Ionization of sputtered material in high power impulse magnetron sputtering plasmas—comparison of titanium, chromium and aluminum

The ionization of sputtered species in high power impulse magnetron sputtering of titanium, chromium, and aluminum targets is analyzed using Abel-inverted spectroscopic imaging to locate the position of ionization. From the spatial emission of neutrals, it is deduced that most of the sputtered titanium particles become ionized within 0.5 mm distance from the target, whereas sputtered aluminum or chromium can travel much further through the discharge before ionization occurs. Probe measurements reveal the reason for this difference to be the unusually high electron temperature of around 4.5 eV for titanium compared to 2.6 eV and 1.5 eV for aluminum and chromium as the target material, respectively. These probe measurements are then compared to a global model derived from the ionization region model. Excellent agreement between model and measurements can be reached, but only if the transport physics for the confinement of the species is adjusted. Using the model, the difference between the three discharges can be traced back to be mostly caused by the sputter yield. Thus, we propose that ionization in discharges with low-yield materials should generally be expected to occur closer to the target surface, leading the ions to be affected more strongly by the electric field across the magnetic trap region, resulting in a more severe deposition rate loss compared to high-yield materials.


Introduction
Magnetron sputtering plasmas are often employed for the synthesis of thin films. In these discharges, magnets are 1 current affiliation: University of Minnesota, Minneapolis, United States of America.
* Author to whom any correspondence should be addressed.
Original Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. positioned behind the cathode (the so-called target) to confine the electrons, leading to efficient ionization even at very low gas pressures. The magnetic confinement creates a plasma torus and, thus, an intense sputtering of the target, leading to a racetrack-like erosion pattern. The sputtered target material is then transported through the discharge volume to the substrate, creating a coating.
The performance of magnetron sputtering plasmas is determined by the flux density and the energy of film forming particles arriving at the substrate. For this reason, magnetron sputtering plasmas are usually operated at pressures between 0.1 Pa and 1 Pa, thus minimizing the amount of collisions that sputtered particles undergo before they reach the substrate. In this way, the flux of sputtered particles remains directed towards the substrate, ensuring a high deposition rate. Additionally, the initially high energy of sputtered particles is maintained, allowing for dense coatings with good adhesion [1].
Further increase of the coating quality can be achieved when the films are not created by neutral species, but instead by ions. These ions are then accelerated in the sheath between plasma and substrate, allowing for a much more energetic growth flux [2]. Increasing the ionization degree of sputtered particles can be achieved by working with short high voltage pulses, as it is realized in high power impulse magnetron sputtering (HiPIMS). In HiPIMS, ionization degrees for the sputtered material can exceed 50% [3][4][5][6] leading to an energetic growth flux yielding coatings with higher density, higher hardness, better adhesion and improved homogeneity compared to those deposited with traditional direct current magnetron sputtering (DCMS) [7][8][9].
However, the high ionization degree implies that most of the film forming species are affected by the strong electric field, present in the magnetic trap region of such plasmas and pointing towards the target surface [10,11]. This electric field back-attracts ions towards the target surface, preventing them from reaching the substrate [12,13]. This return effect leads to usually (but not necessarily [14]) smaller deposition rates for HiPIMS compared to DCMS operated at the same average discharge power [7].
Consequently, much of the research performed on HiPIMS plasmas is dedicated to optimizing the deposition rate of these discharges, e.g. by changing the pulse length [15] modifying the magnetic field configuration [14] or the applied voltage [16]. These optimization efforts are often guided by insight gained from the ionization region model (IRM). The IRM is a time-resolved global model for HiPIMS discharges [17][18][19][20][21][22], which has been highly successful in reproducing measured target currents under a wide range of conditions [23]. However, while this model has delivered invaluable insights into the physical processes in HiPIMS plasmas [23][24][25], it has hardly been validated beyond the comparison of global discharge currents, which is also used as an input for the model [26]. Moreover, since the IRM lacks spatial resolution, it cannot be used to describe local effects, such the so-called spokes-long wavelength oscillations in electron density, temperature and plasma potential [27][28][29][30][31]. Therefore, such local effects are much less understood. For example, the IRM assumes the average ion to be created in the center of the discharge volume, independent of discharge parameters such as the applied voltage or the target material. In reality, however, this position of ionization will have a strong influence of whether ions can reach the substrate or not.
The relevance of the position of ionization is illustrated in figure 1, which shows the potential structure in the magnetic trap region (or ionization region) of HiPIMS discharges according to the published literature [10,11,32,33]. In such a potential structure, ions created close to the target (position A in the figure) need to overcome a few 10 V of potential to reach the substrate. Since the energy distribution of sputtered particles usually peaks around a few eV, most will not be able to escape the magnetic trap region and will instead return to the target [12]. In contrast, ions created closer to the edge of the magnetic trap region (position B) only need to overcome a much smaller potential difference. Thus, such ions need much less energy and have a much higher probability of reaching the substrate.
Therefore, in this paper, we assess where the ionization of sputtered metal occurs inside the discharge volume for the example of titanium, chromium and aluminum as target materials. To this end, spectroscopic imaging of discharges with different target materials is performed. From the spatial variation of titanium neutral emission intensity, the position of ionization for sputtered titanium is determined and compared to the discharges using chromium and aluminum as the target material. The differences between the discharges are then explained using a simple global model based on the IRM as well as probe measurements performed inside the magnetic trap region. The comparison of probe measurements and model results allows to test the reliability and predictive power of such global models for HiPIMS plasmas. Finally, general trends about the spatial ionization rates for different discharges and the consequences on resulting deposition rates are deduced.

Magnetron sputtering plasmas
The experiments were conducted in a vacuum chamber with a base pressure of 4 × 10 −6 Pa. The working gas pressure was 0.5 Pa of pure argon.
The power supply (TRUMPF Hüttinger TruPlasma Highpulse 4002) was connected to the target over an electrical circuitry forming a low pass filter, thus limiting the current rise times and preventing discharge runaway [34]. Current and voltage measurements were performed close to the magnetron assembly, using a high voltage probe (Tektronix P6015A) and current monitor (Tektronix TCP404XL + TCPA400), respectively [35].
The plasma was ignited using a commercial magnetron sputtering source (Thin Film Consulting IX2U) equipped with targets with a diameter of 50 mm and a thickness of 3 mm. The racetrack was at a radial position of 13.5 mm, according to the magnetic field configuration, which can be found elsewhere [36]. Titanium, aluminum or chromium were used as the target materials. For the spectroscopic access to the near target region, the targets were manufactured with recessed edges, to prevent the target clamp from obstructing some of the optical emission from view when observing the plasma from the direction parallel to the target surface. For the same reason, the anode cover was replaced with a thin ring, as described previously [37].
The discharge voltage during the pulse was 450 V, 570 V, and 750 V for titanium, aluminum and chromium, respectively. Voltage trace forms can be found as part of figures 7-9. The pulse lengths were 100 µs for titanium and aluminum, and 150 µs for chromium as the target material. The longer time for Cr was chosen to still allow for multiple spoke revolutions, since these are much slower compared to spokes for the other materials [38]. The resulting discharge currents are shown in figure 2(a). The figure shows that titanium reaches the highest current at about 54 A (target area normalized: 2.8 A cm −2 ) despite being driven by the lowest voltage (450 V). Chromium only reaches 33 A (1.7 A cm −2 ), despite being operated at much higher 750 V. As figure 2(b) shows, the discharges of all three target materials reach about the same instantaneous power of 23 kW (1.2 kW cm −2 ) 100 µs after the pulse begin. The discharge with aluminum as the target materials was operated at 30 Hz, whereas 40 Hz was used for chromium and titanium, as required for long-term stable and reproducible discharge operation over the partly very long measurement times required here. Illustration of the plasma diagnostics that are combined for this study. During the experiments, either the probe or the camera was used for measurements without the other instrument simultaneously present in the system.

Plasma diagnostics
The present work combines probe measurements and spectroscopic imagining techniques that were developed and described elsewhere [32,37,39]. As such, we will only briefly describe these measurements here and refer the reader to the respective papers for further details. Figure 3 gives an overview over two different measurements combined for the present study. However, during the experiments, only one of the diagnostics was employed at a time, without the other instrument present in the system.  emission intensity close to the probe was monitored using a photomultiplier, creating peaks in the signal whenever a spoke moves past the probe position. This information was used to synchronize the simultaneously acquired probe current measurement to the spoke movement, enabling spokeresolved measurements. The obtained current-voltage curves are then fitted to theoretical curves, calculated using the theory of Bernstein, Rabinowitz and Laframboise for the ion current [40][41][42] and the magnetized probe theory described by Arslanbekov et al and by Popov et al for the electron current [43,44]. From the fit, optimized values for electron density, electron temperature and the plasma potential during the discharge pulse are obtained. The diagnostics has been described in more detail in a previous publication [32] where measurements were performed for aluminum as the target material. Here, we compare these results to measurements for titanium and chromium as target materials.

Spectrographic imaging.
Spectroscopic imaging was performed by positioning a gated and intensified camera (Andor iStar sCMOS 18U-E4) sideways of the discharge, as shown in figure 3. Different optical filters were placed between camera and the plasma, to isolate optical emission lines corresponding to neutrals and ions of the target material. The optical filters used for the respective species are listed in table 1.
Abel inversion was then applied to the stored images to recover the actual emissivity profile from the line of sightintegrated raw data (similar to [39]). The Abel inversion was performed using the three point algorithm by Dasch, in the implementation by the PyAbel software package [46][47][48]. Gaussian and median filters were applied to the data, as needed.
Measurements were performed in a time-resolved but spoke-averaged manner, by synchronizing the camera to the beginning of the discharge pulse and averaging over a few hundred acquisitions to remove the random influence of the spokes. The trigger delay between pulse begin and acquisition was varied to perform phase-resolved measurements at different points in time during the discharge pulse. Gate width, amplifier gain and the number of acquisitions were adjusted depending on the brightness of emission lines passing the respective optical filter.
The setup was described in more detail in a recent publication [37], the only difference here being the use of more target materials and the lack of spoke synchronization.

Spatial ionization profile
When tracking the movement of metal ions from the target to the substrate, we must first discuss where in the discharge the ionization of sputtered material occurs. Because of the strong electric field, present in the magnetic trap region of magnetron sputtering discharges [10,11], ions are understood to be back attracted towards the target surface [12,13]. Ions created close to the target surface need to traverse almost the entire magnetic trap region and, thus, need to overcome the entire potential difference across the magnetic trap to reach the substrate (see figure 1). In contrast, ions created further away from the target surface, towards the edge of the magnetic trap region, only need to overcome a much smaller part of this potential difference and have, therefore, a much higher probability to reach the substrate. Thus, the further away from the target a sputtered particle is ionized, the more likely it is to escape the magnetic trap region and eventually reach the substrate. Figure 4 shows the spatial emissivity profiles of titanium neutrals and ions, obtained from the Abelinverted images, that were taken as described above. The figure shows the radial (a)-(c) as well as the axial (d)-(f) direction, at different points in times during the discharge pulse. In the radial direction, the emissivity of both species was normalized to agree for r > 20 mm and then additionally normalized to the maximum of the ion emission. For the axial direction, the emission intensity was normalized to unity. In both directions, each point in time is normalized individually, to keep the figures readable.

Titanium.
We first regard the spatial emissivity in radial direction (a)-(c), at the position z = 1.5 mm. These emissivity profiles were obtained by integrating the two-dimensional emissivity over the axial direction between z = 1 mm and z = 2 mm. The noise in the emissivity around r = 0 is an unavoidable artifact of the Abel inversion. The oscillating pattern, visible on top of the ion emission in radial direction (c), is an artifact caused by the optical fiber coupling between camera intensifier and sensor.
At the beginning of the discharge pulse (figure 4(a)), at t = 18 µs, the spatial emissivities of ions and neutrals overlap, showing maxima centered around r = 13.5 mm, which is the racetrack position for the magnetic field configuration of our experiment [37]. Since the spatial emissivity profiles for ions and neutrals show such close agreement, we can conclude that this spatial profile is governed by the profiles of electron density and temperature (assuming a Maxwellian electron energy distribution [32,49]), determining the local excitation rate. However, later during the discharge pulse, at t = 34 µs, the spatial emissivity profile of neutrals begins to deviate. At this point in time, a local minimum in emissivity around the racetrack position (r = 13.5 mm) can be observed. This minimum becomes more pronounced at the end of the discharge pulse, at t = 98 µs.
Since we do not observe such a minimum for the spatial emissivity of titanium ions, we can deduce that this trend is not created by electron properties (density/temperature) which would affect both the ion as well as the neutral emission in a similar fashion. Thus, we hypothesize that the local minimum of titanium neutral emission is due to a depletion of the titanium neutral density caused by rapid ionization. This depletion occurs at the point of highest ionization rate, which is above the center of the racetrack position, thus creating the observed local minimum in titanium neutral emissivity. Since ions require much larger electron energy to become doubly charged ions, no minimum in the titanium ion emissivity is observed. However, at t = 98 µs we do observe a slight broadening and flattening of the titanium ion emissivity, which could be caused by the onset of titanium ion ionization towards doubly charged ions. These doubly charged ions are difficult to observed with optical emission spectroscopy, but can reach comparatively high densities in HiPIMS plasmas [50,51].
It should be noted that we specifically chose the position of z = 1.5 mm because the local minimum in titanium neutral emissivity is particularly noticeable there. The reason for this becomes apparent when regarding the spatial emissivity in axial direction, shown in figures 4(d)-(f). The figure shows the axial emissivity obtained by integrating the two-dimensional emissivity maps over the radial direction around the racetrack position, between r = 12 mm and r = 15 mm (the emissivity minimum around z = 3.5 mm is caused by the anode cover blocking the field-of-view of the camera). At the beginning of the discharge pulse, the emissivity profiles of titanium ions and neutrals are nearly identical, as was the case for the radial direction. The emissivity initially increases with distance from the target surface and peaks around z = 0.4 mm, which is likely the position of the highest electron density. Then, the emissivity decreases with target distance, since likely both electron density as well as temperature decrease with target distance [37] for z > 0.4mm.
However, later during the discharge pulse, the emissivity of neutrals begins to drop more quickly with target distance compared to the emissivity of ions. At the end of the discharge pulse, at t = 98 µs the emissivity of neutrals already drops below 50% around z = 0.4 mm. At this point, the emission of titanium ions is still at about 90% of its maximum value. The observed rapid drop of the titanium neutral emissivity indicates that the ionization of sputtered titanium above the racetrack occurs very close to the target, at z < 1 mm.
Similar measurements have previously been presented by Hecimovic et al [39] who also found the dip in neutral emissivity and equally proposed the interpretation of neutral depletion by ionization. However, the authors could not identify the position of strongest ionization, since the region z < 5 mm was obstructed from view by their anode cover. Our results point towards the importance of good optical access to the first millimeter target distance, from which the largest part of emission originates.
The observed rapid ionization of sputtered titanium very close to the target surface implies that the newly created titanium ions need to overcome almost the entire potential barrier present in the magnetic trap region. Most ions will not have sufficient kinetic energy to do so, and will return to the target surface. This is consistent with the very dominant return effect that is observed for titanium as target material.

Aluminum and chromium.
In contrast to the results for titanium as the target material, the recorded emissivity profiles for aluminum and chromium targets (not shown here) do not show signs of neutral depletion by ionization. Thus, the ionization rate for these materials seems to be considerably lower. Ionization occurs at larger distances to the target surface, where the electric field is already weaker. Thus, a larger fraction of ions will be able to reach the substrate compared to the titanium discharge.
The ionization rate depends only on electron density (n e ), electron temperature (T e ) and the cross section for electron impact excitation (σ iz ) (neglecting ionization by secondary electrons and Penning processes). Assuming a Maxwellian electron energy distribution function f (E) [32,49], we can write: with the electron energy E and the ionization rate coefficient k iz . The cross sections for electron impact ionization are very similar in shape and magnitude for the atoms of all three target materials and cannot cause the difference in ionization rate [52,53]. Instead, this difference can be explained by considering electron density and, most importantly, the electron temperature, which we will discuss in the following. Figure 5 shows the spoke-resolved electron density ( figure 5(a)) and electron temperature ( figure 5(b)) as a function of time, obtained using the time shift averaging approach described in a previous publication [32]. The fluctuations in both electron density as well as electron temperature that are visible during later times of the discharge pulse are caused by spokes moving past the Langmuir probe location, thus changing the plasma conditions surrounding the probe. When using the time shift averaging method, usually only a single spoke (here at 95 µs) is fully recorded, while all other peaks are strongly attenuated and a beat signal is created, caused by the variations in spoke frequency from one discharge pulse to the next. For the chromium discharge, however, many spoke peaks are visible, because of the highly stable and reproducible spoke frequency during the measurement time. Figure 5(a) also shows an enlarged view of the data acquired in the time window around 95 µs, to more clearly show the density fluctuations caused by the spokes. From this enlarged view, it becomes obvious that we find strong fluctuations with aluminum and chromium as the target material, whereas the spokes in the discharge with titanium seem to be much weaker.

Electron density and temperature
First, we will focus on the absolute numbers of average electron densities and temperatures towards the end of the discharge pulse, independent from the fluctuations caused by the spokes. These values are summarized in table 2, which also lists the operating parameters, as well as calculated ionization rate ν iz and ionization time τ iz , which will be described later.
For all three target materials, figure 5(a) shows the electron density increases with time during the discharge pulse, roughly proportional to the discharge current (compare figure 2(a)). After the end of the discharge pulse at 100 µs for Ti and Al, and 150 µs for Cr, the density decays, reaching values close to zero within about 20 µs. While the electron density follows a similar trend for all three target materials, differences can be found in the density magnitude: neglecting the spoke fluctuations, the electron density peaks around 5.5 × 10 19 m −3 for Ti, around 6 × 10 19 m −3 for Al, and reaches a value of 9.4 × 10 19 m −3 for Cr.
At first, these electron densities seem to contradict our findings from the optical measurements where we found the ionization rate for titanium to be much higher than for the other target materials. If we only consider the effect of the electron density, we would instead expect the ionization rate for titanium to be about 40% lower than the one for chromium. The solution to this apparent contradiction can be found in the electron temperature. There, we find the highest value of T e = 4.5 eV for the discharge with titanium as the target material, and much lower values of 2.6 eV and 1.5 eV for Al and Cr, respectively. Since the ionization rate depends much more strongly on the electron temperature than the electron density, the calculated ionization rates follow this trend. Using the rate coefficients listed in appendix B, we find ν iz = 2.1 × 10 6 s −1 for Ti, ν iz = 8 × 10 5 s −1 for Al and ν iz = 2 × 10 5 s −1 for Cr as the target material, in qualitative agreement with the optical measurements.
From the ionization frequency, we can calculate the ionization time τ iz = 1/ν iz , which describes how long freshly sputtered neutrals will travel through the plasma before being ionized. For titanium, we find a time of τ iz = 0.5 µs, which corresponds to about 0.75 mm, when assuming a mean velocity of 1500 m s −1 [54]. This is in excellent agreement to the length of 0.5 mm that we estimated from the optical measurements, especially considering that we measured the electron density in 8 mm distance from the target and we expect larger densities (and, thus, a smaller τ iz ) closer to the target surface, as recently observed by Dubois et al [55]. In contrast, for Cr as the target material, we find τ iz = 5.4 µs. Assuming a similar velocity as for titanium, the long ionization time implies that chromium atoms can cross half of the magnetic trap region before being ionized, thus drastically lowering the potential barrier the ion has to overcome (see figure 1), increasing its probability of reaching the substrate.
Having found that the observed high ionization rate for the discharge with titanium target is caused by the unusual high electron temperature, the obvious next question is how this high electron temperature can be explained. This is addressed by studying a global model of the discharge, as discussed in the following.

Global model
To explain the trends in electron temperature found from our measurements, we set up a global model, similar to the IRM [19,21,25] for the magnetic trap region of the plasma. The model balances the incoming species from the background gas and the sputtered species from the target. Different probabilities such as the ionization probability and the return probability are adjusted so that the temporal variation of the measured plasma current is reproduced. While the global model employed here is based on the IRM, we use a more primitive version with only five species: argon neutrals and ions, metal neutral and ions, as well as electrons. The equations are listed in appendix A.
The volume considered by the model V IR is illustrated in figure 6, which also shows the position of the Langmuir probe and the magnetic field configuration, reconstructed from measurements using the approach described by Krüger et al [56].
In the model, the ionization region is defined as a torus shaped volume covering part of the magnetic trap region. The electric field inside the ionization region is described by the voltage U IR , dropping over the simulation space in z direction, with a magnitude of few 10 V. The geometry is simplified by defining the surface areas towards the race track S RT and towards the plasma bulk S BP . The surface towards the bulk consists of the top of the torus and its outer and inner lateral surface. This confines a volume of the ionization region V IR with a close distance z 1 and a large distance z 2 to the target and an inner radius r 1 and an outer radius r 2 . The ion flux towards the target is not expressed as a Bohm flux, but rather as a free fall of an ion from a central position in the IR at a potential energy of 1/2U IR .
This global model is validated by comparing the model results with experiments using aluminum, titanium and chromium targets. The input parameters as well as the fitted values in the global model are listed in table 3. The fit parameters, U IR , w and L IR were manually adjusted to reach agreement between model results and measurements. However, β could not be determined from the comparison of model results and measurements, since we found the model to be underdetermined: many combinations of U IR and β can lead to almost the same current, electron density and electron temperature, rendering the choice of β (or of U IR ) arbitrary. This problem is also present for the original IRM, where either additional measurements are used to constrain the model [57], or physical arguments are used to motivate the choice of β [12]. We use the latter approach here and argue that even for the comparatively low ionization rate in case of Cr as the target material, β should be expected to be above 0.8, since only a few volts of potential difference are required to reach such a value [12]. For titanium as the target material, we would expect a much higher value, possibly in excess of β = 0.95. However, while this difference between β = 0.8 and β = 0.95 has an important impact on the predicted ion metal flux fraction at the substrate position, it is much less relevant for the discharge dynamic inside the magnetic trap region, considered by the model. There, the choice of β has only a linear effect on the other determined parameters, e.g. a 10% variation in β causes only an about 10% change in fitted U IR . As such, we here simply choose β = 0.9 for all three target materials, noting that β should actually be expected to be much larger for Ti than for the other materials. The choices for the other input parameters listed in table 3 are explained in appendix A. Table 3. Input and fitting parameters of the global model: β is the return probability of ions, U IR the voltage across the simulation space in axial direction. γ is the coefficient for secondary electron emission by argon ion impact. Y self and Y Ar are the self and argon ion sputter yields, respectively. w is the width of the simulation space and L IR the height in axial direction (see figure 6). (S BP + S RT )/V IR is the surface-to-volume ratio of the model.   Figure 7 shows the model results for aluminum as the target material, together with both electrical as well as Langmuir probe measurement results (both denoted as exp in the figure). During the fitting procedure the values for β and U IR are adjusted as well as the length of the IR L IR and the width of the racetrack w = r 2 − r 1 . This manual fitting is performed until an agreement between the calculated and measured discharge current, electron density and electron temperature is obtained. The measured discharge voltage is used as input data. The initial ionization degree is set to 1% based on the assumption that a weakly ionized medium may remain in front of the target from the previous HiPIMS pulse.
As figure 7(a) demonstrates, excellent agreement can be reached for the discharge current and the absorbed power. Equally good agreement can be reached for the electron density, as shown by figure 7(b), except for the modulations caused by the spokes, which cannot be described by the global The comparison between global model and measured electron densities, temperatures and discharge currents shows equally excellent agreement for titanium (figure 8) as well as chromium (figure 9) as the target material. All three metals have in common that the voltage U IR might differ, but the electric field in the plasma volume is of similar order of E IR = U IR /L ≈ 1000 V m −1 . This seems reasonable given the fact that the electric field in the magnetic trap region is dominated by the magnetic confinement of the electrons with respect to the unmagnetized ions. Since the magnetic field topology is identical for all metals, the electric field is expected to be also similar.
The main difference originates from the different spatial extension of the simulation space, which was adjusted to reach agreement between model and the probe measurements. Here, a large width w and length L IR of the considered volume was required for Ti, while much smaller values are needed for Al and Cr (table 3). The size of the fitted simulation space is inconsistent with the extension of plasma emission, as presented above. In the case of Ti, the length of the model region in axial direction L IR = 24 mm extends well beyond the magnetic null located at about 18 mm, which is incompatible with the assumptions of the model. This discrepancy could be resolved by regarding the surfaces S BP and S RT as effective surfaces that regulate confinement. In any global model, an increasing surface-to-volume ratio implies more losses by fluxes crossing the confining surface relative to the species generation by ionization in the volume. The surface-to-volume ratios are listed in table 3, showing for chromium and aluminum a ratio of around 0.45 mm −1 , whereas a value of 0.28 mm −1 was needed for titanium. Assuming this surface-to-volume ratio as indicative of confinement, the smaller values for Ti would indicate better confinement, i.e. less transport across the magnetic field lines. This interpretation is in agreement with the observed weaker spokes in the case of titanium: since spokes can cause increased transport across the magnetic field lines [58], the weak spokes in case of Ti should be expected to cause less transport than the much stronger spokes for Cr and Al as the target material.
However, the need to adjust the simulation space (or the effective surfaces confining the plasma) limits the predictive power of such global models. This is especially problematic for cases, where only the voltage and current are measured and electron density and temperature are unknown. The limited predictive power of global models for HiPIMS plasmas should not be surprising given the complexity of these discharges where the transport occurs across the magnetic field lines and the shape of the plasma volume can be rather irregular due to the presence of spokes. Similar problems have recently been observed by Babu et al [26] when comparing IRM results to Thomson scattering measurements. Nevertheless, the model can be used to gain insight into the internal physical processes and explain the observed differences in electron temperature between the discharges with the three different target materials. To this end, we can more closely regard the energy balance of the model, which determines T e : d dt with the ionization rate coefficients for argon and the sputtered material, k IZ,Ar and k IZ,M and their respective ionization energies E IZ,Ar and E IZ,M . The first term on the right hand side of the equation describes Ohmic heating due to the voltage drop of U IR across the magnetic trap. This term varies only a few percent between the three materials and can, thus, not cause the observed differences in T e . The second term on the right hand side is independent from the target properties and can, therefore, also not explain the difference. Instead, the difference in electron temperature between the three target materials is mostly caused by the last term of equation (2), which describes the energy loss due to ionization of sputtered material. Since chromium exhibits a particularly high sputter yield, the density of sputtered neutrals n M is high and the loss term large, leading to the measured small T e . In contrast, titanium has a small sputter yield, leading to small losses due to the ionization of titanium neutrals and a correspondingly high electron temperature. This argument has already been proposed by Brenning et al [24] as a general trend for HiPIMS plasmas: discharges with high-yield target materials should be expected to feature low electron temperatures, and vice versa. The observation that the sputter yield of the target material decisively affects the electron temperature leads to the conclusion that also the ionization rate and, therefore, also the position where ionization mostly occurs is determined by the sputter yield of the material. Indirectly, a low sputter yield will lead ionization to occur very close to the target, forcing ions to cross the complete potential barrier present in the magnetic trap region to reach the substrate (A in figure 1). Thus, the already low deposition rate of low-sputter-yield materials should experience a much stronger reduction in deposition rate when switching from a DCMS to a HiPIMS process when compared to high-yield materials. This is exactly what was observed by Samuelsson et al when they measured the deposition rate and deposition rate difference observed between DCMS and HiPIMS processes [7].

Conclusion
In this work, the position of ionization inside HiPIMS plasmas was estimated using spectroscopic imaging. We found that ionization for titanium as the target material occurs very close to the target, likely in a distance of 1 mm to the target surface or less. In contrast, the ionization for Al and Cr as the target material is more distributed over a larger volume, when operating at the same peak power. The difference is caused by the higher ionization rate of the titanium discharge, which in turn is caused by a much higher electron temperature, as Langmuir probe measurements revealed.
In order to explain the differences in electron temperature, a simple global model was introduced, based on the IRM. The model can reproduce the time-resolved electron density and electron temperature obtained from the probe measurements, but only if modifications to the ion confinement process are assumed. This reduces the predictive power of such global models in cases where no independent measurement of the predicted plasma parameters is available. Based on the model, the difference in electron temperature between the discharges with the three different target materials could be traced back to the difference in sputter yield. A high sputter yield will lead to a high density of metal neutrals, which provide the most important electron energy loss term via electron impact ionization.
Based on these observations, we predict that, in general, low-yield target materials should be affected more strongly by the return effect. The low sputter yield will lead to a high electron temperature and a corresponding high ionization rate, which in turn leads to ionization close to the target surface which means that ions need to cross almost the entire potential drop across the magnetic trap region, instead of only part of it. This prediction seems to be in agreement with results from the literature [7].

Data availability statement
The data that support the findings of this study are openly available at the following URL/DOI: https://doi.org/10.5281/ zenodo.7838616.

Acknowledgments
This work has been funded by the DFG within the framework of the collaborative research centre SFB-TR 87.

Appendix A. Global model of the plasma
In the following only the simplest set of balance equations is formulated, omitting any loss channels due to excitation of argon metastables in the plasma or any chemical effect due to the admixture of a reactive gas. The balance equation for argon consists of a re-fill from the ambient argon background, a loss due to ionization and a loss due to the sputter wind. In addition, the argon ion flux towards the target is reflected back as neutrals.
with n 0 the neutral gas density in the background, n Ar and n Ar + the argon neutral and ion density, n M and n M + the metal neutral and ion density, v thermal,Ar and v thermal,M the thermal velocities of argon and metal atoms, and λ M = 1/(n Ar σ) the mean free path of metal atoms using a hard sphere cross section (σ = 10 −19 m 2 ) and with m Ar and m M being the masses of argon and metal atoms. Γ RT Ar + constitutes the flux towards the racetrack. k IZ,Ar the argon ionization rate depending on the electron temperature.
The surfaces towards the race track S RT and towards the rest of the plasma S BP (compare figure 6) are defined as: with r 1,2 = 13 mm ± w/2, where the width w of the simulation space is used as a fit parameter, listed in table 3. The length of the simulation space in axial direction L IR = z 2 − z 1 , is calculated assuming z 1 = 1 mm and using z 2 as a fit parameters, listed in table 3. The balance equation for the argon ions consists of generation via ionization, and the loss towards the racetrack and towards the bulk plasma.
The fluxes are calculated at first by regarding the flux towards the race track. For this a velocity from a free acceleration towards the target in the ionization region potential drop 1/2U IR is assumed. This neglects any collisions. However, U IR is a free parameter in the model that is adjusted by comparing the total current in the model with the measurement. Only a fraction β of the ion density is actually going towards the racetrack, that is expressed as a return probability β. This return probability regulates the loss of the total of number of ions dN/dt over the two surfaces S BP and S RT as: Both equations combined yield a relation between the two flux densities Γ BP Ar + and Γ RT Ar + of: Therefore, only the flux towards the target has to be calculated from the ion density and the IR voltage U IR as: The balance equation for the metal ions consists of generation via ionization, and the loss due the surfaces via the fluxes towards the racetrack and towards the bulk plasma.
The balance equation for titanium neutrals consists of a diffusive loss to the ambient background, a loss due to ionization and a generation due to sputtering by argon ions and by titanium ions. With the sputter yields for argon ion sputtering Y Ar + −>M and for self sputtering Y M + −>M . The electron density is obtained from quasi-neutrality.
The electron energy balance regulates the electron temperature. The heating is assumed to occur due to Ohmic heating given by I D U IR and the loss due to ionization of argon and metal atoms. Any further channels such as attachment, detachment or excitation of metastables and oxygen splitting are not regarded since ionization constitutes the dominant loss channel [21]: with γ SE,Ar + and γ SE,M + the secondary electron coefficient by argon ions and electrons, and r the recapture probability of the electrons describing how the fast secondary electrons can still be trapped by the magnetic confinement. In the energy range up 750 V, usually potential emission dominated the secondary electron emission, which requires the ionization energy of the ion to be at least the work function of the material. Consequently, secondary electron can only be created by Auger neutralization of argon ions. The corresponding value for γ Ar + is calculated by the Hagstrum model [59]. The recapture probability shows only a minimal influence on the fitting result and is set to 0.5. The power to the electrons is given by the sheath acceleration of secondaries into the plasma and Ohmic losses in the IR: The power to the ions is attributed mainly to the acceleration in the sheath: P ion = Γ Ar + S RT (U D − U IR )e + Γ Ti + S RT (U D − U IR )e.
(A. 16) The Ohmic losses are already covered in the expression for the electrons. The total power is P calc = P e + P ion .

Appendix B. Ionization rates coefficients
For both the ionization rate estimation reported in table 2 as well as the global model, ionization rate coefficients for argon and atoms of the three target materials are needed. The equations employed for Ar, Al and Ti are listed in table B1.
For chromium (e + Cr → Cr + + 2e), we use the rate coefficients recommended by Lennon et al [52], calculated as