Investigation of target erosion profiles sputter-eroded by a low-energy broad ion beam

The demand for ion beam sputtering (IBS) coated substrates is growing. In order to find new fields of application for IBS coating technology, it is necessary to understand in detail the distributions of the involved particles in an industrial-scale reactive coating process. In pursuit of this goal, in the present investigation, profiles sputter-eroded from tantalum, silicon, and silicon dioxide targets by a low-energy broad ion beam (ion energy ≤ 1.9 keV, ion source RIM-20) are measured with a mechanical profilometer and compared. To approximate the discrete and two-dimensional erosion data accurately, an empirical function is developed. For an applied target tilt angle of 55 ○ , the results indicate that the actual angle-dependent ion–solid interaction mechanisms at the atomic level have a rather subordinate role in the macroscopic surface modification of the target in terms of the qualitative distribution of the erosion profile. The applied process geometry seems to have a much larger impact. Furthermore, in the case of silicon, a linear erosion rate as a function of erosion time is observed. Thus, the form of the broad erosion profile does not seem to have a measurable effect on the erosion rate.


I. INTRODUCTION
Ion beam sputter deposition (IBSD) is a well-established coating technology in optical thin film production facilities. The properties, applications, and achievable quality parameters have been welldocumented in open literature. [1][2][3] Mirror coatings for gravitational wave detectors 4 and ring laser gyroscopes for inertial rotation measurements 5 are prominent scientific applications. A key element in ion beam sputtering (IBS) is the ion beam-predominantly a composition of primary particles, with which target atoms (secondary particles) are sputtered from a target surface. The removal of atoms by energetic ions is equivalent to an erosion process.
Over the past few decades, IBSD has been continuously improved, 6 new concepts have been implemented, [7][8][9] and systematic investigations of the underlying physical mechanisms have been carried out. 10,11 In contrast, the productivity parameters and economic factors involved have not received much attention. It is only in the last few years that a certain trend toward large-area optical coatings in the field of IBSD has been observed. The achievable uniform deposition areas are still smaller than 1 m in diameter. 12,13 However, it is to be expected that larger coatings with an IBSD quality level will be required for future applications, e.g., meter-sized optical coatings for astronomy and space applications or meter-sized high-power laser optics for large optical systems. 14 To open up new fields of application, there is a need to understand in detail the distributions of primary and secondary particles in an industrial-scale IBSD process. The approximation of the sputtering geometry by a single common point source as the point of origin of all sputtered particles is insufficient in this context if a broad ion beam is applied. 12 More precisely, in order to develop an understanding of how particle fluxes of secondary particles are emitted qualitatively and quantitatively from the target, it is necessary to know how the primary particles impinging on the target surface are distributed. In relation to this, the investigation of erosion profiles, as has been done for magnetron sputtering (MS), ion beam figuring (IBF), and focused ion beam microscopy tools over the past few decades, provides valuable information about the distributions of the involved particles. Comparable investigations in the field of IBSD, ARTICLE scitation.org/journal/adv which apply a broad ion beam and a tilted target, are not known to the authors (in Ref. 15, the RIM-10 ion source is used, which erodes a substrate made of silicon at a normal angle of incidence). The present investigation is intended to present corresponding experimental data and to provide a basis for modeling the distribution of the primary particles on the target surface later.
In the field of MS, which is a coating technology competing with IBSD (e.g., Ref. 16), an erosion profile is often referred to as a racetrack, erosion groove, or depth profile. In the case of reactive MS, target poisoning according to Berg's model 17 or the RSD2013 model 18 is an important additional mechanism and is most probably also relevant to reactive IBSD. Recently published results 19 indicate an almost fully oxidized titanium target surface during IBS in the presence of an O 2 atmosphere. In addition to that, stronger target poisoning of titanium targets compared to tantalum targets was a conclusion of Ref. 20. Basic differences between IBF, IBSD for scientific purposes (with a focus on ion-solid interaction mechanisms), and industrialscale IBSD processes (with a focus on production) are as follows: (1) the open diameter Doptic of the applied ion optic (which corresponds to the initial size of an ion beam 21 ) with which ions are extracted from a plasma and an ion beam is formed, (2) the extracted ion beam current I beam , (3) the distance dtarget between the ion optic and the target (the beam propagation length), and (4) the resulting distribution of ions on the target surface.
In IBF processes, a smaller beam diameter on the workpiece to be machined (after beam propagation) possesses stronger error correction ability. 22 It is preferable that the beam shape and the resulting removal function on the workpiece are Gaussian. To meet these criteria, ion optics with Doptic in the range of 10-50 mm are applied. 22,23 In addition to that, diaphragms with diameters down to 0.5 mm are mounted between the ion source and the workpiece for beam shaping. 22,24 Literature values for I beam vary in the range of 1-40 mA, and values for dtarget of up to ∼80 mm can be found.
For scientific investigations of ion-solid interaction mechanisms, the situation is quite similar. A small ion optic in combination with a corresponding short distance dtarget ensures that only a small area on the target is sputtered by the primary particles (compared to the distance of secondary particle observation), which enables the consideration of a sputtering point source. Furthermore, a shorter ion propagation length reduces the number of ions that do not reach the target as a consequence of a finite mean free path. In Refs. 25-28, for instance, the following configurations were chosen for investigations of IBS and IBSD: Doptic = 16 mm, I beam in the range of 6-10 mA, and dtarget = 150 mm.
For industrial-scale IBSD processes, the situation is different. In order to meet the productivity demands of the optical thin film industry, higher beam currents are required to produce a certain quantity of secondary particles per unit time. From practical experience, I beam varies in the range of 200-500 mA for high-quality thin film production. For beam currents in this range and above, it is necessary to distribute the ions over an appropriate target surface size. Otherwise, the target material is consumed too fast and the manufacturing of complex filters with corresponding long process durations becomes unfeasible. So far, the technically best solution is to apply a broad ion beam produced by a large multiaperture extraction system. Doptic is usually larger than 100 mm, and the market even offers ion optics for IBSD with up to Doptic = 220 mm. A higher beam current and, thus, a higher coating rate are the main benefits of a large ion optic. It is advantageous to adjust dtarget to be as large as possible to prevent fast degradation of the ion optic through particle fluxes originating from the target, although this can affect the productivity of an IBSD process significantly. 20 Thus, productivity values as well as economic factors depend on dtarget. For instance, in the IBSD coating machines NAVIGATOR 1100 and NAVIGATOR 2100, 12,20 manufactured by Cutting Edge Coatings GmbH (CEC), the common setups have dtarget > 350 mm. From practical experience, target distances in the range of 200-550 mm are used in IBSD for the production of optical thin films.
The focus of this work is to investigate target erosion profiles during low-energy (ion energy ≤ 1.9 keV, ion source RIM-20) reactive broad ion beam sputtering on a millimeter scale. Erosion profiles sputter-eroded from tantalum (Ta), silicon (Si), and silicon dioxide (SiO 2 ) targets are experimentally determined and compared with one another. Ta is chosen because it is one of the most common "high-index" materials used for IBSD processes in optical thin-film technology. Equally, Si and SiO 2 are the most commonly used "low-index" materials. All three target materials are preferred for the production of low-loss mirror coatings in the VIS and nearinfrared (NIR) regions. Two different distances of dtarget = 370 mm and dtarget = 550 mm are examined.

II. EXPERIMENTAL METHOD
The sputter-erosion of the investigated Ta, Si, and SiO 2 targets was performed in CEC's NAVIGATOR 1100, 20 an industrial-scale IBS coating machine, with a sputter-up configuration of the main process components. The equipment is evacuated by a cryopump to a base pressure of 4 × 10 −6 Pa in the high vacuum range. To generate a broad ion beam, NAVIGATOR 1100 is equipped with the inductively coupled radio-frequency (RF) type ion source RIM-20. The design is based on the RIT. 29,30 RIM-20 runs with a spherical shaped curve three-grid multi-aperture extraction system (accel-decel technique) made of titanium, with Doptic = 160 mm and a curvature radius Roptic = 400 mm. The ions are extracted from the plasma and accelerated by 847 beamlets distributed in a quasi-hexagonal pattern. All beamlets together make an ion optic transparency of 56.6%. Figure 1 shows the broad ion beam. To compensate for the space charge, a radio-frequency neutralizer (RFN) operates simultaneously with RIM-20 as a filament-less electron source (not shown in Fig. 1).
The sputter-erosion of the initially flat targets took place during several independent production processes of optical thin films and, thus, always in the presence of an O 2 atmosphere. To adjust the ion energy, only the beam voltage was varied (the accelerator grid voltage of −600 V and decelerator grid voltage of 0 V were not varied). The Si target was sputtered with a fixed set of parameters: of 20 SCCM or a Xe flow rate of 15 SCCM was used to operate RIM-20. It is important to note that regulation of the ion energy usually results in a variation of the beam profile. 30,31 The process parameters listed-ion species, ion energy, and beam current-are the result of process optimizations aimed at achieving specific process properties (lateral layer uniformity, coating rate) and layer quality parameters in thin film production. In all processes, the targets were tilted at 55 ○ . In IBSD, target tilt angles (TTAs) in the range of 45 ○ -65 ○ are usually used. At smaller angles, the particle flux of secondary particles increases in the backward direction toward the ion optic (degradation of the ion optic), and the sputtering yield decreases (reduction of productivity). With larger angles, the proportion of primary particles that fly past the target increases (reduction of productivity, adverse parasitic sputtering of process chamber parts behind the target). Additionally, at large angles of incidence, the sputtering yield drops rapidly (reduction of productivity). The target tilt angle is measured between the target surface normal and the symmetry axis ⃗ n beam of the ion beam. ⃗ n beam also corresponds to the direction of propagation of the broad ion beam and is hereinafter also referred to as the beam vector. In the cases of Ta and Si, the target distance-ion optic to the target surface-measured along ⃗ n beam was set to dtarget = 370 mm (the corresponding setup is shown in Fig. 1). For the erosion of the SiO 2 target, a distance of dtarget = 550 mm was applied. Thus, the dielectric target was positioned behind the geometric focal point of the ion optic (dtarget > Roptic), while the Ta and Si targets were located before the geometrical focal point. The target holder was electrically grounded (with a contact resistance from target to ground <1 Ω) to eliminate potential electrical charging of the metallic targets.
To determine an erosion profile, the corresponding target was dismounted from the water-cooled target holder and its erosion was measured with a self-built mechanical profilometer. treated as negative values (z = 0 corresponds to the initial flat surface). xi and y i are measured in the chosen coordinate system of a target, as shown in Fig. 2(a). In the cases of Ta and Si, the target plate thickness amounts to 6 mm. The target plate thickness of the SiO 2 target amounts to 8 mm. In the case of Si, six measurements were performed to investigate the evolution of the erosion characteristics as a function of erosion time T. The Ta and SiO 2 targets were measured once. As described above, the erosion profile of Ta (Figs. 4 and 7) results from erosion processes with different ion beam parameters.
It is plausible to assume that the interaction process between an almost rotationally symmetric broad ion beam with a laterally inhomogeneous beam profile and a flat tilted target surface results in (1) a mirror-symmetric erosion profile and (2) irregular sputter conditions depending on the sputter position. In other words, it is assumed that the number of ions per unit area (and per unit time) and the angles of incidence of the ions are different for each point on the target surface (except for the corresponding symmetry points). Figures 2(a)-2(c) support both assumptions (1) and (2). In Figs. 2(a) and 2(b), the investigated Si target is shown after a total accumulated erosion time of T = 135, 092 s (∼37.5 h). A general observation is a quasi-elliptical-shaped and mirror-symmetric erosion zone (actually, this observation is irrespective of a specific target material, see also Fig. 7 in the Appendix). The maximum erosion depth is zmin = −4.17 mm (shown in detail in Fig. 3). At values zmin ≤ −6 mm, the thickness of the target plate is exceeded, as mentioned above.
For comparison, Fig. 2(c) shows the same target after a shorter erosion time of T = 76, 058 s (∼21.2 h). Without generalizing, especially in the case of Si, two segments can be observed-a smooth inner segment (subjectively smoother than the initial surface) and a rough outer segment (subjectively rougher than the initial surface), separated by a more or less sharp edge [marked No. 1 in Fig. 2(c)]. In the course of sputter erosion, the inner segment reveals a rough spotty appearance as can be seen in Fig. 2(b). On the one hand, this irregular and dynamic structuring of a target surface could be assumed to be an expression of the position-dependent sputter  Table II, and the characteristic values are summarized in Table III ( Outside of the main erosion zone, a wider region of interaction between the charged particle beam and the target can be observed. This region visually extends to the edge, which is marked No. 4 in Fig. 2(a), but even at values zmin ≤ −6 mm, no erosion can be measured with the applied profilometer in this area. Thus, the wide interaction region manifests itself only as a discoloration of the target surface, and it is assumed to result from particles scattered during beam propagation due to a finite mean free path. Besides potential compound formation, additional oxide coverage may occur in the form of an undesired coating when the neighboring target is sputtered. The colored rings at the edge of this wider region indicate dielectric layers with varying layer thicknesses.
Although the Si target was initially fractured (by a handling mistake), it was decided that it should be used anyway for the present investigation. It is conspicuous that the fracture evolved into a mound with a rough side [marked No. 2 in Fig. 2(c)] and a smooth side [marked No. 3 in Fig. 2(c)] during sputtering, most probably as a result of simultaneous redeposition and ion-induced surface modification under varying conditions. No effect of the fracture on the process parameters or quality parameters of the produced films was observed, so the fracture is ignored in the following analyses.

III. EROSION PROFILE APPROXIMATION
For the precise estimation of the characteristics of an erosion profile, each discrete data record zi(xi, yi) is approximated using the following empirical function: The above equation was developed starting from the function R(x, y) presented in Ref. 20. Except for the factor −zB(y), the equations of zAPPROX(x, y) and R(x, y) are identical. The minus sign in Eq. (1) indicates an erosion process (removal of particles) instead of a coating process (accumulation of particles). A mirror symmetry for the x-direction is imposed because of G(x, y). More details on the parameters in Eq. (1) are given in Ref. 20. In total, 14 fitting parameters are included in the 2D function zAPPROX(x, y) without a direct link to a physical model or the beam profile. As a comparison, for the approximation of a rotationally symmetric erosion zone in a planar magnetron, a one-dimensional (1D) function with six fitting parameters was suggested in Ref. 32. The fitting of zAPPROX(x, y) to a determined dataset of erosion depths zi(xi, yi) is performed by the software package Layer-Thickness-Optimization (LTO, developed by Wjatscheslaw Sakiew). The fitting parameters and the corresponding mean squared errors (MSEs) are summarized in Table II.
As a result of the fitting procedure, the following characteristic values of an approximated 2D erosion profile zAPPROX(x, y) are ARTICLE scitation.org/journal/adv TABLE I. Estimated coordinates of the intersection y S between the target plane and the lengthened beam vector ⃗ n beam . The coordinate system is illustrated in Fig. 2(a).

y S (mm)
Ta and Si targets, dtarget = 370 mm 138 ± 9 SiO 2 target, dtarget = 550 mm 152 ± 12 calculated in LTO: x 0 and y 0 (the coordinates of the maximum erosion depth), zmin ≤ 0 (the maximum erosion depth), ΔxFWHM and Δy FWHM (the full width at half maximum (FWHM) in the x-direction at the y-position y 0 and in the y-direction at the x-position x 0 ), and V (the eroded volume). Another advantage of the approximation is the averaging of sporadic erosion depth measurement errors.
In the present work, the erosion profiles are qualitatively compared with one another. For this purpose, the profiles approximated by Eq. (1) are normalized by zmin as zAPPROX(x, y) = zAPPROX(x, y)/zmin.
(2) Figure 3 shows the approximated sputter-eroded Si target after an erosion time of T = 135, 092 s. The 1D distributions zAPPROX(x, yi) in the x-direction [ Fig. 3(b)] and zAPPROX(xi, y) in the y-direction [ Fig. 3(c)] indicate that the accuracy of the approximation for the x-direction is higher than that for the y-direction. It is important to point out that the erosion profile appears symmetrical in the x-direction and asymmetrical in the y-direction as a consequence of the target tilt angle TTA > 0. More precisely, under the conditions considered, the profile is stretched toward the lower target edge (bottom) and squeezed toward the upper target edge (top).
It can be seen that, in Fig. 3, the position of maximum erosion in the x-direction is x 0 = 96 mm, which is not exactly the target center at x = 100 mm. The observed misalignment results from the chosen target holder position and can, therefore, be compensated for by defining a new target holder position. Thus, in the following, the selected erosion profiles are shifted numerically in the x-direction to the target center (x 0 = 100 mm) for a clearer illustration.
In this context, the y-direction is more significant for the present investigation. In Fig. 3, the position of maximum erosion in the y-direction is at y 0 = 148 mm. By measuring the orientation of the target relative to the ion source, the coordinate of the intersection y S of the beam vector (⃗ n beam lengthened) with the target surface could not be estimated with better accuracy than shown in Table I, if the manufacturing tolerances of the vacuum chamber and its warping due to high vacuum are taken into account. It is important to note that y 0 and y S are not necessarily identical.

A. Comparison of the Ta and Si erosion profiles
In Fig. 4, zAPPROX(x, y) for the Si and Ta targets are compared for identical process geometries (TTA = 55 ○ , dtarget = 370 mm). Although (1) different materials were eroded with (2) different ion energies and (3) different accumulated erosion times, resulting in (4) different erosion depths zmin, and (5) in the case of Ta, both Ar and Xe ions have been used, the determined normalized erosion profiles are almost identical (see also Table III Table II, and the characteristic values are summarized in Table III (lines 1 and 7). (b) The 1D distributions of z APPROX (x, 147) are shown as solid lines and z APPROX (100, y) as dashed lines with Si in black and Ta in red. x 0 is centered at x 0 = 100 mm in both cases as described in Sec. III. The coordinates y 0 are within or almost within the range y S = 138 ± 9 mm given in Table I

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The following explanatory approach is plausible: (1) The erosion profiles are mainly influenced by the process geometry (e.g., a rotationally symmetric broad ion beam, a flat and tilted target, the beamlet pattern, and the values of TTA, dtarget, Roptic, and Doptic), and (2) the considered ion-solid interaction processes must be assumed to be qualitatively comparable-this means that the normalized sputtering yields, Y(α), are similar in the corresponding angular range of ions impinging on the target surface.
Calculations using semi-empirical models 33,34 result in at least similar distributions Y(α) (normalized to α = 55 ○ ) for the sputtering of Ta with Ar ions and Xe ions depending on the angle of incidence of the ions α onto the target [ Fig. 4(c)]. The angular dependence of the sputtering of Si compared to Ta appears to deviate more strongly. The variation of the polar angles of incidence along the y-direction is larger than that along the x-direction for the present process geometry, which probably causes the erosion profiles of Ta and Si to differ more in the y-direction than in the x-direction. However, regarding the calculations with the semi-empirical models, it should be noted that, in Ref. 35, it is indicated that the calculation of Y is accurate to within ±20%.
The results in Fig. 4 allow for two further conclusions: (1) If compound formation [17][18][19][20] or undesired oxide coverage occurs (Sec. II), then it can only have a minor influence on the qualitative characteristics of the erosion profiles under the experimental boundary conditions presented herein. In particular, because different target materials are compared, different compound formation rates can also be assumed. However, it is quite conceivable that there is a quantitative effect on the erosion rate (a continuous adsorption of oxygen atoms, which then have to be additionally sputtered), which is not evaluated here. (2) If the regulation of the ion energy results in a variation of the beam profile, then this variation must be sufficiently small so that the widths ΔxFWHM are not influenced by it. Additionally, the experimentally determined erosion profiles confirm that there is no measurable material removal outside the main erosion zone.

B. Evolution of the Si erosion profile
The investigation of the erosion of the Si target and its dependence on the total accumulated erosion time T can be summarized as follows (see Fig. 5 and Table III): Positions: There is no significant variation of x 0 . This means that the direction of propagation ⃗ n beam of the broad ion beam has not drifted within the observation period (e.g., due to degradation of the ion optic). A small increase in y 0 was documented. This is plausible because the target is tilted relative to ⃗ n beam . Dimensions: ΔxFWHM and Δy FWHM increase slightly with increasing T (and increasing zmin). However, the variation of both values is 6% or less at a relative erosion depth of approximately 70% (zmin/6, in comparison with the maximum usable target thickness). Thus, the shape of the erosion profile appears to be almost independent of the erosion time and erosion depth. A similar observation was also documented for DC-MS. 36,37 Rates: A linear scaling could be identified for zmin [ Fig. 5(b)] and V [ Fig. 5(c)]. The following conclusions can be drawn from this: The erosion rate is constant regardless of the erosion time or erosion depth. Such a finding is consistent with what is known for MS. 37 It is plausible that the investigated erosion depths are much smaller than the lateral dimensions of a target plate and the broad erosion profile itself. Nevertheless, a clear macroscopic modification of the surface geometry is evident. Consequently, there is also a certain effect on the distribution of the angles of incidence of the ions onto the target surface. However, this effect seems to be sufficiently small such that the change in the angle-dependent sputtering yield (for each ion) during the sputtering of the target is not reflected in the erosion rate [for clarification, see Fig. 4(c)]. This explanation also implies that, for hypothetical erosion depths, which are most probably greater than the thicknesses of the target plates used, non-linearities in the erosion rate must occur. Furthermore, other effects become relevant at large erosion depths, such as the redeposition of the sputtered material. A critical erosion depth cannot be determined at this point, but it is plausible that the critical erosion depth must be smaller than the lateral dimensions of a profile.
If other influences on the erosion rate occur (for the erosion depths investigated), such as compound formation, 17-20 redeposition, 38 target surface composition modification, 39 or ion-induced ARTICLE scitation.org/journal/adv surface modifications on the micrometer or nanometer scale (roughening, smoothing, nanopattern formation), 40 then they do not affect the linearity in the performed experiment.
With the observed linearity [ Fig. 5(b)], zmin can be extrapolated: zmin reaches a value of 6 mm (the thickness of the Si target plate) at T ≈ 54 h (under the conditions of 1.4 keV Xe ions, I beam = 200 mA, dtarget = 370 mm). At this point, 5% of the target plate has been eroded. In a production process, however, the position of the target holder can be varied. Thus, from practical experience, depending on the target material, dtarget, and other ion beam parameters, a target material utilization of up to 20% can be achieved in IBSD before the thickness of a target plate is exceeded. It should be noted that the target size and dtarget, as applied for present investigation, are optimized for the production of optical coatings with the highest quality level. Through additional technical adaptations (e.g., target segmentation), a higher degree of utilization can be achieved.

C. Comparison of the erosion profiles at different distances d target
In Fig. 4, it is shown that the erosion profiles of Ta and Si are qualitatively almost identical if the target distance dtarget is not changed, despite the different materials. On the basis of this result (process geometry appears superordinate, ion-solid interaction mechanisms appear subordinate), the dielectric SiO 2 target was eroded at a distance 180 mm larger. On the one hand, the greater propagation length of the broad ion beam through the process atmosphere and the associated interaction mechanisms that influence the characteristics of the ion beam should be taken into account. On the other hand, it should be considered that the SiO 2 target was positioned clearly behind the geometric focal point of the ion optic (dtarget > Roptic), while the other two targets were positioned close to but still in front of the geometric focal point (dtarget < Roptic). The following results were obtained (see Fig. 6 and Table III): Positions: The coordinate y 0 of the maximum erosion depth zmin is smaller. More precisely, y 0 shifts below the coordinate y S (Table I). It is assumed that this behavior results from the photometric law and the corresponding beam profile.

Dimensions: The erosion profile becomes broader. ΔxFWHM and
Δy FWHM scale with an almost identical scaling factor of 1.6 by increasing dtarget from 370 to 550 mm, although different target materials are being compared at this point. This result can also be understood as an indication that the erosion profiles are more strongly influenced by geometrical parameters than by ion-solid interaction mechanisms, as mentioned in Sec. IV A. Stretching: Compared to the Ta and Si erosion profiles, the qualitative characteristic of the SiO 2 erosion profile along the ydirection is reversed at the larger distance. The profile is stretched toward the upper target edge (top) and squeezed toward the lower target edge (bottom).
It can be concluded that, in qualitative terms, the erosion depends significantly on the propagation length of the broad ion beam or the characteristics of the ion beam. An uncertainty in the  Table II, and the characteristic values are summarized in Table III (lines 2 and 8). (b) 1D distributions for Si are shown in black and are identical to those in Fig. 4(b). The 1D distributions z APPROX (x, 120) are shown as solid lines and z APPROX (100, y) as dashed lines with SiO 2 in red. x 0 is centered at x 0 = 100 mm in both cases as described in Sec. III. In the case of SiO 2 , y 0 = 120 mm is clearly out of the range y S = 152 ± 12 mm given in Table I. The triangle-shaped points represent the experimentally determined erosion depths z i . They are assigned to the coordinates x i = 100 mm and y i = 122 mm as the closest coordinates to x 0 = 100 mm and y 0 = 120 mm.
result arises from the fact that metallic and dielectric targets are being compared at this point. In the case of SiO 2 , charging effects are conceivable, as well as preferential sputtering. 41

V. SUMMARY AND CONCLUSIONS
The focus of this work was to investigate target erosion profiles during low-energy (ion energy ≤1.9 keV, ion source RIM-20) reactive broad ion beam sputtering on a millimeter scale. Erosion profiles sputter-eroded from flat Ta, Si, and SiO 2 targets were compared with one another. For the precise estimation of the characteristics of an erosion profile, an empirical approximation function was developed.
The experimental data showed similar erosion profiles when comparing Ta (sputtered by 1.8 keV Ar and 1.45 keV Xe ions) and

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Si (sputtered by 1.4 keV Xe ions). In the case of Si, a linear erosion rate as a function of erosion time was observed. The qualitative distribution of the Si erosion profile appeared to be almost independent of the erosion time and erosion depth. Furthermore, a comparison of Si and SiO 2 (sputtered by 1.9 keV Ar ions) target erosion profiles, with the targets being eroded at different distances from the ion optic, showed a clear dependence on the propagation length of the broad ion beam. The lateral dimensions of the erosion profile and the position of the maximum erosion depth both changed. Furthermore, the shape of the profile along the y-direction was completely reversed. This behavior is associated with the beam profile and the photometric law.
The experimental results allow for the conclusion that the qualitative characteristics of the erosion profiles on a macroscopic scale are more strongly coupled to geometrical parameters (e.g., a rotationally symmetric broad ion beam, a flat and tilted target, the distance between the ion optic and the target, and the ion optic radius of curvature and diameter) than to the considered ion-solid interaction mechanisms at an atomic level, which are particularly coupled to the ion species and ion energy. It is conceivable that this result can be transferred to other broad ion beam sources commonly used in IBSD if a similar experimental setup is considered.
The impact of potential compound formation on the meaning of Berg's model, which is hardly accessible experimentally, is unclear. In particular, for modeling of the target erosion in IBS, target poisoning is still a challenge.  Table II lists the fitting parameters of the approximated erosion profiles zAPPROX(x, y); Table III

DATA AVAILABILITY
The data that support the findings of this study are available within this article.