielce EBIS facility, built by the Dreebit (Dresden, Germany), is equipped
with electron beam ion trap (EBIS-A) [55]. The source supplies a wide range of
slow HCI from bare ions of light elements to Ne-like and Ar-like ions of
high-Z elements. The maximum electron energy and current available for
ionization of the trapped ions are equal 25 keV and 200 mA, respectively. The
ions produced in the EBIS-A source can be extracted both in a pulse mode
(pulse width from 2 $\mu$s up to 40 $\mu$s) and leaky mode (DC mode) by
applying an acceleration voltage up to 30 kV. Highly charged ions extracted
from the EBIS-A ion source are guided by ion beam optical elements (einzel
lens and X-Y deflectors) of the first straight section of the facility to the
double focusing analyzing magnet separating the ions according to their mass
to charge ratio. The first section of the beamline includes a quadrupole
section with pressure gauge, 4-jaw-slit collimation system and a Faraday cup.
The ions separated in the analyzing magnet are directed to the second straight
section of the EBIS-A facility. In this section, a pressure gauge, X-Y
deflectors, a Faraday cup and an einzel lens are mounted. Finally, the highly
charged ions collide with a sample mounted on a 5-axis universal manipulator
placed in the experimental chamber. The manipulator allows for x, y, z linear
movements, polar and azimuthal rotations of a sample and variation of its
temperature in the range of 100-1000 K. The beamline can be biased with
positive or negative high voltage allowing ion acceleration or deceleration.
For current facility configuration the ion energies can be set from 2.5 keV x
q up to 30 keV x q, with q denoting the ion charge state. All components of
the EBIS-A facility fulfill the UHV standards and after baking of the system
at 150${}^{\circ}C$ the pressure is in the few 10-10 mbar range (in the
beamline). One of the unique features of the EBIS facility is the ability to
prepare, irradiate by highly charged ions and characterize the studied samples
in the UHV conditions.

###  3.3 Measurements

In the measurements isotopically pure highly charged Xeq+ ions were extracted
from the EBIS-A and, after selecting given ion charge state in the dipole
magnet, were used to irradiate the nanolayers. The ion beam current was
measured with a movable Faraday cup mounted in front of the sample. The spot
radius of the ion beam on the sample was around 1.5 mm $\pm$ 15% as it was
determined by moving the Faraday cup across the ion beam (from the beam
profile). The ion fluence was estimated on the level 1010 ions/cm2 (with
uncertainty of the 10-15%). The samples were first placed in a loading chamber
pumped to about $10^{-7}$ mbar, and then transmitted to the experimental
chamber. The vacuum in the experimental chamber was around $(2-5)\times
10^{-8}$ mbar. After irradiation, the sample was transferred back to the
loading chamber and was stored there until it was removed for atomic force
microscopy investigations, which were performed in the air. The measurements
were performed for two configuration: constant kinetic energy of the ions
equal to 280-290 keV and different charge states of the xenon ions Xeq+, where
q = 25, 30, 35, 36, 40 and constant charge state (Xe35+) of the ions and
different kinetic energies 280 keV, 360 keV, 420 keV and 480 keV.

###  3.4 AFM system

The topographic modifications of the samples surface induced by Xeq+ ions were
investigated using atomic force microscopy in the Analytical Laboratory of
Faculty of Chemistry, UMCS, Lublin, Poland. AFM measurements of the studied
samples were performed using Multimode 8 (Bruker) AFM equipped with NanoScope
software (Bruker-Veeco, USA). The AFM was operated in SCANASYST-HR fast
scanning mode using SCANASYST-AIR-HR probe (Silicon Tip on Nitride Lever)
(Bruker) with the cantilever of force constant k = 0.4 N/m. The lateral and
vertical resolutions were 4 nm and 0.1 nm for the 1 $\mu$m x 1 $\mu m$, and 2
nm and 0.1 nm for the 500 nm x 500 nm images. The obtained images were
analyzed with Nanoscope Analysis ver. 1.40 software (Veeco, USA).

##  4 Results

###  4.1 AFM images

The AFM images of the nanolayers before irradiation (left panel) and after
irradiation with 280-290 keV Xe30+, Xe36+, Xe40+, and Xe35+ of different
kinetic energies are presented in the Fig. 2. The images were analyzed using
the NanoScope Analysis software. The size of presented area is 500 nm x 500
nm. In the images of the irradiated samples, we can clearly see the
modifications caused by the ion impact. We would like to stress here, that
such excellent images of metallic surface modification caused by HCI impact,
to our knowledge, have never been registered. The same modifications were
observed for all irradiated samples, with surface density of the
nanostructures approximately equal to the ion fluence, i.e. one nanostructure
per one HCl ion impact. Analogous efficiency of the nanostructure creation was
observed by Pomeroy [17].

Figure 3: Upper panel: examples of the 3D AFM images of the nanostructures on
Au 100 nm/Si nanolayer surface irradiated by 280-290 keV Xe30+, Xe35+ and
Xe40+. Lower panel: upside-down 3D AFM images of the nanostructures on Au 100
nm/Si nanolayer surface irradiated by 360, 420 and 480 keV Xe35+. The images
were analysed using the software NanoScope Analysis ver. 1.40 (Veeco, USA).

The measured modifications have the form of craters, which is confirmed by
enlarged AFM 3D images of the individual nanostructures which are presented in
the Fig. 3. In the upper panel the example of the 3D AFM images of the
nanostructures on Au 100 nm/Si nanolayer surface irradiated by 280-290 keV
Xe30+, Xe35+, Xe40+ are presented. All observed structures had a similar
crater-like shape, i.e. a cavity, sometimes with a ring around it (check the
middle image). Merkle and Jager [38] and Bringa et al. [29] postulate that
these rings around the cavity arise from the sputtering (or rather an outflow)
of the original atoms being at the place of the structure formation. This was
confirmed by MD simulations presented in the article of Bringa et al. [29].
Similar shape of the crater formed on a Si(100) surface by bombardment of a
Xe44+ HCI was also observed in the simulations performed by Insepov et al.
[27] using plasma model of space charge neutralization based on impact
ionization of semiconductors at high electric fields. In the lower panel of
the Fig. 3 upside-down 3D AFM images of the nanostructures on Au 100 nm/Si
nanolayer surface irradiated by 360, 420 and 480 keV Xe35+ are presented to
confirm crater like shape of the nanostructures.

###  4.2 Analysis of the AFM images

In many surface studies, a common data analysis strategy is to correlate the
mean size of nanostructures (parameters like: diameter, depth, volume) with
different ion parameters, e.g. kinetic energy (ionic velocity) and potential
energy (ionic charge state), nuclear and electronic stopping powers, etc.
Following this strategy we have performed size analysis of the observed
nanostructures. For this purpose, all observed images were first carefully
checked and optimized with NanoScope Analysis software and, after extracting
of the data from the AFM images (using STEP function of the software),
analysed with Origin Pro data analysis software. From the individual profile
of the craters we have extracted their size parameters, including the diameter
on the surface. All unambiguously identified structures on the surface of the
samples were analyzed independently. Example of the individual crater profile
(black points) is presented in the Figure 4.

Figure 4: Example of the individual crater profile (black points) with fitted
Gaussian curve (solid line). The sigma $\sigma$ (standard deviation), FWHM
(full width in the half of maximum) and crater depth d quantities are Gaussian
distribution parameters. The crater diameter on the surface is assumed as
2FWHM.

The profiles were fitted by Gaussian curve (solid line), which reflected very
well the shape of the crater. At this point, we note that the needle used for
the AFM analysis of all samples had a tip curvature radius r = 2 nm, and the
structures after HCI modification were characterized by diameters of about
10-25 nm, so an incorrect tip contact was considered unlikely, especially in
the diameters of nanostructures on the sample surface. The crater diameter on
the surface was defined as double FWHM (2 $\times$ FWHM). In the example
presented in the Figure 4, the crater diameter at surface was fitted as 15.16
nm, while its depth as 0.93 nm. An alternative way to determine the diameter
is to take values of four standard deviations (4$\times\sigma$). In presented
examples, it gives 4$\sigma$ = 12.88 nm. In general, it was observed that
crater diameter defined as 2 $\times$ FWHM was about 10-15$\%$ higher than
4$\times\sigma$ quantity.

For the Au nanolayer irradiated by Xe ions in given charge state, for each
sample around 50 to 150 craters were analyzed in the way described above.
Finally, the mean values of the crater depth and crater diameters for each
irradiated Au nanolayer were calculated. Based on the statistical analysis of
the crater profiles, the dependence of the crater depth and crater diameter on
the Xe ions potential and kinetic energy were studied. In the case of the
crater depth no dependence on the ions potential energy was observed. The
crater depth was on the constant level of about 0.9 nm $\pm$ 0.15 nm. The
linear fit to the data, including uncertainties defined by the standard
deviation of mean value, gave a very week dependence (the slope is equal to
0.001 nm/keV).

The obtained mean values of craters diameter in function of the potential
energy of the Xeq+ ions are plotted in the Fig. 5. The uncertainties marked
for experimental points were calculated as the sum of the mean value standard
deviation and 10$\%$ of the mean value (compensation of the difference between
2FWHM and 4$\sigma$ quantities within uncertainty). The Xe ions charge states
marked by (*) denoted a slightly different kinetic energy (290 keV), caused by
difficulties in setting a given charge state and kinetic energy. As one can
see from the figure we have observed clear influence of the ionic charge state
(expressed via initial potential energy) on the nanocrater diameter. For the
lowest ion charge state (25+) the mean nanocrater diameter is 12.0 nm, next
this parameter systematically grows, reaching for the highest charge state the
value 23.4 nm.

Figure 5: Dependence of the craters diameter on the Xeq+ ions potential
energy. The Xe ions charge states marked by (*) denoted a slightly different
kinetic energy (290 keV).
Figure 6: Dependence of the nanocrater diameter created by the Xe35+ ions
impinging on Au surface on the kinetic energy (this experiment). For
comparison, the results of Donnelly and Birtcher experiment [39] for Xe+ ions
are also presented. In the figure, also the nuclear stopping power S1/2 (solid
line) is presented.

The results of the study of the crater diameter in function of the ions
kinetic energy are shown in the Figure 6 for Xe35+. The nanocrater diameter is
in the range 13-15 nm. The linear function fitted to the experimental points
showed a weak alteration of the dependence. In the Figure 6 the results of
Donnelly and Birtcher experiment [39] for Xe+ ions are also presented which
confirm small dependence of the created nanocrater diameter on the ions
kinetic energy in the considered energy range. On the other hand, the
nanocrater diameters for HCI xenon ions are much higher than for single
ionized xenon.

##  5 Discussion

###  5.1 Theoretical model of the crater formation

In order to interpret the present experiments performed with Xeq+ ions of
initial charges q = 25, 30, 35, 36 and 40 in the interaction with a gold 100
nm nanolayer deposited on Si (110) wafers (nMV-system) at velocity $v=0.29$
a.u., as well as to examine the velocity dependence studied in the case of
Xe35+ for $v=0.29,0.33,0.36$ and 0.38 a.u. we use the micro-staircase model.

The formation of nanocraters we discuss from the standpoint of the energy
dissipation into the surface, which consists both of the neutralization energy
and the deposited kinetic energy [41, 44, 12]. For velocities characteristic
for the crater formation the neutralization is incomplete so that the
corresponding neutralization energy represents only a part of the ionic
initial potential energy. The remaining potential energy $E_{p}-W^{(q,nMV)}$
contributes to the charge dependent potential interaction (Eq.(3)) between the
ion and the target atoms and thus it is converted into kinetic energy of the
target atoms (stopping power calculated in micro-staircase model is charge
dependent). We calculate the neutralization energy according to Eq. (1) for
$W^{(q,nMV)}=W^{(q,MV)}$; taking into account that the neutralization energy
is weakly dependent on the solid work function $\phi$, we consider the
neutralization energy for $\phi=5$ eV (work function of Au is 5.47 eV). For
the calculation of the kinetic energy loss we employ Eq. (2) for the active
interaction length $\Delta x\approx 5\bar{c}\approx 38.5$ a.u., where
$\bar{c}$ is the mean lattice constant for Au-target; we note that the crater
depth $d_{max}\approx 1\textrm{nm}=18.9$ a.u. To define the ion-atom
interaction in solid we use the charge of the projectile $Q=q_{fin}(q,v)$
obtained in [12].

Figure 7: Upper panel: neutralization energy $W^{(q,nMV)}$ and deposited
kinetic energy $E_{k,dep}$ versus ionic velocity $v$ for Xeq+ ions,
$q=25,30,35$ and 40, impinging on the Au nanolayers (formation of the crater
in the present experiment). Lower panel: the critical ionic velocity $v_{c}$
versus initial ionic charge $q$.

In Fig. 7, at upper panel, we present the neutralization energy $W^{(q,nMV)}$
and the deposited kinetic energy $E_{k,dep}$ relevant for the surface
nanocrater creation by the impact of Xeq+ ions with core charges $q=25,30,35$
and 40 on 100 nm Au nanolayer on Si (110) wafers as a function of the ionic
velocity $v$. The neutralization energy $W^{(q,nMV)}$ decreases with
increasing of the ionic velocity $v$; on the other hand, the deposited kinetic
energy $E_{k,dep}$ increases with increasing of $v$. The results indicate the
interplay of these two energies in the process of the surface nanocrater
formation. That is, we define [12] the critical velocity $v_{c}$ by the
relation:

$W^{(q)}(v_{c})=E_{k,dep}(v_{c}).$ (4)

For velocities $v\ll v_{c}$ (very low ionic velocities) dominant role in the
energy participation in the solid has the neutralization energy $W^{(q,nMV)}$,
while for $v\gg v_{c}$ (swift heavy ions) the deposited kinetic energy
$E_{k,dep}$ completely determines the process of the nanostructure formation
[12]. The quantity $v_{c}$ we present in Fig. 7 at lower panel as a function
of the initial ionic charge $q$. The values of the critical velocities are
also given in Table 1.

Table 1:  Critical velocities $v_{c}$ in the case of the surface nanocrater
formation in the nMV-system by the impact of Xeq+ ions.  100 nm Au nanolayer
---
$q$ | 25 | 30 | 35 | 40 |
$E_{k}$ (keV) | 280 | 280 | 280 | 280 |
$v_{exp}$ (a.u.) | 0.29 | 0.29 | 0.29 | 0.29 |
$v_{c}$ (a.u.) | 0.07 | 0.17 | 0.22 | 0.23 |

For all considered ionic charges the critical velocities $v_{c}$ are lower
compared to the experimental value $v_{exp}=0.29$ a.u.
($E_{k}=Mv_{exp}^{2}/2,M=131\cdot 1836$ a.u. for Xeq+ ions, where $E_{k}$
denotes the initial ionic kinetic energy). For charges $q=35$ and $q=40$, the
critical ionic velocities $v_{c}$ are close to the experimental one (see Table
1), indicating that both energies contribute to the crater formation. The
values of $v_{c}$ for Xe25+ and for Xe30+ are much smaller than the
experimental ones, so that the main contribution in the nanostructure
formation gives the deposited kinetic energy $E_{k,dep}$. Concerning the type
(shape) of the nanostructures, the appearance of the nanocraters in experiment
is in accord with the prediction of the micro-staircase model. On the other
hand, the hillocks have been obtained in experiment with Xe35+ ions [18]
impinging upon the surface of the 50 nm gold layer at velocity 0.19 a.u.,
while the critical one is 0.22 a.u. [12]. In the case of 25 nm titanium
nanolayers the experimental velocities for $q=20,25,30$ and 35 were 0.144,
0.16, 0.176 and 0.19, in a.u., respectively. The corresponding critical
velocities are 0.06, 0.16, 0.22 and 0.24, in a.u. [12]. The results of the
present experiment and the results of the previous ones [18, 52, 17] confirm a
common conclusion: for the ionic velocities $v<v_{c}$ or $v\approx v_{c}$ the
surface modification leads to the nanohillocks formation [18, 12], while for
$v>v_{c}$ the predominant surface structures are the craters (rings) [52, 17,
12].

The neutralization energy $W^{(q,nMV)}$ and the deposited kinetic energy
$E_{k,dep}$ can be also connected to the size of the formed nanostructures.
The experimental results for the crater diameters show the significant
increasing from $q=25$ to $q=40$, see 5. For $v_{exp}=0.29$ a.u. and Xe25+ ion
the diameter $D=12$ nm (226.8 a.u.) and for Xe40+ ion diameter $D=$ 23.4 nm
(442.3 a.u.). The ionic neutralization energy (and also the initial ionic
potential energy) exhibits the same increasing behavior ($W^{(25,nMV)}=47$
a.u. and $W^{(40,nMV)}=162$ a.u.), see Table 2.

Table 2:  Neutralization energy $W^{(q,nMV)}$, deposited kinetic energy
$E_{k,dep}$ and crater diameter $D$ in the case of the surface nanocrater
formation for $v=v_{exp}=0.29$ a.u. in the nMV-system by the impact of Xeq+
ions, for $\Delta x\approx 38.5$ a.u.  100 nm Au nanolayer
---
$q$ | 25 | 30 | 35 | 40 |
$W^{(q,nMV)}$ (a.u.) | 47 | 88 | 127 | 162 |
$E_{k,dep}$ (a.u.) | 557 | 569 | 577 | 587 |
$D$ (nm) | 12 | 13 | 15 | 23.4 |

The $q$ dependence of the deposited kinetic energy, obtained on the base of
Eq. 3, is less pronounced ($E_{k,dep}$ for Xe25+ is 557 a.u. and for Xe40+,
$E_{k,dep}=587$ a.u.), see Table 2. For these reasons, it is convenient to
present the experimentally obtained crater diameters as a function of the
potential (or the neutralization) energy.

The velocity effect on the crater diameter $D$ for Xe35+ ions we study for the
experimental values $v_{exp}=0.29,0.33,0.36$ and 0.38 a.u. From the
experimental results one recognize the weak decreasing of the quantity $D$
with increasing of the ionic velocity (kinetic energy) see Fig. 6; (for
$v=$0.29 a.u. diameter $D=15$ nm (283.5 a.u.) and for $v=$0.38 a.u. diameter
$D=12$ nm (226.8 a.u.)). On the other hand, the deposited kinetic energies
$E_{k,dep}$ increase slightly with increasing of $v$ (for $v$=0.29 a.u.
$E_{k,dep}$= 577 a.u. and for $v=$0.38 a.u. $E_{k,dep}=$635 a.u.), while the
neutralization energy $W^{(35,nMV)}$ show a noticeable decreasing character
(for $v=$0.29 a.u. $W^{(35,nMV)}=$127 a.u. and for $v=$0.38 a.u.
$W^{(35,nMV)}=$35.5 a.u.), see Tab. 3.

Table 3:  Neutralization energy $W^{(q,nMV)}$, deposited kinetic energy
$E_{k,dep}$ and crater diameter $D$ in the case of the surface nanocrater
formation for $v_{exp}=0.29,0.33,0.36$ and 0.38 a.u. in the nMV-system by the
impact of Xe35+ ions, for $\Delta x\approx 38.5$ a.u.  100 nm Au nanolayer
---
$v_{exp}$ (a.u.) | 0.29 | 0.33 | 0.36 | 0.38 |
$W^{(q,nMV)}$ (a.u.) | 127 | 66.8 | 47.2 | 35.5 |
$E_{k,dep}$ (a.u.) | 577 | 600 | 608 | 612 |
$D$ (nm) | 15 | 12.9 | 13.9 | 12.15 |

The role of the neutralization energy $W^{(q,nMV)}$ and the deposited kinetic
energy $E_{k,dep}$ can be more precisely discussed from the relation between
the crater diameter and the total deposited energy:
$E_{tot,dep}=E_{k,dep}+W^{(q,nMV)}$. Assuming that the energy $E_{tot,dep}$ is
localized in the cylindrical region od the diameter $D$ and depth $\Delta x$,
we get the relation:

$D=f\sqrt{{E_{k,dep}+W^{(q,nMV)}}},$ (5)

where the factor $f$ reflects the target properties. Both energies $E_{k,dep}$
and $W^{(q,nMV)}$ are charge dependent, so that the nanocrater size will
express the same behavior. From Eq. 5 and Tables 2 and 3 one conclude that the
main contribution to the diameter $D$ gives the deposited kinetic energy.
However, the neutralization energy term in Eq. 5 must be taken into account in
order to obtain the experimentally observed behavior of the crater diameter
$D$ discussed in Tables Tab. 2 and Tab. 3: pronounced increasing od $D$ with
increasing of $q$ and weak decreasing of $D$ with increasing of the ionic
velocity $v$. The discussed significance of the deposited kinetic energy and
the role of the neutralization energy is characteristic for the moderate
velocity case used in the experiment. We note that for the very low
velocities, the neutralization energy (close to the potential energy) plays a
dominant role. The increasing of $D$ with increasing of $q$ and the
$v$-dependence of the crater diameter obtained in the present experiment is in
a qualitative agreement with the prediction of the proposed model.

Within the framework of micro-staircase model, the mechanism of the
nanocraters and nanohillocks formation at metallic surfaces is different. At
velocities $v<v_{c}$ characteristic for the hillock formation, a dominant role
has the neutralization process: the strength of the bonds between atoms
decreases inducing their stretching. The rearrangement of atoms leads to the
rise of the volume above the surface and hillock formation. The deposited
energy is insufficient for melting the material (the hillocks are formed
without melting). The predicted mechanism of the nanohillock formation on
metal surface [12] is different in comparison to the thermal spike model used
in the case of nanohillock formation on insulator [56]. In the case of crater
creation (for $v>v_{c}$) considered in the present paper, the neutralization
(above the surface) induces the lattice vibration and the first
destabilization of the target. Inside the solid, the elastic collisions of the
charged projectile with target atoms and produced recoils lead to the
disordering of the target atoms generating the highly disturbed near surface
area $V$. A large amount of kinetic energy deposits into the solid, resulting
in a significant decrease in the target cohesive energy. The strength of the
bounds between the target atoms inside the crater volume tends to be zero and
a number of atoms are ejected from the surface. In the intermediate stages of
the craters formation, in the centre of the active volume $V$, it is possible
that the temperature far exceeds the melting temperature. The deposited
neutralization energy during the process above the surface has a small
contribution to the nanocrater formation in comparison to the deposited
kinetic energy during the collision cascade below the surface; however, the
main $q$ and $v$ dependence of the crater size are governed by the
neutralization energy.

###  5.2 MD simulations

We also compare the present experimental results with molecular dynamics (MD)
simulations presented in [29]. We compare our results for HCI xenon ion with
Xe+ ion after fitting the data on Fig. 5, and further normalization to the
potential energy equal to the potential energy of Xe+. The results of the
comparison we present in Fig. 8. In the figure, the nuclear stopping power
S1/2 (solid line) and the ion energy E1/3 (dashed line) curves are also
presented. We obtain very good agreement with the experimental data of
Donnelly and Birtcher [39] and MD simulations [29], which confirms the
validity of our experimental procedure.

Figure 8: Comparison of the results of crater radius, as a function of the ion
kinetic energy, obtained by our group with the results of the experiment
(Donnelly and Birtcher) for single charged Xe+ ion impinging on Au surface
[39] and MD simulations [29]. In the figure, the nuclear stopping power S1/2
(solid line) and ion energy E1/3 (dashed line) curves are also presented.

It is important to mention that, very recently, molecular dynamics methodology
coupled with two-temperature model (2T-MD) [57], was used by Khara et al. to
simulate the structural evolution of bcc metals (Fe and W) and fcc metals (Cu
and Ni) following irradiation by SHI (electronic stopping power regime) [23].
They found that number of material parameters (melting temperature, electronic
thermal conductivity and electron-phonon coupling strength), and their
electronic properties temperature dependence, have a strong influence on the
resistance of metals to damage induced by SHI irradiation. They also showed
that high thermal conductivity and relatively low electron-phonon coupling of
fcc metals render them relatively insensitive to damage, in spite of their
relatively low melting temperatures. The strong electron-phonon coupling of
the bcc metals (Fe and W) is primarily responsible for the sensitivity of
these metals to damage [23]. The cited calculations are in contradiction with
the experimental results for Au (fcc metal) - HCI systems, for which we obtain
the surface nanocraters in the velocity range $v\in[0.29,0.38]$ a.u. and the
nanohillocks for lower ionic velocities $v\in[0.144,0.19]$ a.u. [18]. In the
case of nanocrater formation, both the deposited kinetic energy and the
neutralization energy participate in the process; the nanohillocks are formed
predominantly by the participation of the neutralization energy. The
calculations [23] showed a significantly different response of bcc and fcc
metals to the deposition of energy in the interaction of SHI ions with
surfaces and encouraged us to undertake such tests for HCI. At the moment,
similar calculations does not exist for HCI, where it is necessary to take
into account the neutralization process. The model proposed here represents a
theoretical approach of that kind, stimulated by the experimental findings.

##  6 Conclusions

Understanding of mechanism of the nanostructures creation on metallic surfaces
is very important both from the theoretical and possible application point of
view. In this paper we have studied Au nanolayers surfaces irradiated by slow
highly charged Xeq+ ions ($q$ = 25, 30, 35, 36 and 40). For the first time,
for such systems, well pronounced modifications of the nanolayers surfaces,
due to impact of the HCI ions, in the form of nanocraters have been observed.
This allowed for systematical study of dependence of the size of
nanostructures on potential and kinetic energy of the ions. Analysis of the
crater diameter $D$ for different initial charge states $q$ of the Xe ions
showed a significant dependence of the quantity $q$ (expressed via potential
energy in Fig. 5). Additionally, for interaction of the Xe35+ ions with Au
nanolayers the dependence of the structure formation on the ion kinetic energy
(280 keV, 360 keV, 420 keV and 480 keV) was studied. Week alteration of the
crater diameter (Fig. 6) with the ion kinetic energy was observed in the
analyzed energy range. Our results were qualitatively interpreted within the
micro-staircase model for the neutralization energy combined by the charge
dependent kinetic energy deposition. The experimental results are also
compared with the available simulations and the previous experimental data.
The results will be potentially of great importance for further development of
modern technologies (e.g. single HCI nano-pattering [58], role of the HCI
impurities in tokamak plasma-metallic wall interaction [59]) and will open up
many application possibilities (e.g. DNA sequencing or water desalination
[60]).

## Acknowledgments

The equipment was purchased thanks to the financial support of the European
Regional Development Fund in the framework of the Polish Innovative Economy
Operational Program (contract no. WNP-POIG.02.02.00-26-023/08), the
Development of Eastern Poland Program (contract no. POPW
.01.01.00-26-013/09-04) and Polish Ministry of Education and Science (project
28/ 489259/SPUB/SP/2021). N. N. Nedeljković and M. D. Majkić are grateful for
the support of the Ministry of Education, Science and Technological
Development of the Republic of Serbia (projects 171016, 171029).

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