Secondary electron emission from magnetron targets

Ion-induced secondary electron emission of surfaces occurs in all gas discharges which have contact to surfaces such as electrodes or chamber walls. These secondary electrons (SEs) play an important role, for instance, in the performance of DC discharges, RF discharges and magnetron sputtering discharges. SE generation can be separated into potential electron emission (PEE) due to the neutralization of the incident ion upon impact and kinetic electron emission (KEE) due to the electronic stopping of the penetrating ion in the solid. SE due to neutralization is usually described by Auger processes and the density of states of the electrons in the solid, whereas KEE scales with the electronic stopping of the ion in the solid, as being calculated by ion collision simulations. The measurement of the energy distribution of the SEs of three metals (Al, Ti, Cu) and their oxides reveals the occurrence of Auger peaks, which are not reflected by standard models such as the Hagstrum model. Instead, in this paper, a model is proposed describing these Auger peaks by Auger neutralization of holes created by the collision cascade of the incident ion. This shows decent agreement. The contribution of Auger peaks in the metals Al and Ti is very significant, whereas it is negligible in the case of Cu. The implication of these energy distributions to the performance of magnetron sputtering discharges is discussed.


Introduction
Electrons are crucial to sustain a gas discharge for example by ionization processes. Thus, the generation of additional electrons from a surface by ion impact is of special interest since these secondary electrons (SEs) change the performance of the discharge. One prominent example, where SEs play an important role in the discharge behavior, are magnetron sputtering discharges: SEs generated at the target surface are accelerated into the plasma, are trapped in the magnetic * 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. confinement region, and dissipate their energy and heat the discharge thereby. A high density plasma is created leading to an intense sputtering of the target (the cathode). The sputtered atoms from the metal target travel through the discharge and condense on a work-piece to be coated by a thin metal film [1,2]. When reactive gases such as oxygen are added to the discharge, composite materials such as metal oxides are deposited. The surface processes at the plasma-target interface play an essential role for the performance of magnetron sputtering discharges: (i) the efficiency of sputtering depends on the energy of the ions, but also on the surface composition since any variation of the surface binding energy of the topmost atoms directly affects the sputter yield. This surface binding energy is affected by the reaction of reactive gases with the metallic target. For example, if oxidation of the metal target occurs during the sputter process, the surface binding energy increases and the sputter yield decreases [3][4][5]. (ii) The plasma heating depends sensitively on the ion-induced secondary electron emission coefficient or yield (SEEC or γ). These electrons are generated upon ion impact inside the metal target, are released from the metal, and are accelerated into the discharge by the cathode sheath voltage. Also, this γ depends sensitively on the composition of the topmost atoms at the target, because the work function and the energy transfer from the incident ion to the material determines the efficiency for this electron release. The effect of these topmost atoms of an electrode on SE was investigated in various gas discharges [6,7]. For example, experiments in helium abnormal discharges showed that the coverage of electrodes with impurities has a higher impact on the performance of the discharge than a variation of the electrode material itself [7]. Current-voltage characteristics of these discharges with gas covered electrodes become S-shaped upon a higher SE emission of the surfaces.
The electron emission processes can not only be analyzed directly in the discharge, but also by elemental surface science experiments employing ion beams of the species of interest impinging on a well defined surface [8][9][10][11][12][13][14]. In the case of pure metal targets, SE emission has been measured in such experiments being consistent with calculations, the same holds for the investigation of sputtering processes [15]. In the case of oxidized surfaces, however, the measurement of γ and sputter yields is more complicated since the ion bombardment continuously alters the surface composition and the equilibrium surface composition in a plasma cannot easily be reproduced in a beam experiment. Therefore, plasma experiments are often combined with plasma modeling, where the surface processes are to some extent fitting parameters [16,17]. This indirect reasoning regarding the surface processes, however, is hampered by the fact that many plasma species interact with a target surface at the same time so that synergism or antisynergism might hide the contribution of individual elemental processes. For example, plasma species such as electrons [18,19], ions [14], atoms [14], photons [20], meta-stables [21,22], and molecules [23,24] may release simultaneously electrons from a surface, when they de-excite or recombine upon impact. This makes the identification of an individual process very difficult.
In the past, we used a different approach than measurements inside a plasma, namely a beam experiment employing argon ions and oxygen atoms impinging on metal surfaces to mimic the plasma-target interface and to measure γ [10][11][12][13]. We investigated three different metal surface conditions, namely 'clean', 'oxidized', and 'untreated' (=oxidized surface with hydrocarbon adsorbents). The beam measurements perfectly reproduced γ for argon ions impinging on various metal surfaces and their oxides. For example, γ for nickel and copper oxide are higher than for the clean metals. This was explained by the fact that the energy transfer from the ion onto the electronic system of the oxide is more efficient than for the metal despite the fact that the work function of an oxidized metal is higher than of the metal, which would lower the γ. Apparently, the net effect is an increase in SEs. It was also interesting to note that untreated surfaces corresponding to a contamination of theses oxidized surfaces, show an even higher γ, which was explained by a lowering of the work function due to the adsorption of contaminants (for example residual hydrocarbons from the ambient). These contaminated and slightly oxidized surfaces are apparently a good proxy for plasma exposed electrodes, because these γ fitted within 30% to the γ data collection of Phelps and Petrović on clean and dirty (untreated/contaminated) surfaces, as being determined in swarm experiments [14].
SE emission from metals can be separated into potential electron emission (PEE) originating from the neutralization of the incident ion in front of the surface upon impact and into kinetic electron emission (KEE) originating from the electronic stopping of an ion penetrating a solid. PEE usually occurs at low ion energies below about 500 eV, while KEE only works with high energetic ions above about 500 eV. At high ion energies, both processes, PEE and KEE, contribute to γ [14,22,25].
PEE: PEE is well studied and can be described by the Hagstrum model [22] as illustrated by an energy diagram in figure 1(a). This process is dominated by Auger neutralization, where the ion at the surface is neutralized by an electron from the solid at energy E ′ . The released energy is transfered back to an electron at energy E ′ ′ . The kinetic energy of the electron leaving the surface is E k , if measured with respect to the vacuum level: with E i the ionization energy of the ion and E 0 the sum of work function Φ and the Fermi energy E F of the solid. The kinetic energy of the electron outside the solid with respect to the bottom of the Fermi well is E k : The rate of generating SEs is determined by Fermi's golden rule that combines the density of final states and a matrix element ⟨i|H|f ⟩ for the transition between initial |i ⟩ and final state | f ⟩. In the Hagstrum model, the difference in γ for different metals originates mainly from the different density of states of the electrons at energies E ′ and E ′ ′ whereas ⟨i|H|f ⟩ can be set to unity. This yields the number of electrons N i (E k ) that are excited inside the solid to a given energy E k . A fraction of these electrons travel towards the surface and might be able to surpass the surface barrier given by the work function of the material. This is described by an escape probability P e (E k ). The electron energy distribution function (EEDF) of escaping electrons is then N 0 (E k ): with P t the probability for an incident ion to neutralize upon impact. This factor P t is usually set to unity for PEE [22]. The SE emission yield γ potential for PEE is finally the integral over all possible energies E k of the free electrons: For details of these calculations see [17,22,26] or the appendix. A typical result is shown in figure 1(b) for the neutralization of argon ions at a copper surface (E F = 7 eV). The function N i (E k ), denoted as red solid line, reflects the distribution of excited electrons inside the solid, when the ionization energy of 15.4 eV of the argon ions is dissipated into the Auger process. The black dashed line denotes the escape probability P e (E k ) and one sees that only a small fraction of the excited electrons are able to escape the solid denoted by the green solid line. In this study, we refer to the EEDF of the excited electrons inside the metal by N i (E k ) and outside the solid by N 0 (E k ) or SE EEDF.
KEE: At higher ion energies (typically above 500 eV), also KEE contributes to γ, when the electronic stopping of an incident ion creates a collision cascade of excited electrons inside the solid. These excited electrons originate from the conduction band (CB). Some of these electrons may overcome the surface barrier and being emitted as SE. Due to the collision cascade of electrons in the metal and the associated energy loss, the energy distribution of the emitted electrons is sharp at a few eV.
Despite its complexity, KEE has been modeled in a rather simplistic manner in the literature [27][28][29][30][31] assuming that γ for KEE is merely proportional to electronic stopping power S e (E) of the ion: with a material dependent constant C b . C b , depending on the ion and the surface material, is in the range of 0.05-0.11 Å eV −1 for ion energies of more than 10 keV amu −1 (amu: atomic mass unit) according to the literature [30]. This approach in equation (5) has been chosen in our previous study as well [10]. Here, we also took into account a depth x dependent electronic stopping power S e (E, x) and a finite escape length λ escape for SEs, to calculate γ for metals based on KEE: Here, we still assume a linear relationship between γ and the integrated S e (E, x). The electronic stopping power S e (E, x) is deduced from SRIM calculations (SRIM=stopping and range of ions in matter). SRIM is a Monte-Carlo based code for calculating the interaction of ions with material using electronic and nuclear stopping for the energy loss mechanisms [32]. The exponential function in equation (6) and its normalization N describe that only a fraction of 1/e of electrons generated at depth λ escape contribute to γ, as explained in detail in [10]. The kinetic emission model (equation (6)) has only one fitting parameter, the factor C metal . C metal is constant across the whole ion energy range, similar to the factor C b from the literature in equation (5). In this paper, a good agreement between experiment and model was achieved with C b = 0.006 Å eV −1 for Cu and Ti, and 0.008 Å eV −1 for Al. The discrepancy in C b = 0.006 between experiment and literature is reasonable since the ion energies in this study (below 250 eV amu −1 ) are much lower.
This model can be extended also to oxidized surfaces by assuming an oxygen coverage Θ and different γ for a metal and an oxidized surface site [10]. Experiment and model agree within 5% in the kinetic energy range. This agreement proves that the very simple linear scaling of γ kinetic (E) with the electronic stopping S e (E, x) is indeed a good approach.
To gain a better understanding of potential and kinetic electron emission, SE EEDFs are measured. It is now striking to note, that the SE EEDF in the energy range of KEE contains peaks at higher electron energies which cannot originate from electrons from the CB. This was, for example, observed for Al [12]. Since these peaks are distinct, they are supposed to be connected to Auger processes inside the solid. This is further analyzed in this paper by measuring the energy dependence of the SE in beam experiments and developing an extension of the Hagstrum model, where the source of ionization is not the neutralization of the incident ion in front of the surface, but rather the neutralization of a hole inside the solid that has been created in the collision cascade of the penetrating ion. We refer to this approach as an extended Hagstrum model.

Experimental setup
The particle beam experiments were performed in a dedicated vacuum setup employing two plasma ion sources and an atomic oxygen source. The plasma sources generate beams of single charged argon ions which reach the target at normal incidence, whereas the beam of atomic oxygen from the atomic oxygen source is oriented at 45 • to the target normal. The plasma sources are applied for measuring the ioninduced secondary electron emission and the atomic oxygen source to oxidize the targets in-situ. The first plasma source is an electron cyclotron resonance (ECR) plasma, which was used by Corbella et al to measure ion-induced secondary electron emission of aluminum and titanium targets [12]. The second plasma source, called Colutron, is applied to measure ion-induced secondary electron emission of copper targets. The atomic oxygen source is a hot capillary source generating a beam of atomic oxygen based on dissociation. Details of the setup and the particle sources are described in [10]. For measuring ion-induced secondary electron emission, a collector system was used which is already described in [12,33]. The collector system consists of cylindrical shaped electrodes surrounding the target and allows the determination of both, γ and EEDF. Therefor, target currents and currents on a biased collector surrounding the target were measured. Currents were measured with a Keithley 487 picoammeter. The collector electrode was biased with ±300 V using a Kepco bipolar operational power supply. Details on the calculation of γ and the EEDF based on the measured currents can be found elsewhere [12].
Polycrystalline aluminum (25 µm, purity of 99.999%), titanium (127 µm, purity of 99.99%), and copper (254 µm, purity of 99.9%) targets with a size of 2.8 cm × 2.8 cm were investigated. The surfaces of these targets are distinguished in our study as being 'clean', 'untreated' and 'oxidized': Clean refers to a sputtered clean target, untreated to an air-exposed (= oxidized surface with hydrocarbon adsorbates), and oxidized to a pure in-situ oxidized target [10]. Figure 2 shows the SE EEDF for aluminum (Al) and aluminum oxide (Al 2 O 3 ) for three different argon ion energies of 500 eV, 800 eV, and 1000 eV from [12]. The choice of ion energies was according to the optimum ion currents that can be generated by the ECR or the Colutron source, respectively. The EEDF for metallic Al for an energy of 1000 eV shows a peak at 78 eV, 28 eV and around 5 eV. The peak at 78 eV may constitute a typical Auger peak, which occurs at 68 eV in photoelectron spectroscopy [34]. Since electron generation originates mainly from electronic stopping of the penetrating ion within the collision cascade, further excitation in the electronic system of the solid may affect this (such as shake-up processes from plasmons). The peak at 38 eV constitutes an Al2p Auger peak for Al 2 O 3 and the peak at 5 eV corresponds to PEE, as described by the original Hagstrum model [22].

Aluminum
For the lower ion energies of 800 eV and 500 eV, the peak at 78 eV vanishes and peaks at 38 eV and 54 eV become dominant. Like the peak at 38 eV, the peak at 54 eV also originates from Al2p Auger electrons from Al 2 O 3 . Apparently, at lower ion energies, the EEDF of SE exhibits the electronic signature of an oxidized surface. This is reasonable, if we assume that the ion-induced sputter cleaning of the surface is in equilibrium with the residual oxidation from the vacuum background. Since Auger neutralization is very surface sensitive, and the experiment is not designed for ultra-high vacuum conditions, even very small concentrations of residual gases are immediately visible. As a consequence, at lower ion energies and thus smaller sputter yields, the continuous re-oxidation of the surface alters its electronic structure. The measurements with 500 eV and 800 eV ions thus do not show an atomically clean, but a slightly oxidized surface. For comparison, a defined oxidized surface was also examined as also presented in figure 2. These surfaces were oxidized in-situ prior to the EEDF measurements by employing oxygen atoms.
In the experiments employing argon ions and oxygen atoms, the SE EEDFs change their characteristic shape and the absolute values are much larger. It is important to note that the SE EEDF of the metallic Al is enhanced by a factor of 5 in figure 2. The SE EEDF of Al 2 O 3 at 500 eV shows a peak at 10 eV, 30 eV, and 55 eV. With increasing ion energy, the peaks shift to higher electron energies. Peak shifts can originate from interactions of the electrons leaving the solid with other excitations in the solid leading to an increase or decrease of the kinetic energy of the electrons. Also, screening effects due to the oxidation layer can lead to peak shifting as it is known from photoelectron spectroscopy.
Given the amplitudes, the SE for Al 2 O 3 is ten times larger than for metallic Al. The Auger peaks at lower SE energies for Al 2 O 3 become more pronounced at lower ion energies compared to metallic Al, because the balance between oxidation and sputter cleaning of the surface shifts towards an oxidation. This oxidation is intended by applying the O atom beam source. Since Auger peaks originating from Al 2 O 3 are also present for the metallic Al samples, this may indicate an unintentional oxidation of the metallic Al by residual gases from the vacuum background, as discussed before. The peaks for Al 2 O 3 are much more pronounced indicating that the intentional O atom beam creates a stable Al 2 O 3 layer on top of the Al sample. Figure 3 shows the measured SE EEDF as solid symbols for titanium (Ti) for ion energies of 500 eV (a), 800 eV (b), 1000 eV (c), and 2000 eV (d) and for titanium oxide (TiO x ) at ion energies of 500 eV (a) and 2000 eV (d). Also, in (c) the SE EEDF of the extended Hagstrum model is shown as solid lines, which is discussed later. One can see a pronounced peak around 0 eV corresponding to PEE and peaks at 33 eV and 58 eV presumably originating from Auger processes from the Ti3s and Ti3p state, respectively. The peak at 80 eV and even higher for TiO x cannot directly be explained by Auger transitions. The difference in SE EEDF when metallic Ti and TiO x are compared are much smaller as in the case of Al.  Figure 4 shows the SE EEDF for copper oxide (Cu 2 O) at argon ion energies of 4000 eV (a), and 2000 eV (a), indicated by solid symbols. The solid lines present the SE EEDF of the extended Hagstrum model using P t,63 = 0.01, which is discussed in the following chapter. One can see a pronounced peak around 0 eV corresponding to PEE and a very small peak at 63 eV that could be linked to an Auger process involving the Cu3p state. Apparently, the generation of high energy electrons in the SE EEDF from Cu 2 O is almost absent if compared to Al and Ti.

Discussion
We now apply the concept of the Hagstrum model to the generation of SE during KEE. The idea for such an extended Hagstrum model is illustrated in figure 5. The discrete energies of the SEs in the EEDFs (figures 2-4) suggest that these electrons originate from Auger processes. This Auger process is triggered by the ion-induced ionization of inner shells of the atoms in the solid. This hole can be filled by a CB electron at energy E ′ and an electron at energy level E ′ ′ is ejected. In the framework of the Hagstrum model, the ionization energy E i of the incident ion is replaced by the energy of the hole of the inner shell. The interpretation of the individual factors in equation (3) changes: (i) the number of excited electrons N i (E k ) results from an analysis of the convolution of the density of states at energies E ′ and E ′ ′ in relation to the ionization energy of the ion. In the extended Hagstrum model, these energy dependencies of the density of states do not affect the SE anymore since all Auger electrons inside the solid exhibit an energy E k above the vacuum level; (ii) the escape probability P e approaches 0.5, because all electrons have enough energy to overcome the surface barrier. Half of these electrons move towards the surface; (iii) finally, the probability for neutralization P t may now differ from unity, because it describes now the probability that an incident ion creates an inner shell hole within the collision cascade. This quantity P t can also be larger than unity, if several holes are generated during the collision cascade of a high energy incident ion. To test if the extended Hagstrum model is reliable, it is at first tested for the measured SE EEDF of aluminum and aluminum oxide before being applied to the data of titanium and copper as well. For bench-marking our model approach, we choose the data for aluminum and aluminum oxide, which are already presented in [12]. Since aluminum oxide yields very high SE values and thus a large signal-to-nose ration of the SE EEDF data, it represents a good data set to evaluate the validity of the extended Hagstrum model.
As an estimate for the binding energies of the hole states in Al 2 O 3 , one can use binding energies from photoelectron spectroscopy of ∼72 eV for the Al2p state and ∼23 eV for the O2s state, as being referenced to the Fermi energy. For example, if an electron from the Fermi edge recombines with a hole in the Al2p or the O2s state, a free electron at energies of ∼68 eV and of ∼19 eV should be observed for the work function of 4.2 eV. An Auger electron at 68 eV also constitutes the main Auger signal in photoelectron spectra of Al. In the case of Al 2 O 3 , new lines may appear, because the density of states in an oxide is no longer a simple Fermi well and additional peaks for the Al2p line of 54 eV and of 38 eV are reported [35]. In addition, the electronic system of the solid is also collectively excited by the collision cascade of the penetrating ion. An ioninduced excitation of plasmons (with an energy of 15 eV in metallic Al) and the consecutive shake-up or shake-down processes of the electron on its way to the surface may alter its kinetic energy. Thereby, the line positions from photoelectron spectroscopy can only serve as an initial guess for fitting the SE EEDF spectra.
In the extended Hagstrum model, we use for the sake of simplicity only a single binding energy for the hole state (and not an energy band) and keep the model of free electrons in a Fermi well for the density of states in the valence band. For metallic Al, we use equation (1), to calculate the model input parameter E i , and an E k = 68 eV and assume that E ′ + E ′ ′ = E F as an average value. Such a simple estimate is reasonable to describe the energy balance of the creation of the high energy Auger electrons. In the original Hagstrum model, the different combinations of selecting E ′ and E ′ ′ in a range of E ′ + E ′ ′ = 0 to E ′ + E ′ ′ = 2E F produce the different shapes of the SE EEDFs for different metals. Since only a fraction of the electrons can escape the particular solid, different SEs are predicted. In case of the higher energy Auger electrons, all electrons have the energy to overcome the surface barrier and the different combinations of E ′ and E ′ ′ determine the width of the Auger peak in the SE EEDF. Since our experimental resolution is rather poor in the range of 10 eV, such a detailed EEDF peak analysis is not possible in our case and the simplification of setting E ′ + E ′ ′ = E F as an average value is sufficient.
Given that simple approach based on equation (1), we can convert an Auger peak at E k = 68 eV into a rough estimate for E i of 86.1 eV, which can be compared to the binding energy of the Al2p electron from photoelectron spectroscopy (76 eV) [34] plus the work function (4.2 eV) yielding 80.2 eV. This is consistent given the rather simple estimate following equation (1). More important, the extended Hagstrum model now produces a peak around 68 eV for the emitted electron, which is consistent with tabulated Auger peaks for Al. We then model the SE EEDF by assuming three hole states leading to Auger electrons at, 38 eV (Al2p/Al 2 O 3 ), 54 eV (Al2p/Al 2 O 3 ) and 68 eV (Al2p) plus PEE at ∼5 eV due to the neutralization of the ion. The probability for the Auger process during neutralization is P t ∼ 1 according to the original Hagstrum model. The parameters P t for the neutralization of the valence band electrons with the hole states are free parameters in the extended Hagstrum model. P t is adjusted until the integrated peak areas of experiment and model agree. The resulting SE EEDF is convoluted with a Gaussian width of 8 eV to account for the finite resolution of the energy measurement in our experiment. A similar broadening may also originate from a distribution of the hole states rather than a single energy E i . This cannot be distinguished in our experiment. A typical modeling result is shown in figure 6 for the SE of 1000 eV argon ions incident on Al and Al 2 O 3 . In figure 6, the results of the original Hagstrum model for Al are also presented. These are the peaks around 0 eV. In the extended Hagstrum model for metallic Al, we use P t,38 = 0.1 (the index denotes the generation of a hole that eventually leads to the emission of a 38 eV kinetic energy Auger electron), P t,54 = 0, P t,68 = 0.15; for aluminum oxide, we use P t,38 = 0.2, P t,54 = 1.2, P t,68 = 0.9 (in the modeling of the SE EEDF for the metal, the energy of the Auger electron released from the recombination of the Al2p hole had to be increased by 10 eV to reach decent agreement between model and data. Apparently, the rather simple model is not yet able to reproduce all details of the SE EEDF accurately). Since the extended Hagstrum model can reproduce each high energetic peak in the SE EEDF rather well, it can be used to estimate typical SE EEDF spectra of other metals as well.
In the case of Al 2 O 3 , the contribution of the peaks at 38 eV and 54 eV being a proxy for the presence of the oxide is much more pronounced compared to Al, as being expected. In addition, the factors P t for the oxide are much higher than for the metal. Apparently, the ability to induce an Auger electron by creating a hole on the inner shells of the atoms is much higher in the case of an oxide.
The interpretation of SE EEDF from the extended Hagstrum model is similar to the standard analysis of surfaces using Auger electron spectroscopy, where the occurrence of particular peaks in the SE EEDF is exploited to distinguish the contributions of metallic Al and of Al 2 O 3 in a sample.
The differences in the spectra originate from the factors P t , which are much higher for the oxide than for the metal. The electronic stopping of the incident ion in Al 2 O 3 leads apparently very efficiently to the creation of holes that trigger Auger processes. In the case of a metal, this electron stopping is less efficient in ionizing inner shells and only very few high energy Auger electrons are generated. Now, we apply the extended Hagstrum model to further ion energies, namely 500 eV and 800 eV. Figure 7 shows the SE EEDFs of the beam experiment (data points) and of the original and extended Hagstrum model for argon ions incident on Al 2 O 3 at 500 eV (c), 800 eV (b) and at 1000 eV (a). Results for 1000 eV are the same as in figure 6. The results of the extended Hagstrum model (the energy distribution inside the solid N i (E) and the distribution outside the solid N 0 (E)) are indicated as solid lines. For comparison, the results of the original Hagstrum model for clean Al are presented as dashed lines. Comparing the SE EEDF of the different energies, at 500 eV, a peak around 30 eV occurs which is not reflected by the previously used Auger peaks at binding energies of 38 eV (Al2p/Al 2 O 3 ), 54 eV (Al2p/Al 2 O 3 ) and 68 eV (Al2p). A fourth peak is modeled now: for Auger electrons generated from holes in the O2s state, an Auger peak energy at E k = 27 eV is used to calculate E i , the model input parameter, following equation (1). To summarize, Auger peaks at 27 eV, 38 eV, and 54 eV indicate an oxidized surface, while peaks at 68 eV a metallic surface. Now, the results of the extended Hagstrum model for the three different ion energies are compared using the parameter P t : One can see that the contributions of the different peaks change with energy: at 500 eV P t,27 = 1, P t,38 = 0, P t,54 = 0, P t,68 = 0; at 800 eV P t,27 = 0, P t,38 = 0.7, P t,54 = 1.2, P t,68 = 0; at 1000 eV P t,27 = 0, P t,38 = 0.2, P t,54 = 1.2, P t,68 = 0.9. Comparing the different P t , one clearly sees that the contribution of the different Auger processes shifts from the O2s peak (around 27 eV) to the metallic Al2p (around 68 eV) peak with increasing ion energy. This is reasonable, because the surface is continuously sputter cleaned by the more energetic ions creating a more metallic topmost surface.
The integrated area of the convoluted EEDF, γ model , agrees well with γ exp from the particle beam experiments. The extended Hagstrum model is also applied to the analysis of SE EEDF of titanium, as shown exemplary in figure 3(c). For the SE from the metal, one can observe SE peaks at high energies of 30 eV, 60 eV and 80 eV, especially for ion energies of 800 eV and above. According to the extended Hagstrum model, these peaks should correspond to SEs from Auger transitions in metallic Ti. The binding energies of 37 eV for the Ti3p state and of 62 eV for the Ti3s state should lead to Auger electrons at 23 eV and 58 eV, which is consistent with the data, although the E k ∼ 30 eV is very small. The peak at 80 eV cannot be explained. Even more interestingly, the peak around 0 eV, corresponding to PEE can be reproduced very well, applying the original Hagstrum model. In the case of the SE EEDF for titanium oxide, SE at much higher energy This extended Hagstrum model is also applied to the analysis of SE EEDF of copper oxide, as shown by the solid lines in figure 4. The SE EEDF is dominated by low energy peaks, and high energy SE are almost absent. Only a small peak at 60 eV becomes visible, consistent with photoelectron spectroscopy data for Auger electrons, generated from the relaxation of a hole at the Cu3p level. The measured SE EEDF around 0 eV is much higher than predicted by PEE following the original Hagstrum model. Apparently, KEE in the case of Cu 2 O occurs via a collision cascade among the electrons in the solid that produces low energy SE. The creation of a hole at the Cu3p and the consecutive emission of an Auger electrons is very unlikely. This extended Hagstrum model of the SE EEDF shows decent agreement and is able to motivate peaks in the SE EEDFs qualitatively although the weights P t of the individual Auger transitions remain fitting parameters. The integral over all energies, however, yielding the total SE emission yield scales linearly with the electronic stopping, as already shown in [10]. The linear dependency is expressed by a constant C metal for the metal case (equation (6)) and C oxide for the oxide case with C oxide = C metal · f oxide according to [10]. In the following, we use C b to refer to both constants. This coefficient C b of the KEE model of [10] correlates the linear dependence of the γ with the electronic stopping. This is compared to the fitting parameter P t of the extended Hagstrum model. An SRIM calculation [32] shows that the fraction of the energy loss due to electronic stopping of 1000 eV argon ions in different metals yields almost identical values as for example 33% in Al and 30.5% in Ti. Therefore, the sum of the P t for a single ion energy should scale with C b , when comparing different elements. The values for ∑ P t and C b are compared for the impact of 1000 eV ions, because KEE dominates at this ion energy and C b is an exclusive parameter for KEE only.
To determine C b , the model of [10] was applied using fluxes of oxygen and argon ions of j O = 2.85 × 10 −16 cm −2 s −1 at the samples [12] and j Ar = 2.5 × 10 14 cm −2 s −1 · e −1000 eV/E ion . The oxygen sticking coefficient of 0.015 on Al was measured [15]. For Ti, the same s O is approximated, since it was not measured. Best agreement between experiment and model is achieved for C b = 0.008 for Al, C b = 0.048 for Al 2 O 3 , C b = 0.006 for Ti, and C b = 0.012 for TiO x . For comparison, the sum of P t for 100 eV argon ions is ∑ P t = 0.25 for Al and ∑ P t = 2.3 for Al 2 O 3 . For Al, one can see that C b in fact scales with ∑ P t . For titanium, only P t for metallic Ti could be determined yielding ∑ P t = 0.12. For oxidized Ti, the model does not reproduce the experiments, as explained above.
This indicates that the generation of SEs in the energy range for KEE is strongly linked to the ion-induced ionization of inner shells. The contribution of theses processes is so significant, because these Auger electrons inside the solid exhibit high energies and can easily overcome the surface barrier and escape. The cross-sections for the ionization of inner shell electrons can be found in typical databases [36], which for example show much higher values for Ti and Al compared to Cu. As a result, we do see pronounced high energy SE peaks for Ti and Al, but not for Cu. The inner shell ionization depends on the electronic energy transfer from the penetrating ion to the electrons of the atom in the solid and from the electronic shielding of the individual hole states. Such shielding seems to be significant for Cu with the filled 3d band in comparison to Ti and Al. In the case of the oxides, this shielding is apparently reduced leading to a higher efficiency for the Auger processes and to a higher energetic SEs. The extended Hagstrum model works very well for Ti and Al, where the SE is dominated by Auger effects and even the PEE part at very low energies can be reproduced very well. In the case of Cu, the contribution of high energy Auger peaks is very small, but instead the low energy peak around a few eV is much larger than predicted by the original Hagstrum model. Apparently, in these cases where the shielding of the inner levels is good, the energy transfer by electronic stopping predominantly induce a collision cascade among the electrons of the Fermi see, which eventually escape the solid.
Both models, the extended Hagstrum model and the KEE model can be improved. For the KEE model, γ of only four ion energies were available. More measurements and thus more accurate fits of the KEE model are needed. The sticking coefficients need also be measured more accurately using a quartz microbalance, as explained in [15]. The extended Hagstrum model can be further improved by regarding the proper density of states of oxides instead of the assumption of a simple Fermi well, which is only valid for metals.
A comparison of the γ from the extended Hagstrum model with detailed high resolution γ experiments would be helpful and quantum mechanical model to describe the electrons in the solid. This is, however, beyond the scope of this paper, which is at explaining electron distributions of the SE quantitatively, but in a simplified picture.
The different SE EEDF have an impact on plasma heating in magnetron sputtering discharges. SEs released from the target surface are accelerated in the cathode sheath and are injected in the plasma to dissipate their energy and contribute, thereby, to plasma heating. The energy input into the plasma per SE consists of the acceleration in the plasma sheath and the Auger energy of the electron. This makes the plasma heating in those cases more efficient, when the target consists of metals or metal oxides where the contribution of Auger processes for KEE is significant. This should hold for all transition metals and their oxides. Noble metals should exhibit a smaller contribution from Auger processes to the SE EEDF due to the good shielding of the inner shell electrons. Consequently, the additional plasma heating due to the higher energy Auger electrons in the SE EEDF is less efficient for those materials. Since the energy of Auger electrons is typical 10% of the applied sheath voltage, this difference in energy input to plasma heating by SE is only 10% as well.

Conclusion
The SE EEDF has been measured for Al, Ti, and Cu and compared with an extended Hagstrum model, where the Auger neutralization of an inner shell hole triggers SE emission. Good agreement between measurement and model has been found. These SEs are an important energy input for magnetron sputtering discharges and the additional energy from the Auger process constitute an additional energy input into the plasma. The higher energy peaks in the SE EEDF are dominant for materials with a high cross-section for inner shell ionization by electronic stopping. This holds for most of transition metals and their oxides. In the case of noble metals, this effect should be small. More detailed experiments are required to explore and benchmark this model.

Data availability statement
The data cannot be made publicly available upon publication because the cost of preparing, depositing and hosting the data would be prohibitive within the terms of this research project. The data that support the findings of this study are available upon reasonable request from the authors.

Acknowledgments
This work has been funded by the DFG within the framework of the collaborative research centre SFB-TR 87. The paper reports on the work being performed in the 3rd funding period of the subproject C7 in the SFB-TR 87.

Appendix. Hagstrum model
The original Hagstrum model [22] describes the electron emission of clean metals upon potential electron emission based on Auger neutralization. Figure 1(a) illustrates Auger neutralization for an ion approaching a solid.
During the so-called Auger neutralization, an incident ion is neutralized in front of the surface by an electron at energy E ′ above the bottom of the Fermi well. The released energy is given to an electron at energy E ′ ′ . The kinetic energy of the electron leaving the surface is E k with respect to the vacuum level: or E k with respect to the bottom of the Fermi well: The rate of generation of these SEs is determined by Fermi's Golden Rule: Here, the densities of states are N(E k ), N(E ′ ), N(E ′ ′ ). The Matrix element ⟨i|H|f⟩ is rather energy independent and can be set to unity. The energy dependence of SE is dominated by the changes in the density of states for different metals. To calculate the rate for an Auger transition for all possible states leading to an electron at energy E k , it is necessary to integrate over all states E ′ and E ′ ′ .
with P Ω (θ, E k ) the probability of an electron to escape at an angle θ to the surface normal. This integral can be more easily calculated by using the substitution E ′ ′ = E + ∆ and E ′ = E − ∆. Thereby, when integrating over ∆, the sum of E ′ and E ′ ′ remains the same (see equation (A1)), thus the energy of the electron E k is also fixed. This simplified integral Z over the mean energy E and ∆ is split into two parts: This can be written abbreviated as: with the so-called Auger transform T [37]. The argument of this function corresponds exactly to the value for E at which the argument of the delta function δ(2E + E i − E 0 − E k ) yields zero and thus δ = 1.
Here the quantities N(E) are the occupation of the states in the solid at energy E and results from the product of density of states times the Fermi-Dirac distribution. Since the SE are at high energies, one can neglect the temperature dependence and it is sufficient to consider the density of states up to the Fermi energy. In the simplest model of a free electron gas, this would be just: with n the electron density. The total rate of excited electrons per ion is now obtained by integrating over all states. The coefficient C summarizes the prefactors such as the matrix element.
The probability of exciting an electron to energy E k is for E k > E F : The final number of electrons N i (E k ) produced in the solid must still take into account the probability P t (s, v 0 ) of neutralization of an incident ion with velocity v 0 at location s in front of the solid surface. This quantity is close to unity at the low energies regarded here. P Ω (θ, E k ) is the probability for emission at an angle θ to the surface normal. The final number of excited electrons inside the solid is: Pt(s, v 0 )P k (E k , s)P Ω (θ, E k ) sin θdθdϕ ds.
(A12) Finally, one needs the probability P e (E k ) that the released electron leaves the solid. Here, it is only necessary to integrate over a part of the angular distribution up to a critical angle θ c as illustrated in figure 6 in [22].
Finally, the SEEC γ is: When an electron with energy E k is emitted at angle θ through the surface barrier with height E 0 , one gets an electron at energy E k − E 0 and angle θ ′ in vacuum.
Experiments show that the angular distribution of emission P Ω (θ) is not homogeneously distributed over 4π. Instead, it applies For an isotropic distribution f = 1, and a density of states for free particles ∝ √ E, the escape probability is That is, for E k = E 0 , P e = 0 and for E k → ∞, P e = 0.5. The preference for forward scattering is accounted for by an empirical expression as: For f = 1 i.e. an isotropic distribution, we again get the simple expression (A17). The final number of free electrons produced outside the solid at energy E k is The SE coefficient γ is then the integral over all possible energies of the free particles E k : ORCID iDs R Buschhaus  https://orcid.org/0000-0001-6074-9089 A von Keudell  https://orcid.org/0000-0003-3887-9359