Applied Surface Science 570 (2021) 151204

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Sputter yields of rough surfaces: Importance of the mean surface inclinationangle from nano- to microscopic rough regimesC. Cupak a,∗, P.S. Szabo a, H. Biber a, R. Stadlmayr a, C. Grave a, M. Fellinger a, J. Brötzner a,R.A. Wilhelm a, W. Möller b, A. Mutzke c, M.V. Moro d, F. Aumayr a

a Institute of Applied Physics, TU Wien, Fusion@ÖAW, Wiedner Hauptstraße 8-10/E134, 1040 Vienna, Austriab Institute of Ion Beam Physics and Materials Research, Helmholtz-Zentrum Dresden-Rossendorf e.V. (HZDR), Bautzner Landstr. 400, 01328 Dresden, Germanyc Max–Planck Institute for Plasma Physics, Wendelsteinstrasse 1, 17491 Greifswald, Germanyd Department of Physics and Astronomy, Uppsala University, Box 516, 751 20 Uppsala, Sweden

A R T I C L E I N F O

Keywords:SputteringSurface roughnessSputtering simulationQuartz crystal microbalanceTungsten

A B S T R A C T

The roughness of a surface is known to have a strong influence on the sputtering process. Commonly used1D Monte Carlo codes for calculating sputter yields show good agreement with experimental data only forcomparably flat surfaces, whereas local ion incidence angles, shadowing and redeposition influence the sputteryields in both magnitude and angular dependence on rough surfaces. In the present work, we thereforeinvestigated tungsten samples of largely different roughness, characterised by atomic force and confocalmicroscopy. A highly sensitive quartz crystal microbalance was used to determine sputter yields during ionirradiation. Low ion fluences were applied to ensure that the surface morphology did not change duringirradiation. The results were used to benchmark our new ray-tracing simulation code SPRAY, which cantake microscopy images without limitations in size as input. SPRAY was furthermore applied to performsystematic simulations for artificially roughened and computer-generated surfaces. A clear result was that thegoverning parameter for description of the sputtering behaviour is the mean value of the surface inclinationangle distribution, rather than the commonly used root mean square roughness. Our simulations show thatthis parameter is universally applicable for a wide range of different surface structures.

1. Introduction

Sputtering of surfaces by ion bombardment is a current topic ofhigh relevance in surface technology and applied sciences: PhysicalVapour Deposition (PVD) methods employ sputtering to create nm thincoatings for application in semiconductor industries [1], to enhancewear resistance [2] or to change optical or electro-chromic proper-ties [3,4]. Furthermore, Focused Ion Beam (FIB) cutting methods utiliselocalised sputtering to modify materials in the nanometre regime [5],while nano patterning techniques like ion lithography can be used tocreate laterally larger and oriented surface patterns [6]. Sputteringeffects can also occur in outer space on objects which do not possessa protecting atmosphere, where impinging solar wind ions lead tocontinuous erosion as part of space weathering [7–10]. In nuclearfusion research, erosion of first wall materials due to sputtering isunder continuous examination, since sputtering by fuel or seeding gasions limits the lifetime of plasma facing components and also leads toincreased plasma impurity abundances, which are disadvantageous forthe performance of fusion reactions [11–15].

∗ Corresponding author.E-mail address: cupak@iap.tuwien.ac.at (C. Cupak).

Well-known dependencies of the sputter yield (defined as the meannumber of sputtered atoms per incoming ion) on parameters like ionenergy, ion incidence angle or the atomic mass of the target atomscan be satisfactorily described by theoretical concepts which havebeen established for decades [16,17]. Furthermore, established BinaryCollision Approximation (BCA) simulation codes like SRIM [18], TRI-DYN [19] or SDTrimSP [20], which simulate ion-induced collisioncascades, are available for sputter yield prediction. However, signif-icant deviations between simulated and experimental results can befound under certain conditions, which often originate from complexsurface properties demanding more detailed modelling. For instance,Schlueter et al. recently showed that the sputter yield of polycrys-talline targets can substantially deviate from numerical results basedon amorphous target models, which are often employed in simulationcodes [21]. Furthermore, it is also well known that properties likesurface roughness can severely change the effective sputter yield incomparison to flat surfaces [22–28].

vailable online 9 September 2021169-4332/© 2021 The Authors. Published by Elsevier B.V. This is an open access a

https://doi.org/10.1016/j.apsusc.2021.151204Received 29 July 2021; Received in revised form 26 August 2021; Accepted 4 Sept

rticle under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

ember 2021

Applied Surface Science 570 (2021) 151204C. Cupak et al.

On the one hand, this motivated alternative implementation ofroughness in 1D simulation codes, for example by using fractal ge-ometry [29] or density gradient models [30]. On the other hand,complex surface patterns may not always be satisfactorily described bysuch models. State-of-the-art 3D BCA codes like SDTrimSP-3D [31] orTRI3DYN [32] are advantageous as they provide the opportunity for di-rect surface topography implementation from microscopy, which is es-pecially useful for simulation of complex structures like e.g., tungsten-fuzz [33]. Modern codes like ERO2.0 furthermore enable considerationof magnetic forces in the plasma of fusion devices for particle trans-port [34]. Recent studies which employed such 3D simulation codessupport the hypothesis, that enhanced roughness often leads to lowereffective sputter yields and also affects the angular emission distribu-tion of sputtered atoms and reflected ions [33–36]. However, many3D codes typically demand computational cluster infrastructure and/orare limited to surface areas of comparably small lateral image size(several 100 nm) which prevents investigation of larger scale roughnesseffects. In addition, dynamic surface modification cannot be neglectedin most experimental studies, making it difficult to assess static sputter-ing properties of a rough surface. Common parameters like e.g., RootMean Square (RMS) roughness, which is defined as the quadratic meanvalue of vertical deviations with respect to the average surface height,are often used for characterisation of real surfaces, while it is notclear whether this parameter is suitable for a consistent assessment ofsputtering.

The works of Küstner et al. [22], Hu et al. [37], Stadlmayr et al. [38]and Arredondo et al. [26] highlighted that the Surface InclinationAngle Distribution (SIAD) (see supplementary material Section A) isof high relevance for understanding rough surface sputtering by ionirradiation, since it is connected to effects like variation of local ionincidence angles, geometrical shadowing, redeposition or secondarysputtering due to reflected ions (see Fig. 1). In this work we demon-strate that the first moment (or mean value) 𝛿𝑚 of this distributionis already a very good and scale-independent parameter to charac-terise non-dynamic sputtering of rough surfaces. The applicability for awide range of different surfaces was investigated experimentally usingthe highly sensitive QCM technique established at TU Wien. With 2keV Ar+ ions from a mass-filtered low-flux ion source, quasi-staticsputter yields of W samples with roughness values ranging from thenano- towards the micrometre RMS regime were investigated (Sec-tion 3). In addition, these results were used to benchmark our newlydeveloped ray-tracing simulation code SPRAY, which enables rapidcalculation of effective sputter yields considering complete microscopyimages without lateral size limits or demands for computational clusterinfrastructure. SPRAY was then used for artificially roughened andcomputer-generated sample surfaces to investigate the role of differentsurface roughness parameters (Section 4).

2. Materials and methods

2.1. Tungsten samples

In the course of this study, three individual samples were used andcharacterised prior to the QCM experiments. The samples labelled S1and S2 consisted of tungsten-coated quartz crystals with a diameterof 14 mm. The virgin quartz crystals were manufactured by the com-pany KVG Quartz Crystal Technology GmbH, Germany. The top layer oftungsten with a thickness of several 100 nm was deposited via PVD ina collaboration with Max Planck Institute of Plasma Physics, Garching,Germany, using magnetron sputtering. While sample S1 showed a veryflat and mirror-like surface, S2 intentionally exhibited higher roughnessand a matte optical appearance. This was achieved by using quartzcrystal substrates with different surface finishes, being either polishedor not. Therefore, the roughness of the deposited tungsten layers wasstrongly affected by the topography of the underlying interface. Thethird sample labelled S3 was produced via Chemical Vapour Deposition

2

Fig. 1. Visualisation of local roughness related effects on sputtering for a targetunder ion bombardment. A and B: Local sputtering and ion reflection; C: Geometricalshadowing of surface sections; D: Secondary sputtering due to reflected projectiles; E:Redeposition of sputtered atoms.

(CVD) in a collaboration with Forschungszentrum Jülich, Institute ofEnergy and Climate Research, Germany. A tungsten layer with about 700μm thickness was deposited on a 1 mm thick silicon wafer platelet with10 × 10 mm2 size. Using this approach, a very high surface roughnesswas achieved. The silicon wafer was used as a substrate since theelevated temperatures of 870 K during the CVD process would havetriggered a non-reversible phase transition in a quartz crystal [39].

Since surface roughness is a key property in this study, microscopyinvestigations were performed before and after the experiments.Tapping-mode Atomic Force Microscopy (AFM) is a versatile techniquefor imaging nanoscale surface features and was therefore of interestfor the smoother samples in this campaign [40]. Our device Cypher Sacquired from Asylum Research, Oxford Instruments (United Kingdom)enables to record images with up to 1024 × 1024 px2 resolutionand 20 × 20 μm2 lateral size. However, in order to enable mappingof nanoscale features a maximum image size of 2 × 2 μm2 wasutilised in this study. In addition, also Con-Focal Microscopy (CFM)was employed especially for investigation of the rougher samples,which could not be investigated by AFM. The 𝜇surf explorer microscopemanufactured by NanoFocus AG, Germany was used to generate imageswith 512 × 512 px2 [41]. Using a 100x objective, a lateral image size of160 × 160 μm2 was achieved. Based on quantitative information fromthe obtained microscopy images, both the RMS roughness value and 𝛿𝑚were calculated for characterisation.

The results of roughness investigation are collected in Fig. 2. Thethree columns from left to right indicate data from sample S1, S2 andS3, respectively. In the top row of Fig. 2, selected AFM microscopyimages of the samples are visualised in 3D using the software Meshmixer(Autodesk Inc.) [42]. The second row includes analogue visualisationslike in the top row, but which are based on CFM. The third rowshows diagrams of the SIAD obtained by all recorded images fora specific sample. Only AFM was applied for sample S1, since thenanoscale topography could not be resolved with CFM. A flat surfacewith round scales of nm-height can be seen in the 1 × 1 μm2 image(Fig. 2aa). In total, four images from different locations on this samplewere recorded and used for calculation of roughness parameters. Thenanoscale smooth surface is indicated by a small RMS roughness valueof 1.7 ± 0.1 nm and is also characterised by the shape of the SIAD,which shows a pronounced peak for angles close to surface normaldirection (Fig. 2ca). A mean value 𝛿𝑚 of 7.6 ±1.2◦ was determined fromthis distribution.

Sample S2 was investigated with AFM and CFM, therefore selectedimages are shown for both methods (Fig. 2ab and 2bb). The 2 × 2 μm2

AFM image shows a corrugated surface with pronounced inclinations

and superposition with round scales. Since the lateral size of the AFM

Applied Surface Science 570 (2021) 151204C. Cupak et al.

Fig. 2. Collection of results regarding sample characterisation. The surface visualisation was created using the software Meshmixer [42]. Columns from left to right: SampleS1–S2–S3. Top row: 3D visualisation of sample surface topographies based on AFM, if available. Second row: 3D surface visualisation based on CFM, if available. Third row:Results regarding the surface inclination angle distribution (SIAD).

images was already comparable to the height of surface features, it wasassumed that their representativeness is limited. Therefore, a larger setof 15 AFM images was used to gain more data for the determinationof roughness parameters, which were 34.5 ± 26.9 nm for RMS and19.7 ±4.2◦ for 𝛿𝑚. The comparably large standard deviation in RMScorroborates the assumption, that the recorded AFM images were nota reliable basis for RMS calculation. Furthermore, any superimposedsurface structures which exist on a larger lateral scale, would havebeen hard to include with these images. Nevertheless, the AFM im-ages of sample S2 revealed important characteristics of the nanoscaletopography on the locally investigated surface sections. In contrast tothe results of AFM, the same sample surface exhibits smooth scalesaccompanied by some circular pores in the corresponding 160 × 160μm2 CFM image. A better representativeness of CFM images may beassumed due to their significantly larger lateral size, but the resolutionwas not high enough to map the local nanoscale features found inthe AFM images. Resulting differences can also be seen in the SIADtendencies, where CFM based results (blue line) suggest characteristicsof a smooth surface similar to the data of S1, while the AFM basedresults (red line) show more contributions from tilted surface features(Fig. 2cb). The values of roughness parameters based on five CFMimages were determined with 187 ± 5 nm for RMS and 11.2 ±0.2◦ for

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𝛿𝑚. It is important to mention that the smaller value of 𝛿𝑚 was mainlyattributed to the lack of CFM resolution, which resulted in artificialsmoothing of the topography. Similar limitations were observed byKelemen et al. who utilised confocal microscopy to generate input forSDTrimSP-3D [28]. In contrast, the larger lateral image size of CFMallowed to detect surface features on a larger scale, resulting in a higherRMS value.

Sample S3 was only investigated using CFM, since it was too roughfor AFM. A corrugated topography with surface features of several μmheight was found (Fig. 2bc). Five CFM images were used for roughnessparameter determination, resulting in 1551 ± 48 nm for RMS and 36.5±1.2◦ for 𝛿𝑚. The corresponding SIAD shows a broad width, indicatingthat locally substantial surface tilts are present on this sample (compareFig. 2cc).

Considering the wide range of RMS and 𝛿𝑚 values between thesamples, our set of experimental specimens provided a basis to inves-tigate roughness-induced sputtering effects from the nano- towards themicroscale roughness regime. Consideration of additional roughnessparameters like for example the autocorrelation length or the hurstparameter were beyond the scope of this study [43]. The recordedmicroscopy images were furthermore used for numerical simulationsusing the code SPRAY (see Section 2.3). The complete set of images

Applied Surface Science 570 (2021) 151204C. Cupak et al.

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can be inspected in the supplementary material Section E. All sampleswere also investigated by AFM or CFM after the ion beam experiments,but no qualitative difference in the topography was observed. Sincethe determined roughness parameters were furthermore well within thescatter of a-priori measurements, it can be assumed that no significanturface modification occurred during the experiments. The obtainedoughness parameters for all surfaces are summarised in Table 1 inection 3 for comparison with measured and simulated sputter yields.

In order to validate the purity of the tungsten layers, depth-resolvednformation of the samples’ composition was obtained by means of Ioneam Analysis (IBA) [44]. Coincidence Time-of-Flight/Energy Elasticecoil Detection Analysis (ToF-E ERDA) was carried out with 36 MeV

8+ as probing beam [45]. Except near surface contaminations withight impurity species like hydrogen, carbon or oxygen, a high tungstenurity of at least 98 at.% was validated for all samples. Composi-ional depth profiles and more detailed information regarding IBA cane found in the supplementary material Section B. Since all QCMxperiments included an in-situ Ar sputter cleaning procedure to re-ove surface contaminations and adsorbates, the assumption of pure

ungsten surfaces can be justified in this study.

.2. Quartz Crystal Microbalance setup

The Quartz Crystal Microbalance (QCM) is a versatile techniquehich allows to determine net mass variations of a quartz crystal withigh precision by recording the quartz’s resonance frequency. Sauer-rey established a basis for the QCM in 1959, describing the relationetween relative mass and frequency changes in form of Eq. (1) [46].𝛥𝑚𝑚

= −𝛥𝑓𝑓

(1)

Eq. (1) shows that a mass loss (or gain) results in a proportional fre-quency increase (or decrease). It remains valid also for quartz crystalswith a thin layer of different material on top of its surface. At TUWien, application of this technique for ion sputtering investigation hasa long history and was continuously improved over the years [47–49].For QCM samples under ion bombardment, the resulting change of theresonance frequency with time 𝛥𝑓∕𝛥𝑡 can be recorded via dedicatedelectronics. Using this frequency change, a calculation of the sputteryield 𝑌 by consideration of Eq. (1), ion current density 𝑗 and a constantfactor 𝐶𝑡 is possible. The connection is given by Eq. (2) [47].

𝑌 [atoms/ion] = 𝐶𝑡 ⋅1𝑗⋅𝛥𝑓𝛥𝑡

(2)

𝑡 =𝑒0 ⋅ 𝑞 ⋅ 𝑙𝑄 ⋅ 𝜌𝑄𝑚𝑛 ⋅ 𝑓 ⋅ 𝑚𝑡

𝑡 can be calculated by the electron charge 𝑒0, the atomic mass unit𝑚𝑛 and the ion charge state 𝑞. Also the atomic mass of tungsten𝑚𝑡 and quartz crystal parameters like density 𝜌𝑄, thickness 𝑙𝑄 andnitial resonance frequency 𝑓 are contributing to this constant. The ionurrent density 𝑗 is determined by Faraday cup measurements priornd after each QCM irradiation. It is important to mention that pureungsten samples are assumed in this calculation and direct sputterield determination is only possible for tungsten layers deposited onCM crystals like for samples S1 and S2.

For investigation of sample S3, which was not a QCM crystal butonsisted of a tungsten film on a silicon wafer, we used a techniqueased on the work of Berger et al. [50]. Here, a QCM is used as a catcheror the sputtered material, which results in a mass gain signal duringarget irradiation. In our setup, this C-QCM, which also incorporates a

-coated QCM quartz, can be positioned along a circular path aroundhe target sample in order to probe the angular distribution of sput-ered particles. A scheme describing the geometrical conditions in ourxperimental setup is presented in Fig. 3. More detailed informationegarding the utilised C-QCM technique can be found in Ref. [50] and

4

he supplementary material Section C.

Fig. 3. Scheme of geometrical conditions in the QCM experiments. The scanned 2keV Ar+ beam (red) was directed on the central target sample holder (A), which wasoriented for an ion incidence angle of 𝜑 = 60◦. The target holder allowed usage of eithera QCM crystal or other targets. The C-QCM system (B) was positioned independentlyalong a circular path around the target, maintaining a constant radial distance 𝑟 = 21.4mm, which enabled to probe the angular distribution of sputtered atoms and reflectedions from the target.

Our experimental setup consists of an Ultra High Vacuum (UHV)chamber with base pressures on the range of 10−9 mbar. The SPECSQE 12/38 sputter ion source, equipped with a Wien-filter for masseparation, was used for creation of a low intensity 2 keV Ar+ ion beam

with a flux on the range of 𝛷 ≈ 1016 ions/m2/s. A total Ar+ fluence persample on the order of 1.5 × 1020 ions/m2 was chosen to ensure thatno significant surface modifications were induced during irradiation.Assuming a typical sputter yield of 2 W/Ar, this resulted in erosion ofabout 5 nm per sample.

A target holder was used to mount QCM crystals or other sampletypes centrally in the vacuum chamber (see Fig. 3). It also incorporatedthe Faraday cup for determination of ion beam currents. Using a 4-axesmanipulator, accurate positioning and exposition of the target sampleholder towards the ion beam was achieved. Most of the experimentswere performed at a fixed ion incidence angle of 𝜑 = 60◦ and theion beam was homogeneously scanned over the target, covering thefull sensitive area of the QCM quartz [51]. Via an additional 5-axesmanipulator, the C-QCM was simultaneously positioned around thetarget sample. The radial distance 𝑟 between irradiated sample andC-QCM was fixed with 21.4 mm, while the angular position was variedwithin an interval of −15◦ to 37.5◦ respective the target surface normalirection.

Prior to all experiments, short-time Ar cleaning was applied toeduce adsorbates both on the target and on the catcher quartz. In ad-ition, the C-QCM measurements were repeated twice for each angularosition in the interval (back and forth), allowing to exclude possibleynamic effects during the experiment.

.3. SPRAY simulations

Our newly developed simulation code SPRAY (SPuttering simu-ation via RAY tracing of particles) was used in this study to modelputtering and redeposition in the case of rough surfaces. The maindvantage of this code is its ability to use microscopy images limitless of

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size for sputter yield calculation, utilising an approach similar to ray-tracing techniques in 3D rendering. The code is written in PYTHON3.8 language, supported by the open-source package VTK 9.0 [52,53]for implementation of ray-tracing features and can be executed onconventional desktop PCs. Since this code was initially developed in thecourse of this study, a brief overview on its features and implementedphysics is given in this section. A more detailed technical descriptionof the code can be found in the supplementary material Section D.

The latest version of SPRAY supports roughness dependent sputteryield calculation under consideration of ion incidence angle variation,redeposition, shadowing effects and secondary sputtering from locallyreflected ions. In addition, three-dimensional emission distributions ofsputtered particles and reflected ions can be calculated for a roughsurface. For this work only a pure tungsten surface was considered,while it is principally also possible to simulate multicomponent sam-ples. Furthermore, simulations are limited to static calculations only,which implies that the surface topography and composition are fixedand will not vary with fluence as e.g., in the dynamic versions ofSDTrimSP-3D [31] or TRI3DYN [32].

Data regarding the sputter yields of a flat surface and the corre-sponding angular distributions have to be provided as inputs for SPRAY,in example from BCA codes. Principally, the data origin is not limitedto a certain BCA code, but can be taken liberally from any source.In this study, W sputter yields were generated by SDTrimSP [20]. Inddition, three-dimensional emission distributions for sputtered atomsnd reflected ions were generated with TRI3DYN [32]. This highlightsdifference to other simulation codes which follow a similar strategy,here the angular distribution of sputtered or reflected particles isostly approximated by using a cosine distribution [22,54,55].

As a next step, one or more microscopy images of the sample surfaceere used as input for SPRAY. In this study, the same images alsorovided the basis for calculation of roughness parameters RMS and𝑚 (see Section 2.1). It should be mentioned that the use of SPRAYs limited to surface features exceeding the extension of the collisionascade in size. E.g., fibrous structures with a fibre thickness smallerhan the mean ion range might not be properly calculated with SPRAY.

The general routine during SPRAY execution can be described byour main tasks: Primary ion impact on randomly selected surfaceoints, simulation of local sputtering, computation of local ion re-lection and consideration of secondary sputtering by reflected ionscompare Fig. 4a–d). At first, a primary ion is directed on a randomlyelected impact point on the surface, while the raytracing algorithmntrinsically considers shadowing effects (Fig. 4a). For a given impactoint the local incidence angle is calculated, which determines the localputter yield from the input data. Secondly, trajectories for sputteredtoms are launched, while the raytracing algorithm determines theumber of redeposited atoms (Fig. 4b). This allows to compute aedeposition factor, which scales down the local sputter yield. Orig-nating from the same primary impact point, trajectories of reflectedons weighted by their corresponding reflection coefficient are launchedsing a similar approach (Fig. 4c). Special treatment of secondary ionmpact points is implemented, since they provide a starting point forecondary sputtered atoms (Fig. 4d). In analogy to the simulation ofrimary sputtered atoms, secondary sputtering is calculated based onhe local incidence angle and redeposition.

The whole routine is repeated for all simulated primary ions, whichinally allows to calculate a mean effective sputter yield for a givenurface and output lists with effectively sputtered particle trajectories.

. Experimental results and comparison to simulations

For initial benchmarking, sputter yields of the samples S1 and S2s a function of ion incidence angle 𝜑 were determined both by QCMxperiments and SPRAY simulations. A summary of the results is shownn Fig. 5. For the smooth sample S1, two measurements under ionncidence angles 𝜑 = 0◦ and 𝜑 = 60◦ were performed (green data

5

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oints). Very good agreement in comparison to SPRAY simulationsas found (dashed green line), where the full set of available AFM

mages was used. For the medium rough sample S2, the ion incidencengle 𝜑 was varied in an interval between 0◦ to 70◦ in steps of 5◦,xploiting the maximum angular range available in our experimentaletup. Again, a good overall agreement between measured (black dataoints) and SPRAY simulated sputter yields (dashed black line) wasound over the whole angular interval, with small deviations (max.0%) at around 𝜑 = 40◦. In addition, a perfectly flat surface was alsosed as input for SPRAY. As expected, the code reproduced repositoryesults which were obtained from SDTrimSP [20] (dashed orange line).n comparison to the results of sample S1, it can be seen that evenanometre-smooth topographies affect the sputter yield, especially forrazing ion incidence angles.

In the following, experimental C-QCM signals are presented by theata points in Fig. 6 for all samples, allowing to discuss the angularistribution of sputtered atoms. The ion incidence angle 𝜑 was keptt 60◦ in this case. In addition, SPRAY simulated angular distributionsf sputtered atoms are presented in form of colour-shaded areas. Forhis, the distributions were discretised using bins of 2.15 × 10−3 sr sizelong the plane of ion incidence, before re-normalisation was appliedith a constant factor (for all samples). This factor was chosen for bestgreement of the angular distribution to the C-QCM signal of S1 atosition 𝜑 = 0◦.

During ion irradiation of the smoothest sample S1, the highestxperimental C-QCM signal (green) of all samples was measured withinhe accessible angular interval (Fig. 6a). A maximum was found in theorward-sputtering regime at 𝛼 = 30◦, which probably originates fromingle knock-on sputtering events [56]. Simulated results on the basisf AFM images (magenta shaded area) show good agreement to the ex-erimental data. However, the forward sputtering peak appears shiftedt 50◦, which corresponds well to simulated results for a perfectlylat surface using TRI3DYN (compare figure 3 in the supplementaryaterial Section D). For the rougher samples, the measured signalsere generally lower and the single knock-on peak was not found.

Fig. 6b shows the comparison for sample S2, with SPRAY simulationesults on the basis of both AFM (magenta) and CFM images (orange).specially the AFM based data set is located well within the errorars of the experimental data (black), while a clear offset between theimulated data sets is visible. The CFM data generally shows a higherrend than the AFM based data and indicates the importance of highlyesoluted images for SPRAY simulations. In fact, the tendency of theFM based data is comparable to the results for the smoother sample1, in accordance to the similar appearance of microscopy images (seeig. 2).

The results for the roughest sample S3 show a measured C-QCMignal (red) with a very collimated orientation along the sample surfaceormal direction at 0◦ (see Fig. 6c). A similar result was also foundy Eksaeva et al. [34] and can be explained by a reduced number ofuccessfully sputtered atoms escaping in a tilted direction respective tohe surface normal due to a higher probability for local redeposition.ower C-QCM signals indicate that the sputter yield decreased forhis rougher surface. The simulated angular distribution shows goodgreement to the experimental data with respect to the orientation,hile the experimental values between −10◦ to 0◦ appeared to be

lightly higher.Since the samples S1 and S2 were QCM quartzes, also direct de-

ermination of sputter yields was feasible during the experiments. For1, the highest sputter yield of 2.30 ± 0.23 W/Ar of all samplesas found, while a decreased sputter yield of 1.95 ± 0.19 W/Aras measured for the medium rough sample S2. Since for sample S3o direct evaluation of the sputter yield was possible, an estimationrocedure was applied by using the results for sample S2 as a reference.olynomial functions of maximum order 3 were fitted to the C-QCMata sets in Fig. 6. Then, the integral of each fit function within the

ccessible angular interval was calculated. Finally, the ratio of integrals

Applied Surface Science 570 (2021) 151204C. Cupak et al.

Fig. 4. Simulation scheme for SPRAY. (a) Primary ion (red) hits the surface on a randomly selected impact point (yellow asterisk), enabling choice of local sputter yield from theinput data via the local incidence angle 𝜑. (b) Raytracing of trajectories for sputtered atoms (black) is initiated. Sputtered target atoms which hit the surface again are consideredas redeposited. (c) Raytracing of trajectories for reflected ions (red) is initiated. (d) Secondary sputtering by reflected ions is calculated, by consideration of specific input data setfor the local ion impact. The whole procedure is repeated for every simulated primary ion.

Fig. 5. Comparison of sputter yield values 𝑌 from QCM experiments (points) andSPRAY simulations (dashed lines) under variable ion incidence angle 𝜑 for samplesS1 (green) and S2 (black). The SPRAY simulation for a flat surface (orange dashedline) reproduces the repository data results from SDTrimSP.

between the samples S3 and S2 was multiplied with the referencesputter yield. Via this approach, a value of 1.51 ± 0.40 W/Ar wascalculated for S3, while this procedure introduced a comparably largeuncertainty. For completeness, the sputter yield of S1 was also deducedthis way (2.38 ± 0.59 W/Ar), which agrees well with the directlymeasured value. All experimental sputter yields are listed in Table 1for comparison.

The SPRAY simulations also provide sputter yield results based onall available microscopy images, which allowed to assess standard devi-ations to the numerical values. For samples S1 and S2, simulated sputteryields for the AFM based cases (2.29 ± 0.03 W/Ar and 1.95 ± 0.14W/Ar, respectively) indicated excellent agreement with experimentaldata, which was already shown in Fig. 5. However, the simulated valueof 2.30 ± 0.01 W/Ar based on CFM images of sample S2 is comparable

6

to the results of sample S1, which corresponds well to the similarityin their roughness parameter 𝛿𝑚 deduced from the utilised microscopyimages. It has to be noted, that at the same time the RMS roughnessvalues of these two samples differ by a factor of 100. For sample S3,SPRAY simulations on the basis of CFM images resulted in a sputteryield of 1.53 ± 0.04 W/Ar, in good agreement to the experimentallyestimated value. This highlights, that for microscopically rough samplesan application of CFM can still be a viable option.

Considering the trends in sputter yields and roughness parameters inTable 1, a general tendency can be seen that higher surface roughnessmay lead to a decreased sputter yield. Still, the case of sample S2indicates that RMS roughness is not a suitable parameter for sputteryield estimation and that the utilised microscopy method strongly in-fluences the results of SPRAY and roughness parameter determination.The simulated results regarding sample S1 and S2 further indicate thatsimilar 𝛿𝑚 values can be connected to similar sputter yields and providea better basis for empirical modelling. However, the low number ofavailable experimental samples and data does not yet allow to drawfundamental conclusions regarding the relation between the sputteryield and 𝛿𝑚 or the universality of this approach. Still, the results of thisbenchmark study show that SPRAY is a versatile tool for detailed inves-tigation of roughness related sputtering effects and that good predictionof sputter yield values can be obtained if suitable microscopy imagesare taken as input. In order to further investigate the applicabilityof roughness parameter 𝛿𝑚, the following Section 4 is focusing on adedicated SPRAY investigation which allows to corroborate the resultsfrom this benchmark.

4. Systematic simulations with artificially generated rough sur-faces

In order to further investigate the role of roughness parameters RMSand 𝛿𝑚 for sputtering, a more comprehensive numerical study withSPRAY was performed. For this purpose, not only microscopy imagesof real samples, but also artificial computer-generated surfaces wereused as input. At first, the original CFM images of samples S2 and S3

Applied Surface Science 570 (2021) 151204C. Cupak et al.

Fig. 6. Comparison between the experimental C-QCM signal (points with errorbars)and the simulated angular distribution of sputtered atoms from SPRAY (shaded areas)based on AFM (magenta) or CFM (orange) images. The angle of 0◦ corresponds tothe surface normal direction of the irradiated sample. (a) Results for the smoothestsample S1; (b) Results for the medium rough sample S2; (c) Results for the roughestsample S3. The simulated angular distributions were created by angular binning with asize of 2.15× 10−3 sr within the plane along ion incidence. For visualisation, consistentre-normalisation of these simulated angular distributions was performed by applicationof a constant factor for all three samples.

were used to produce sets of surface topographies with continuously in-creasing roughness. In the following, the original surfaces’ height valueswere multiplied with a scaling factor. Application of a factor smallerthan 1.0 therefore led to artificial smoothing, while a factor biggerthan 1.0 corresponds to enhanced roughening. All surfaces of such a setwere evaluated regarding RMS and 𝛿𝑚 for roughness characterisation.The original surface of S2 was scaled in an interval between 0.0 and6.0, using a step size of 0.1 for the scaling factor in order to cover thewhole RMS range between 0 and 1 μm. For the surface of S3, only aninterval from 0.0 to 1.0 was used, since the original topography wasalready very rough on the microscale. These two surface data sets arehereinafter called S2-s and S3-s.

7

Table 1List of roughness parameters (RMS, 𝛿𝑚) and sputter yields (experimental results &SPRAY simulations) for the benchmark test case. Irradiation was performed with 2keV Ar+ on W under 60◦ incidence angle; Usage of both AFM and CFM was onlypossible for sample S2.

S1 S2 S3

RMS AFM [nm] 1.7 ± 0.1 34.5 ± 26.9 –RMS CFM [nm] – 187 ± 5 1551 ± 48

𝛿𝑚 AFM [deg] 7.6 ± 1.2 19.7 ± 4.2 –𝛿𝑚 CFM [deg] – 11.2 ± 0.2 36.5 ± 0.6

exp. QCM Y [W/Ar] 2.30 ± 0.23 1.95 ± 0.19 –exp. est. C-QCM Y [W/Ar] 2.38 ± 0.59 1.95 ± 0.19 1.51 ± 0.40

SPRAY Y AFM [W/Ar] 2.29 ± 0.03 1.95 ± 0.14 –SPRAY Y CFM [W/Ar] – 2.30 ± 0.01 1.53 ± 0.04

In addition, a set of artificial topographies generated by a computeralgorithm was introduced, which are labelled G in the following. Theirindividual height values were chosen from a Gaussian distribution oneach point of an equally spaced lateral grid with 5 × 5 μm2 side lengthand 50 nm spacing, following the same approach as Li et al. [35].The desired RMS values were generated in a range between 0.0 and0.5 μm. The roughest surface generated this way already showed verypronounced needle-like features, appearing similar to the berylliumsurface structures found after deuterium plasma exposure in a studyby Doerner et al. [57] or to the computer-generated structures used byvon Toussaint et al. [31]. A more detailed description of the surfacepreparation and an overview over all utilised topography sets can befound in the supplementary material Section F.

As a starting point, all surfaces were used in SPRAY simulations forinvestigation of sputtering due to 2 keV Ar+ ions, for two selected casesof fixed ion incidence angle 𝜑 = 0◦ (normal incidence) and 𝜑 = 60◦. Theformer is of special interest, since for this case, shadowing effects canbe neglected for our set of investigated surfaces. In contrast, the lattercase corresponds to the same situation as in our C-QCM experimentspresented in Section 3.

The results for the 𝜑 = 0◦ case are presented via scatter plots inFig. 7(a) and (b), which show the simulated sputter yields versus RMSor 𝛿𝑚, respectively. A perfectly flat surface is indicated by a value of 0.0for both RMS and 𝛿𝑚. As can be seen in Fig. 7(a), RMS is not a goodroughness parameter, since individual sputter yield tendencies deviatesignificantly for different surface sets. Especially for surfaces used inthe data set G, corrugated structures with substantial inclinations weregenerated already for selection of relatively low RMS values, whichresulted in redeposition effects on the sputter yield. However, thiscannot be observed for surfaces of the other data sets with similar RMSvalue. Characterisation with 𝛿𝑚 shows better agreement (see Fig. 7b),especially for small values below 𝛿𝑚 < 20◦. In this region, a moderateincrease of the sputter yield was found, starting to rise from a value of1.38 W/Ar for a flat surface to 1.5 W/Ar (or about +10%) at 𝛿𝑚 = 20◦.This can be explained by a corresponding increase of the effective ionincidence angle, which has a similar effect as for a flat surface beingirradiated under an ion incidence angle of 𝜑 = 𝛿𝑚 (orange dashed line).This allows for a rough approximation in this regime without need ofsimulations. Beyond 𝛿𝑚 = 20◦, the data becomes more scattered, whilea clear reduction of the sputter yield becomes visible for larger valuesof 𝛿𝑚 due to redeposition of sputtered atoms. Here, the approximationvia the flat surface sputter yield 𝑌 (𝜑 = 𝛿𝑚) is no longer possible.

In Fig. 7(c) and (d), the results for an ion incidence angle 𝜑 = 60◦

are shown. Again, RMS did not allow a satisfying characterisation ofsputtering (see Fig. 7c). In contrast, quite a universal behaviour for allsimulated surfaces is found when using 𝛿𝑚 as roughness parameter (seeFig. 7d). For very small values of 𝛿𝑚 < 4◦, the sputter yield valuesremained on a level of 2.45 W/Ar, before a continuous decrease isfound. The data indicates that between 𝛿𝑚 = 4◦ and 𝛿𝑚 = 70◦ alinear dependence of the sputter yield on 𝛿 can be assumed, which

𝑚

Applied Surface Science 570 (2021) 151204C. Cupak et al.

cb𝜑f

fvf

sdwoa

Fig. 7. Comparison of SPRAY simulated sputter yields under fixed ion incidence angles 𝜑 = 0◦ and 𝜑 = 60◦ for various scaled surfaces. The roughness of all surfaces washaracterised either by RMS or by 𝛿𝑚. The green and blue data corresponds to simulated sputter yields based on scaled CFM images of the samples S3 and S2, respectively. Therown data was simulated using computer generated surfaces with Gaussian distributed height values. (a) Sputter yield Y versus RMS for 𝜑 = 0◦. (b) Sputter yield Y versus 𝛿𝑚 for= 0◦. The orange dashed line is the sputter yield of a flat W surface as a function of ion incidence angle 𝜑, assuming 𝜑 = 𝛿𝑚 for visualisation. (c) Sputter yield Y versus RMS

or 𝜑 = 60◦. (d) Sputter Yield Y versus 𝛿𝑚 for 𝜑 = 60◦. The black dashed line is a linear fit between 4◦ ≤ 𝛿𝑚 ≤ 70◦.

is highlighted with the linear fit in the plot (dashed black). For thiscase of 𝜑 = 60◦, we deduced the following empirical relation betweenthe sputter yield Y and the mean inclination angle 𝛿𝑚 of the sputteredsurface, allowing estimations within an error of ±0.1 W/Ar.

𝑌 (𝛿𝑚) = 𝑌 (0) ⋅ (1 − 0.01 ⋅ (𝛿𝑚 − 4◦)) 4◦ ≤ 𝛿𝑚 ≤ 70◦ (3)

The parameter 𝑌 (0) = 2.45 W/Ar in Eq. (3) is the sputter yield of aperfectly flat tungsten surface under 𝜑 = 60◦ Ar+ ion bombardment,simulated by SDTrimSP.

In order to judge the general importance of the roughness parameter𝛿𝑚, SPRAY simulations were also conducted for various other ionincidence angles 𝜑 between 0◦ and 85◦. The results are presented inorm of a 3D plot in Figs. 8(a) and (b). Two GIFs which show variousiews on these data are available in the online supplementary materialor the interested readers.

Again, 𝛿𝑚 seems to be a better suitable parameter, which is vi-ualised in Fig. 8(b). For perfectly flat surfaces, the sputter yieldependence on the ion incident angle 𝜑 follows a characteristic trendith a maximum at 60◦. Between 𝛿𝑚 values of 0◦ to 50◦, the dependencef the sputter yield on the ion incident angle becomes less pronouncednd settles at a level of about 1.30 ± 0.05 W/Ar, independent of 𝜑.

For cases with 𝜑 between 0◦ to 20◦ and also for grazing ion inci-◦

8

dence (𝜑 ≥ 70 ), a moderate value of 𝛿𝑚 resulted in higher sputter

yields. Similar as for the results in Fig. 7b, this can be explained byenhanced local sputtering due to favourable incident angle conditions,while redeposition effects do not yet contribute to severe reductions.

For higher 𝛿𝑚 values beyond 50◦, the sputter yields decline contin-uously and settle below 1 W/Ar. An additional decrease of the sputteryield was found for irradiation with ion incidence close to the surfacenormal direction in combination with simulated surfaces having high𝛿𝑚 values, which originated from a very spiked and corrugated topog-raphy. If an ion impinges on such a rough topography under surfacenormal direction, sputtering can occur on highly inclined surface facetsonly. Under such conditions, the emission distribution of sputteredparticles has a strong forward orientation, which supports redepositionon other surface features and strongly reduces the sputter yield, similarto results found in literature [33,35].

The results in Fig. 8 substantiate the hypothesis that 𝛿𝑚 can be apromising parameter for description of rough surface effects on sput-tering for a wide range of topographies. The computer-generated dataset G, which covered the whole parameter range for both ion incidenceangle 𝜑 and 𝛿𝑚, furthermore enabled us to develop a fit formula (seeEq. (4)) for the sputter yield of rough W surfaces under 2 keV Ar+

irradiation. This fit function, which is indicated by the black dots inFig. 8b to guide the eye, incorporates three parameters: ion incidenceangle 𝜑, roughness parameter 𝛿𝑚 and the sputter yield of a flat Wsurface under normal incidence, 𝑌0 = 1.38 W/Ar. The latter value was

again obtained from SDTrimSP. In total, a set of seven fit parameters

Applied Surface Science 570 (2021) 151204C. Cupak et al.

Fig. 8. Comparison of SPRAY simulated sputter yield values under ion incidence angles 𝜑 for various scaled surfaces. The roughness of all surfaces was characterised by bothRMS and 𝛿𝑚. (a) Sputter yield Y versus RMS and ion incidence angle 𝜑; (b) Sputter Yield Y versus 𝛿𝑚 and ion incidence angle 𝜑. The green and blue data sets correspond tosimulated sputter yields based on scaled CFM images of the real samples S3 and S2, respectively. The brown data set G was simulated via usage of computer-generated surfaceswith Gaussian distributed height values. The latter also provided the basis for creation of a fit function (black dots).

was necessary to achieve satisfactory fitting towards the simulated data,which are listed in Table 2. Subfunction 𝐴(𝜑, 𝛿𝑚) in Eq. (4) describesthe sputter yield dependence on the ion incidence angle 𝜑 for smoothsurfaces with 𝛿𝑚 ≈ 0. This part is motivated by a Taylor series expansionof an empirical formula developed by Yamamura et al. [22,58]. Theexponential function reduces the contribution of 𝐴(𝜑, 𝛿𝑚) for higher val-ues of 𝛿𝑚. Subfunction 𝐵(𝜑, 𝛿𝑚) is introduced in order to fit the data inthe regime with high 𝛿𝑚 and normal ion incidence, where large amountof redeposition occurs. Finally, subfunction 𝐶(𝜑, 𝛿𝑚) introduces simplepolynomial dependencies to achieve a good overall shape. The resultsshow good agreement to the simulated data, except for recognisabledeviations for rougher surface structures in the 𝜑 ≥ 80◦ ion incidenceregime. It can be assumed that a similar fit may also be found forother ion-target combinations, as long as kinetic sputtering remains thedominant mechanism for particle ejection.

Different results from this numeric study may be obtained if ide-alised surfaces like e.g., pyramidal or sawtooth profiles are used, orif anisotropic structures are investigated. Deviations are also expectedfor scenarios where the sputtered atoms are not emitted along straighttrajectories, which was out of the scope of this study. In example, mag-netic forces inside the plasma of nuclear fusion devices cause gyrationof sputtered and ionised atoms. This can redirect emitted atoms towardsthe surface, introducing further enhancement of redeposition [12].

𝑌 (𝑌0, 𝜑, 𝛿𝑚) = 𝑌0 ⋅[

𝑓1 ⋅ 𝐴(𝜑, 𝛿𝑚) ⋅ 𝐵(𝜑, 𝛿𝑚) + 𝐶(𝜑, 𝛿𝑚)]

(4)

𝐴(𝜑, 𝛿𝑚) = 1 +(

𝑓2 ⋅ 𝜑2 + 𝑓3 ⋅ 𝜑

4) ⋅ 𝑒𝑥𝑝(

−𝛿𝑚𝑓4

)

𝐵(𝜑, 𝛿𝑚) = 1 − 𝑒𝑥𝑝

(

−

√

𝜑2 + (90◦ − 𝛿𝑚)2

𝑓5

)

𝐶(𝜑, 𝛿𝑚) = 𝑓6 ⋅ 𝜑 + 𝑓7 ⋅ (90◦ − 𝛿𝑚)2

5. Summary and conclusion

The main goal of this study was to systematically investigate theinfluence of surface roughness on static sputtering and to identify whichroughness parameter is suitable to characterise sputtering behaviour ofcorrugated surfaces. As a test case, three different W targets with sur-face topographies ranging from nano- towards microscopic roughnesswere investigated during 2 keV Ar+ bombardment. ToF-E ERDA wasperformed to validate the purity of the tungsten samples, while both

9

Table 2Fit parameters for 𝑌 (𝑌0 , 𝜑, 𝛿𝑚), based on data set G.Fit parameter Value 10𝑥

𝑓1 2.230 +0𝑓2 3.992 −4𝑓3 −5.372 −8𝑓4 3.636 +1𝑓5 6.224 +1𝑓6 −1.122 −2𝑓7 −8.701 −5

AFM and CFM investigations allowed to characterise the specimens interms of two selected roughness parameters, being the well-known RMSvalue and also the newly introduced 𝛿𝑚 value. The latter correspondsto the mean value of the Surface Inclination Angle Distribution (SIAD)with respect to the global surface normal direction. QCM experimentsallowed both to measure target sputter yields and to probe the an-gular distribution of sputtered atoms simultaneously and in-situ foreach individual sample. A low ion flux ensured that no severe surfacemodifications were introduced, allowing to neglect dynamic effects. Inaddition, the new simulation code SPRAY was presented, which canbe used to calculate effective sputter yields of rough surfaces. Keyfeatures of SPRAY are the opportunity to utilise microscopy imageswithout limitations in lateral size and an efficient ray-tracing algorithmwhich is used to extrapolate a-priori simulated BCA code results offlat surfaces. Using this ray-tracing approach, effects like local ionincidence variation, shadowing, redeposition or secondary sputteringwere successfully implemented. The data from QCM experiments wasthen used for a benchmark of SPRAY. Even though small deviationswere identified regarding the angular distribution of sputtered atoms,a very good agreement was found for the effective sputter yields, welljustifying its further application. Results from these experiments andsimulations confirm that in the case of 𝜑 = 60◦, the sputter yieldbecomes lower for increasing surface roughness, which is in generalaccordance with literature. However, the experimental data from threetargets were not sufficient to draw a firm conclusion regarding thequestion which roughness parameter is better suited to characterisesputtering of rough surfaces.

In order to further investigate the effect of surface roughness, acomprehensive SPRAY study was performed using both surface inputsbased on artificially roughened microscopy images and computer gen-erated structures. It was revealed that RMS is not a suitable parameterto assess the sputter yield of rough surfaces, since structures with

Applied Surface Science 570 (2021) 151204C. Cupak et al.

aptwrsb𝜑r

same RMS value can have very different sputter yields. In contrast, 𝛿𝑚ppears to characterise rough surfaces reasonably well and allows toredict the sputter yield independent from the scale of roughness. De-ermination of 𝛿𝑚 is achievable with common microscopy techniques,hile high image resolution was found to be important for consistent

esults. A major outcome was that under normal ion incidence, roughurfaces with 𝛿𝑚 < 20◦ show sputter yields which can be approximatedy the value for a perfectly flat surface under ion incidence angle= 𝛿𝑚. We furthermore presented an empirical fit formula, which only

equires 𝛿𝑚, 𝜑 and a sputter yield value under normal ion incidence fora flat tungsten surface as input parameters to describe the sputter yieldfor a wide range of ion incidence angles 𝜑 and roughness parameters𝛿𝑚. Although the presented results were only obtained for argon ions ontungsten, the SPRAY code just considers geometric effects. Therefore,we expect that similar trends can also be found for other ion-targetcombinations, even though the actual magnitude and angular depen-dence of the sputter yield are of course strongly material dependent.Key applications range from process optimisation in PVD techniqueswhere the surface roughness of crucibles can alter deposition rates, tolifetime predictions in nuclear fusion devices. The revealed correlationbetween sputter yield and 𝛿𝑚 may also provide a good starting pointfor a more refined theoretical description of sputtering effects on roughsurfaces in future studies.

CRediT authorship contribution statement

C. Cupak: Conceptualization, Data curation, Formal analysis, In-vestigation, Methodology, Software, Visualization, Writing – originaldraft. P.S. Szabo: Verification, Software, Conceptualisation, Writing –review & editing. H. Biber: Verification, Software, Writing – review &editing. R. Stadlmayr: Conceptualisation, Writing – review & editing.C. Grave: Software, Investigation, Writing – review & editing. M.Fellinger: Investigation, Writing – review & editing. J. Brötzner: Soft-ware, Writing – review & editing. R.A. Wilhelm: Conceptualisation,Writing – review & editing. W. Möller: Resources, Writing – review &editing. A. Mutzke: Resources, Writing – review & editing. M.V. Moro:Investigation, Writing – review & editing. F. Aumayr: Supervision,Funding acquisition, Conceptualisation, Writing – review & editing.

Acknowledgements

The authors are thankful for the continuous support with theQCM electronics by Michael Schmid (TU Wien). Sample manufacturingwas in part performed by Leonard Raumann, Jan Willem Coenen(Forschungszentrum Jülich, Institute of Energy and Climate Research, Ger-many) and Martin Oberkofler (Max Planck Institute of Plasma Physics,Garching, Germany) and is highly acknowledged. The computationalresults presented have been achieved in part using the Vienna ScientificCluster (VSC-3), project ID 70998.

This work has been carried out within the framework of the EURO-fusion Consortium and has received funding from the Euratom researchand training program 2014-2018 and 2019-2020 under Grant Agree-ment No. 633053. The views and opinions expressed herein do notnecessarily reflect those of the European Commission. Financial supporthas also been provided by KKKÖ (commission for the coordination offusion research in Austria at the Austrian Academy of Sciences - ÖAW).The authors acknowledge the TU Wien Bibliothek for financial supportthrough its Open Access Funding Program.

Appendix A. Supplementary data

Supplementary material related to this article can be found online

10

at https://doi.org/10.1016/j.apsusc.2021.151204.

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