Synergy of experiment and model for reactive HiPIMS: effect of discharge parameters on WOx composition and deposition rate

Reactive high-power impulse magnetron sputtering of tungsten oxide films using metallic tungsten target (72 mm in diameter) in argon-oxygen atmosphere (total pressure of 0.75 Pa) was carried out. The effect of various discharge parameters on the deposition rate and film oxygen concentration was investigated. Moreover, a model combining a reactive high-power impulse magnetron sputtering model and a discharge plasma model for the ionization region was successfully used for deeper insight into the effect of particular discharge parameters such as voltage pulse length (from 100 –800 µs), oxygen partial pressure (from 0.25–0.50 Pa) or the value of pulse-averaged target power density (from 2.5–500 W cm−2). The results of the presented model, most notably trends in the target- and substrate oxide fraction, composition of particle fluxes onto the substrate, degree of W atom ionization or degree of O2 molecule dissociation are discussed and put into context with experimentally measured quantities.


Introduction
In the field of thin-film research and development, reactive high-power impulse magnetron sputtering (r-HiPIMS) has become the centre of attention in recent years. This is thanks to the ability of this technique to produce densified, high-quality defect-free oxide, nitride and oxynitride coatings [1][2][3][4][5][6]. The maximization of the deposition rate during r-HiPIMS has also been studied intensively and many approaches allow one to 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. produce thin films at high deposition rates without sacrificing film quality [7,8]. Much attention is also devoted to the investigation of processes connected with the presence of reactive gas (RG, typically oxygen and/or nitrogen) in the gas mixture and its interaction with the target and substrate surface. There are a few theoretical models describing the complex behaviour of r-HiPIMS plasma discharge that have been developed. In order to be applicable to high-power impulse magnetron sputtering (HiPIMS) discharge conditions, the models of conventional reactive sputtering (e.g. [9][10][11][12][13][14]) were extended to account (especially) for the ionization and return of sputtered metal atoms onto the target [15][16][17][18][19] and the dissociation of RG in the discharge plasma [15,16,19]. Some of those models simulated mainly the composition of the reactive surfaces and the balance of RG in the discharge chamber and the hysteresis effect [17,20], while another focused on the simulation of the discharge plasma during the pulse for a fixed composition of the reactive surfaces [19].
However, there are a lack of publications focused on the deeper understanding of the effects responsible for different film stoichiometry under different discharge conditions (namely voltage pulse length, pulse-averaged target power density, RG partial pressure,etc). In this publication, we clarify the relation between the abovementioned discharge parameters and WO x properties, namely the deposition rate and oxygen content in the film. We have chosen the W-O system since WO 3 is a material that is in demand due to its many potential applications such as the active layer of hydrogen gas sensors [21,22] and as part of electrochromic [23,24] or gasochromic [25] devices. Moreover, tungsten oxide is a convenient choice thanks to its relatively high electrical conductivity that provides fair discharge stability. A new model of the reactive sputtering process was used to calculate the oxide coverage of the target and substrate, the deposition rate of films and other discharge parameters based on the experimental currentvoltage waveforms. For the first time, this model combines an r-HiPIMS model [15] and a discharge plasma model for the ionization region (IR) in front of the sputtered target [26]. By comparing the simulated and experimental results and by evaluating the discharge parameters that cannot be easily measured, we explain the observed experimental trends.

Film preparation
The tungsten oxide films were deposited using HiPIMS sputtering from a tungsten target with a diameter of 72 mm in a stainless-steel vacuum chamber (Leybold-Heraeus LH Z400) pumped by a turbomolecular pump (backed with a scroll pump) and a cold trap (cooled by liquid nitrogen). The magnetron was powered by a unipolar HiPIMS power supply (SIPP2000_USB, Melec GmbH). The base pressure before each deposition was below 1 mPa. The substrate-to-target distance was 70 mm. The depositions were carried out in a mixture of argon and oxygen. The working pressure was set to a constant value of 0.75 Pa. The average target power density was kept constant for all experiments (2.35 W cm −2 ). During the experiments, the values of the oxygen partial pressure, p ox , voltage pulse length, t on , and/or pulse-averaged target power density, S da , were varied.
All specimens were prepared on 10 × 10 mm 2 Si (100) substrates (625 µm thick). Before the deposition, the substrates were cleaned by sonication for 5 min in demineralized water and then isopropyl alcohol. The thickness of the films was within the range of 800-1000 nm.

Film characterization
The elemental composition of WO x films was measured by wavelength-dispersive spectroscopy (WDS, Magnaray Ther-moScientific) conducted in the chamber of a scanning electron microscope (SEM, Horiba, SU-70). The used primary electron energy was 10 keV, the standards of pure tungsten metal (99.95% purity) and hematite (Fe 2 O 3 , 99.97 purity) (Astimex Standards) were used for the quantification of W and O, respectively. For comparison with the model, it is important that the precision of the WDS method can be considered below 1 at.% for both W and O content. The trueness of our measurement, though, can be accurately estimated to be about 3 at.%, but this does not affect the observed trends. The deposition rate was calculated as the film thickness to deposition time ratio. The thickness was evaluated from SEM cross-sectional images.

The r-HiPIMS model
An r-HiPIMS model was used to simulate the HiPIMS deposition processes to gain more insight into the process parameters that are difficult to measure experimentally and to explain the measured dependencies. The model has two parts: (a) a model describing the time evolution of RG partial pressure and the composition of relevant surfaces (target, substrate and chamber walls), and (b) an IR model describing the time evolution of relevant plasma species densities in the region in front of the magnetron (IR) where the electrons are trapped by the magnetic field of the magnetron. Thus, this region is most relevant for capturing the ionization and RG dissociation processes in the discharge plasma. A schematic representation of the model is shown in figure 1.
The composition of the target, substrate and chamber walls is described using compound fraction Θ, which is the fraction of surface covered by stoichiometric compound (Θ = 0 for pure metal while Θ = 1 for stoichiometric compound) as in the well-known Berg model [9]. The compound fraction is calculated from balance equations of the form: where n 0 is the atomic density of the target material (pure metal), h is the layer thickness for which its composition is simulated (~one monolayer), x c is the stoichiometry of the compound, i.e. the number of oxygen atoms for each metal atom in the compound, Θ is the compound fraction in the layer and Γ j is the flux of oxygen atoms to or from the layer. The right-hand side accounts for all the processes changing the compound fraction, such as sputtering, chemisorption and ion implantation for the target, and deposition of sputtered atoms and chemisorption on the substrate and chamber walls. The ionization of the sputtered atoms and subsequent return and implantation into the target is also included. This was confirmed to be critical in r-HiPIMS where the probability of ionization of sputtered atoms is high [27]. This part of the model is based on our previous work [15,16] where you can find more details about the model description of the balance equations.
In this work, the model was extended by (a) adding the balance equation for the RG partial pressure in the vacuum chamber and (b) including several equidistant target layers allowing us to improve the accuracy of modelling the ion implantation. The former accounts for all gains and losses of RG molecules in the vacuum chamber and allows us to calculate the RG partial pressure for a varying RG flow rate. The latter allows us to calculate a depth-resolved composition of the target. Strict mass conservation is enforced for the target layers that are coupled by the transport of material between them. As the target material is sputtered away from the target surface, the oxygen in the target is moved across the layers towards the target surface. On the other hand, when target material ions are implanted into the target, the oxygen in the target layers below the depth of implantation is moved deeper into the target. The IR model calculates the plasma species densities in the IR during a period of the HiPIMS pulse. This is a volumeaveraged model assuming constant densities in the IR, similar to our previous work [26]. The species include Ar, M, R 2 , R, R s , Ar + , M + , R 2 + and R + , where M stands for the sputtered metal atom, R 2 for the RG molecule, R for the RG atom and R s for the (fast) RG atom sputtered from the target. The IR model equations have the form: where the left-hand side is the number change of species k in the IR, the first term on the right-hand side accounts for changes due to the transport of particles from the IR and the second term accounts for the change of particle density due to reactions (mainly, but not exclusively, those involving electrons). A necessary parameter of the IR model is the fraction of ions created in the IR that return onto the target. This return

Ymm
( O sputtering yield as function of Θt

YmmΘt
Ion return probability 0.6 Gas temperature 300 K probability, β, is assumed to be constant and equal for all species. As the rate of ionization of neutral species depends on the electron temperature, T e , and the ion density determines the ion current onto the target, the model uses a known (user input) target current waveform to calculate T e (t) assuming a known (constant) secondary electron emission yield. This T e (t) then determines all the electron reaction constants in the particle balance equations. The two parts of the simulation are coupled together as follows. The RG partial pressure and the compound fractions on the target, substrate and chamber walls calculated for a given time by the reacting surface model enter the IR model. They are assumed to be constant during a single HiPIMS pulse period, see [15,28]. The IR model then provides the densities of species in the IR and the corresponding total fluxes of species onto the target, substrate and chamber walls, which are used in the model for the reactive surfaces. Thus, the two parts of the model are solved repeatedly with mutual exchange of data to integrate in time. It should be noted that due to the significantly different characteristic time scales of the two models (typically µs for the IR model compared to ms or longer for the reactive surface model), it is not reasonable to solve the coupled equations of both models simultaneously.
In the present paper, the model is used to simulate depositions of WO 3 . The geometrical parameters of the model, such as the chamber volume, target diameter and target-substrate distance were set according to the experiments. The oxygen partial pressure is set constant as in the experiments, with the total pressure always 0.75 Pa. The necessary material parameters of the model were set according to table 1. The sputtering yield of W from a W target, Y mm , and the implantation depth profiles for W and O atoms into a W target (not included in the table) were calculated by SDTrimSP [29] as a function of ion energy. Due to the lack of reliable data for sputtering yields from the compound targets, we assumed that the sputtering Te [38] yield of W from WO 3 , Y mc = Y mm /7, and the sputtering yield of O from WO 3 , Y rc = 7 Y mc , to take into account preferential sputtering of O from WO 3 [30]. These fixed values were estimated based on a comparison of experimental and simulated deposition rates of WO 3 and W. The sputtering yield at arbitrary compound fraction Θ t , is calculated by linear interpolation between the sputtering yields from W and WO 3 . The ion return probability is an unknown parameter for the simulated discharge setup. We tested a broad range of values from 0.3-0.9 based on the paper [31] where possible values of the ion return probability span this range depending on the target voltage. The value of 0.6 was used for the final series of calculations in the hope that this is a reasonable mean value suitable for all analyzed regimes, although [32,33] suggest values closer to our upper limit of 0.9. As will be shown in the results, the particular value of the ion return probability has a weak effect on the modelling results. The reactions in the discharge plasma and the corresponding reaction rate constants are summarized in table 2. The model is calculated from initial conditions until a steady state is reached that corresponds to the deposition-averaged conditions obtained in the experiments.
To summarize, the model uses experimental geometry, current and voltage waveforms, Ar and oxygen flow rate or partial pressure, ion return probability and other material parameters (densities, sticking coefficients, sputtering yields, implantation profiles) as input. It solves balance equations for several plasma species in the IR of the discharge plasma and balance equations for oxygen in the target, substrate, chamber walls and chamber volume. Most notably, the model takes into account (a) the ionization of sputtered atoms and the dissociation of oxygen in the discharge plasma and calculates those based on the electron density and temperature, (b) the dissociation of oxygen in the discharge and different sticking coefficients for oxygen atoms and molecules, (c) chemisorption as well as implantation of oxygen into the target and (d) the return of ionized sputtered atoms onto the target and their implantation into subsurface layers of the target. The model is used to calculate the composition of the target and substrate, deposition rate of films and densities of species in the discharge plasma.
Finally, we mention the limitations of the current model. The model is based on the volume-averaged approach (assumes homogeneous density in the IR and homogeneous oxide fraction in the studied surfaces). Thus, it does not resolve spatial inhomogeneities of the calculated quantities and is inherently less accurate than any spatially resolved simulation. Therefore, negative ions are not included now, although their role in r-HiPIMS has been studied [39]. Some of the material parameters such as sputtering yields and sticking coefficients are not well known and can vary significantly based on fine details of the experimental system. Therefore, the absolute values of the calculated quantities should be taken with a pinch of salt. Instead, we focus on observing the trends and make conclusions based on the comparison of model results among different regimes. The oxide fraction Θ is inherently limited to values Θ < 1, and for oxygen-rich conditions, Θ slowly approaches unity. Therefore, in contrast to reality, the model cannot give over-stoichiometric composition of a surface, and, for compositions close to the stoichiometric oxide, the corresponding Θ is likely to be underestimated. The deposition rate of films was calculated from the flux of W atoms onto the substrate assuming a fixed density of the film equal to the density of the stoichiometric oxide, while in reality the density of films is expected to vary with the exact film composition. These limitations of the model will be considered in the ongoing discussion.

Results and discussion
In the following, we present the experimentally measured and calculated deposition rate and oxygen content in the film obtained under different deposition conditions. Phenomena determining the observed trends are explained using different model output quantities, such as target-and substrate oxide fraction, degree of O 2 dissociation, degree of W atom ionization, composition of particle flux onto the substrate or time evolution of particle densities in front of the target. First, we discuss the different behaviour of the reactive DC and HiPIMS processes. Next, we report on the effect of pulse-averaged target power density on the abovementioned quantities. In the last section, we discuss the effect of the voltage pulse length at a constant pulse-averaged target power density.

Comparison of DC and HiPIMS discharge regimes
In figure 2, a comparison of the deposition rate (a) and oxygen content in the film (b) as a function of p ox is shown. In the case of DC, the deposition rate decreases with increasing p ox , which is the expected behaviour observed for many target materials. This is explained by the fact that the oxide coverage of the target surface increases with the increasing oxygen partial pressure and, consequently, the sputtering rate of the metal atoms decreases [30,40]. This is confirmed by the model (not shown), which implements a pre-set dependence of the sputtering yield on the target oxide coverage, Θ t . This is also qualitatively in agreement with the increasing oxygen content in the film, C ox , 75.4 at.% at p ox = 0.25 Pa to 78.6 at.% at p ox = 0.35 Pa, which is correlated with Θ s calculated by the model.
In the case of r-HiPIMS, the situation is more complicated. Higher S da = 250 W cm −2 ('high-power regime') leads to a gradual increase of C ox from 68.1 at.% to 75.1 at.% with increasing p ox (similar to the DC regime), whereas, C ox is almost constant (~75.2 at.%) for the low value of S da = 25 W cm −2 ('low-power regime'). This is not observed in the model results where Θ s monotonously increases with the oxygen partial pressure for both S da = 25 W cm −2 and 250 W cm −2 . In contrast to the DC case, there is no decrease in deposition rate for both the low-and high-power regime. Moreover, for p ox of 0.30 and 0.35 Pa, the deposition rate in the HiPIMS case is higher than in the DC case. This potentially surprising result is not entirely unusual. It was also reported by Hemberg et al for tungsten oxide [41] and Hála et al for niobium oxide [42]. This is primarily caused by a lower oxide fraction on the target (see figure 3). The model results indicate that the oxide coverage of the target decreases with increasing target power density (in a pulse in the case of HiPIMS). Moreover, in figure 3, one of the r-HiPIMS benefits is clearly seen; the Θ s /Θ t ratio (at given p ox ) increases with increasing S da . This means for higher S da the discharge is close to the desired regime; production of stoichiometric films, while the target is as metallic as possible.
There are several processes that affect Θ t and they all change simultaneously when the pulse-averaged target power density in a pulse is changed. Figure 4 shows the effect of the ion return probability on the oxide coverage for the DC and high-power regime. It should be noted that realistic values of the ion return probability probably lie in the range of 0.5-0.9 [31,32]. Overall, for the given conditions, the effect of pre-selected ion return probability is weak and does not change the trends observed, especially the fundamental difference between the DC and HiPIMS case. More specifically, the calculated oxide fraction changes by a few percentage points and the calculated deposition rate (not shown) decreases by 5% in the DC case and 15% for the HiPIMS high-power case when the ion return probability increases from 0.6 to 0.9. In the DC case, Θ t slightly increases and Θ s slightly decreases with an increasing ion return probability. As the sputtering rate of W and its ionization are low in this case, this trend can be explained by the increased attraction of O 2 + ions and their implantation into the target. On the other hand, in the HiPIMS case, Θ t decreases and Θ s increases with the increasing ion return probability, see the blue curves. In this case, the degree of ionization of W in the discharge is high (~70% for S da = 250 W cm −2 resulted from the model, not shown) and W + ions reimplanted into the target effectively decrease the oxide coverage of the target.
If oxygen dissociation was neglected (see the violet curve), the decrease of Θ t would be even more pronounced. However, O 2 dissociation increases the reactivity of O atoms generated in the high-density plasma during the pulse and, thus, increases Θ t and partly compensates the effect of target metallization by W + ion implantation (see again the blue curve, which includes both W + implantation and O 2 dissociation). Overall, the return of W ions onto the target is a significant factor causing the decrease in Θ t in r-HiPIMS discharges in agreement with recent studies [27].
As mentioned, a fraction of the sputtered metal atoms returns onto the target as ions. However, there is considerable increased flux left on the substrate, which is not complemented by a sufficiently high flux of O atoms. This leads to a slightly lower Θ s when compared to the DC case. Figure 5 shows that the ratio of O/W fluxes onto the substrate decreases when the discharge regime is changed from DC to HiPIMS. Here, the difference between the low-and high-power regime is negligible.
As can be observed in figure 6, the current waveform for the high-power regime has a typical shape indicating gas rarefaction [43,44] in front of the target. Note that this effect is difficult to calculate accurately with a volume-averaged model of the discharge plasma [45] and it cannot be adequately implemented in the present model. In the case of reactive sputtering, not only argon but also RG (oxygen in our case) particles (molecules, atoms and ions) are pushed away from the volume between the target and the substrate and, thus, a lower amount of oxygen particles reacts with the arriving W species on the substrate surface. Therefore, it is suggested that gas rarefaction in r-HiPIMS (especially in the high-power regime) also contributes to the lower oxygen concentration in the films, which is in agreement with the measured film elemental composition, see figure 2(b).

Pulse-averaged target power density effect
In this section, the effects of pulse-averaged target power density (ranged from 100-500 W cm −2 at constant t on = 100 µs) on oxygen content in the film and deposition rate will be discussed. Depositions and model calculations were carried out under two different oxygen partial pressures: 0.25 Pa ('lowoxygen regime') and 0.50 Pa ('high-oxygen regime').
Experimentally determined oxygen content in the film, C ox , and model calculations for oxide fraction formed on the substrate and target surface are presented in figure 7. As can be expected, C ox is significantly higher for the high-oxygen regime compared to the low-oxygen regime. With increasing S da , C ox slightly decreases for both low-and high-oxygen regimes, i.e. the film becomes more metallic. In accordance with that, the target surface is also more metallic with increasing S da , as confirmed by the calculated oxide fraction on the target surface (Θ t ), see top panel of figure 7. As expected, the calculated Θ t is also systematically higher for the highoxygen regime. On the other hand, the trend for C ox is not fully confirmed by the model; Θ s is practically constant for the high-oxygen regime, but it slightly increases for the lowoxygen regime. This indicates that the model overestimates the flux of oxygen with respect to the flux of W particles towards the substrate. The bottom panel in figure 7 depicts trends in deposition rate and also shows qualitative compliance between experimentally measured and calculated deposition rates. For the low-oxygen regime, the deposition rate decreases with increasing S da , which is mainly caused by increased ion return onto the target, while the sputtering rate of metals from the target is constant (indicated by the model results, not shown). For the high-oxygen regime, the experimental deposition rate slightly increases with increasing S da , while the calculated deposition rate remains practically constant. This can be explained by the decrease in Θ t , see figure 7 (top panel), which results in a slight increase in the sputtering rate of metals from the target. At the same time, the change in ion return flux is less pronounced in the presented range of S da values (indicated by the model results, not shown). Figure 8 shows the calculated flux of W and O particles (atoms and ions) onto the substrate. For the high-oxygen regime, the flux of O decreases with increasing S da , while the flux of W remains practically constant. Thus, the O/W flux ratio decreases and, therefore, Θ s decreases with increasing S da . On the other hand, for the lowoxygen regime, both O and W fluxes decrease and the O/W flux ratio slightly increases leading to the observed increase in Θ s . Figure 9 shows the degree of O 2 dissociation and W ionization in front of the target as calculated by the IR model. As expected, we observe an increase in both quantities as S da increases. It is interesting to note that for the high-oxygen regime, the W ionization degree between 200-500 W cm −2 does not increase as fast as for the low-oxygen regime. It could be explained by the fact that for the high-oxygen regime, the high fraction of O 2 in the discharge is dissociated (E diss = 5.15 eV) and/or ionized, which consumes part of the energy delivered during the pulse, which cannot be used for W ionization (E iz = 7.86 eV). Thus, the lower amount of W atoms in the high-oxygen regime (because fewer W atoms are sputtered from the target, see higher Θ t in figure 7) and the not so high ionization of W leads to lower losses of sputtered W by the ion return effect, resulting in the non-decreasing dependence of the flux of W onto the substrate on S da (figure 8).
The experimentally measured deposition rate decreases from 44 to 26 nm min −1 , while it slightly increases from 12 to 19 nm min −1 with increasing S da for the low-and high-oxygen regime, respectively. These trends are in very good agreement with the model calculations. The decrease in deposition rate for the low-oxygen regime is well known in non-reactive HiPIMS [46]. Here, it can be mainly attributed to the return of ionized metal atoms onto the target as the degree of ionization  of metal atoms increases with increasing target power density, see figure 9. The model estimates the degree of W ionization in the discharge plasma during the pulse to increase from 50% to 80% when S da increases from 100 to 500 W cm −2 .
Although this ion return effect is also present in r-HiPIMS, the situation is more complicated. First, the film density depends on the film composition and, thus, the deposition rate of metal atoms does not exactly correspond to the deposition rate of films measured in nm/min. Second, the sputtering rate of metal atoms from the target is affected by its oxide coverage which can, in principle, be either increasing or decreasing with the increase in S da , depending on the complex balance between metal sputtering and oxygen implantation.
It is interesting that both the deposition rate and film oxygen concentration decrease with increasing S da simultaneously. In other words, despite the fact that films (as well as the target, according to the model -see target oxide fraction in figure 7) are more metallic for higher S da , the deposition rate is lower compared with lower S da . This is in contrast to the situation in conventional DC, RF or mid-frequency reactive magnetron sputtering where the decrease in oxygen content in the film is always connected with an increase in deposition rate [47]. Again, this is a consequence of the increased return of W + ions onto the target, which effectively lowers the flux of W atoms onto the substrate.
As mentioned above, the deposition rate in the case of the high-oxygen regime slightly increases with increasing S da , which is the opposite behaviour to that observed in the lowoxygen regime. The calculated deposition rate remains practically constant with increased S da , in general. This is also related to the above-discussed fact that the flux of W onto the substrate is practically constant for the increasing S da . However, there is a momentary increase in the calculated deposition rate for S da increasing from 200 to 300 W cm −2 , which is also observed in the experimental results. For the target power density of 300 W cm −2 , the model shows a slight increase in the W flux onto the substrate, which leads to a decrease in the oxide fraction on the substrate and a small increase in the deposition rate.

Voltage pulse length effect
Finally, we report on the effect of voltage pulse length, t on , (at constant p ox = 0.25 Pa, constant S da~2 50 W cm −2 and constant period-averaged target power density of 2.35 W cm −2 ). Thus, we have varied the repetition frequency to keep both pulse-and period-averaged target power densities constant. This complements the previous section where S da was varied at constant t on . The main results are presented in figure 10. The deposition rate slightly increases from 35 to 40 nm min −1 when t on increases from 100 to 200 µs. The same trends were presented, for example, by [48,49] in r-HiPIMS depositions of HfO 2 and WO 3 when t on increases from 80 to 200 µs. This is also in very good agreement with the deposition rate calculated by the model. This could be caused by the lower total amount of W and W + particles produced during the pulse for t on = 100 µs (see values of mean particle densities in figure 11). There is always a time delay between the start of the voltage pulse and the production of sputtered/ionized target particles. In our case, this delay is approximately 20 µs for all voltage pulse lengths, so there is practically no sputtering up to 20 µs into the pulse, i.e. up to 20% of the pulse-on time is 'wasted' for t on = 100 µs, while it is only 10% for t on = 200 µs and it further decreases for longer pulse lengths. The slight decrease in deposition rate from 40 to 38 nm min −1 when t on is increased from 200 to 800 µs (also visible in the calculated trend, see figure 10 bottom panel) is caused mostly by a higher degree of ionization of sputtered W atoms (see figure 12 top panel) and thus more pronounced ion return of W + onto the target.
A monotonous decrease in C ox from 74.0 at.% to 68.1 at.% is observed (figure 10) with increasing t on from 100 to 800 µs. Presumably, this increases the film mass density, which might also explain the abovementioned decrease in the deposition rate for voltage pulse length increasing up to 800 µs.
For the increasing voltage pulse length, the simulations predict a slightly decreasing oxide fraction (figure 10 top panel) on the target and substrate, i.e. the films tend to be more metallic. This is in qualitative agreement with the experiment, although the decrease in oxide fraction in the substrate is not nearly as pronounced as the experimental oxygen content in the film. We suggest that (reactive) gas rarefaction in front of the target due to the sputtering wind effect can cause this more pronounced decrease in film stoichiometry. This effect is not included in the simulation due to its spatial complexity.
The pulse-averaged degree of W ionization and O dissociation, as calculated by the model, are shown in figure 12 (top panel). The increase in W ionization facilitates increased metallization of the target as a result of more ions returning to the target. The bottom panel of the figure shows that the ratio of O/W atoms arriving onto the substrate decreases with increasing t on , which results in the observed decrease of O content in the films.

Conclusion
The presented results show the successful application of a model combining an r-HiPIMS model with a discharge plasma model for the IR. It was used in conjunction with experimental results obtained for r-HiPIMS of WO x films. The main results could be summarized as follows. It was found that there is a fundamental difference between reactive DC and HiPIMS of WO x films. In the case of DC, the deposition rate decreases with oxygen partial pressure (as expected) whereas it is almost constant for HiPIMS deposition. A higher value of pulse-averaged target power density (at constant voltage pulse length) leads to a decrease in oxygen content in the film for both low-and high-oxygen regime. The deposition rate slightly decreases for the low-oxygen regime whereas it slightly increases for the high-oxygen regime (confirmed by the model quantitatively), mostly due to the lower amount of W + and thus lower losses caused by the ion return effect. Finally, it was found that longer voltage pulses lead to lower oxygen content in the film, probably due to more effective oxygen rarefaction caused by the sputtering wind. For short pulse (<100 µs), the deposition rate is lowered due to a significant role of 'wasted' time (~20 µs; time delay between creation of the plasma discharge and release of a significant amount of W atoms from the target). For longer pulses (>200 µs), there is a higher degree of W atom ionization and thus the deposition rate is lowered due to a more pronounced ion return effect.