Physics of high power impulse magnetron sputtering discharges

Physics of high power impulse magnetron sputtering discharges

7

Daniel Lundina , Ante Hecimovicb , Tiberiu Mineaa , André Andersc , Nils Brenningd , Jon Tomas Gudmundssond,e a Laboratoire de Physique des Gaz et Plasmas - LPGP, UMR 8578 CNRS, Université Paris–Sud, Université Paris–Saclay, Orsay Cedex, France, b Max-Planck-Institut for Plasma Physics, Garching, Germany, c Leibniz Institute of Surface Engineering (IOM), Leipzig, Germany, d Department of Space and Plasma Physics, School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, Stockholm, Sweden, e Science Institute, University of Iceland, Reykjavik, Iceland

The most striking difference between HiPIMS and other magnetron sputtering discharges, in terms of the plasma process itself, lies in the high-power discharge pulses applied and the large discharge currents generated. We will therefore start this chapter on the physics of HiPIMS by exploring the current composition at the target surface and the physical and chemical mechanisms operating at different stages of the discharge pulse and afterglow, which give rise to large discharge currents. Of particular interest is how internal process features such as gas rarefaction, ionization of the sputtered species, self-sputter recycling, and working gas recycling can be influenced by (as well as influence) the choice of pulse length, repetition frequency, applied power density, magnetic field strength and topology, target material, working gas, and so on. Using our understanding of the physics behind the discharge pulse, we will then turn to discussing several key aspects in non-reactive and reactive HiPIMS, which includes dealing with the much debated issues of deposition rate as well as loss and transport of charged particles. The latter topic will, by necessity, also address plasma instabilities in HiPIMS.

7.1

The discharge current

The discharge currents realized in the HiPIMS discharge are indeed very high. Typical discharge currents are in the range of a few tens to a few hundreds of Amperes depending on the target size. Thus the observed discharge currents are significantly higher than commonly observed in conventional dcMS or asymmetric bipolar magnetron sputtering discharges. In the following sections, we explain why and how the discharge current is composed and how it evolves in time. In the context of magnetron sputtering discharges, we define the term “nominal power density” as the power of the discharge divided by the area of the target. In this way, we define a useful and simple parameter that helps to compare phenomena of different reports. At the same time, High Power Impulse Magnetron Sputtering. https://doi.org/10.1016/B978-0-12-812454-3.00012-7 Copyright © 2020 Elsevier Inc. All rights reserved.

266

High Power Impulse Magnetron Sputtering

we stress that the nominal power density (or the similarly defined current density) is a simple parameter, whereas the physics is governed by the actual local power density, which can significantly deviate from the nominal, especially when we observe plasma instabilities. The majority of reports in the literature drop the word “nominal” and report target current density.

7.1.1 The discharge current composition To understand the large discharge currents observed in HiPIMS discharges, we start by reviewing an analysis by Huo et al. (2017) of two distinct HiPIMS discharges using the IRM code introduced in Section 5.1.3. Their study gives an insight into the discharge current composition at the target surface as well as the ionization fractions and electron heating mechanisms. The first set of experimental data analyzed was taken from the work of Anders et al. (2007), who used a planar balanced magnetron sputtering discharge equipped with an Al target. The target was 50 mm in diameter. The discharge was operated with argon as the working gas at a pressure of 1.8 Pa. The pulse length was 400 µs, and the power supply maintained the discharge voltage throughout the entire pulse. The complete set of discharge current characteristics was already shown in Fig. 5.9A. The second set of experiments were performed by Mishra et al. (Mishra et al., 2010, Bradley et al., 2015) using a 150 mm-diameter Ti target. The discharge was operated with argon as the working gas at a pressure of 0.54 Pa. Here the discharge voltage was not maintained constant throughout the entire pulse. Fig. 7.1 shows the discharge current composition at the target surface for the discharge with Al target at discharge voltages of 360 V, 400 V, and 800 V calculated by the IRM. Note that for all discharge voltages, the ions carry almost all the discharge current, and the contribution of secondary electrons ID,se is small. When the discharge is operated at 360 V (Fig. 7.1A), the peak discharge current is in the range of a few hundred mA, and the current density is roughly ∼ 30 mA/cm2 (averaged over the entire target area) or in the middle of the dcMS regime (see Section 1.2.1). We see in Fig. 7.1A that the Ar+ ions contribute to roughly 2/3 of the discharge current whereas Al+ ions contribute roughly 1/3. At 400 V (Fig. 7.1B) the peak discharge current has risen to a few Amperes, and the current density to ∼ 250 mA/cm2 , whereas the power density is now ∼ 100 W/cm2 , just below the HiPIMS limit given in Fig. 1.13. Now the contributions of Al+ and Ar+ ions to the discharge current are very similar, whereas the contributions from Al2+ ions and secondary electrons are much smaller. Note that, however, in the initial current peak the Al+ ions have a slightly higher contribution whereas in the plateau region, Ar+ ions contribute roughly to 2/3 of the current. When operating at 800 V (Fig. 7.1C), the peak discharge current is in tens of Amperes, the current density > 1 A/cm2 , the power density ∼ 1 kW/cm2 , and the discharge is operated well into the HiPIMS regime. Now the Al+ ions dominate the discharge current, whereas the contribution of Ar+ ions is below 10% except at the initiation of the pulse. Al2+ ions and secondary electrons have almost negligible contributions. The small contribution of Al2+ ions is consistent with the findings of Jouan et al. (2010) that while sputtering an Al target in an Ar/N2 mixture, they detected Al2+ ions, but their intensity was orders of magnitude lower than for Al+ ions. Thus, when operating

Physics of high power impulse magnetron sputtering discharges

267

Figure 7.1 The temporal variation of the discharge current composition at the target surface for an argon discharge at 1.8 Pa with a 50 mm-diameter Al target for a discharge voltage of (A) 360 V (JD,peak ≈ 0.04 A/cm2 ), (B) 400 V (JD,peak ≈ 0.26 A/cm2 ), and (C) 800 V (JD,peak ≈ 1.32 A/cm2 ). Note the different scales of the y-axes. Reprinted from Huo et al. (2017). ©IOP Publishing. Reproduced with permission. All rights reserved.

a HiPIMS discharge with Al target, the discharge goes into a self-sputter dominated mode as will be discussed in Section 7.2.1. The discharge current composition for the HiPIMS discharge with Ti target is different, as shown in Fig. 7.2, for a peak current density of JD,peak ≈ 3.84 A/cm2 . The largest contribution is here from Ar+ ions (∼ 53%), whereas the contribution of Ti+ ions is somewhat smaller (∼ 28%), and Ti2+ ions have an even smaller contribution (∼ 17%) but still significant. The contribution of Ar+ ions and the sum of the contributions of Ti+ and Ti2+ ions are of similar magnitude. This is consistent with experimental findings that HiPIMS discharges with Ti target can produce significant amounts of multiply charged titanium ions (Bohlmark et al., 2006a, Andersson et al., 2008, Hippler et al., 2019). Bohlmark et al. (2006a) claim that while sputtering a Ti

268

High Power Impulse Magnetron Sputtering

Figure 7.2 The temporal variation of the discharge current composition at the target surface for an argon discharge at 0.54 Pa and pulse frequency of 75 Hz with a 150 mm-diameter Ti target (JD,peak ≈ 3.84 A/cm2 ). Reprinted from Huo et al. (2017). ©IOP Publishing. Reproduced with permission. All rights reserved.

target in an argon discharge up to 24% of the ion flux consists of Ti2+ ions. The difference between the presented two discharges with Al and Ti targets will be discussed further within the framework of generalized recycling in Section 7.2.1.1. One way of evaluating the discharge properties is to compare the ionized density fractions Fdensity as given by Eq. (4.4). We will first focus on the argon working gas. For the discharge with Al target, the ionized density fraction for argon is always well below 10% (Huo et al., 2017). For low discharge voltages, the ionized density fraction for argon follows rather well the time-evolution of the discharge current, whereas for higher discharge voltages, it decreases with increased discharge voltage. Huo et al. (2014, 2017) showed that whereas the discharge current increased with increased discharge voltage, the electron temperature Te substantially decreases. This explains how there can be a decreasing ionization efficiency of Ar with increasing discharge voltage. For the modeled discharge with Ti target, the ionized density fraction for argon reaches at most 18% for the highest peak current, which is significantly higher than for the modeled discharge with Al target. The ionized density fraction for the sputtered metal is considerably higher for the singly charged metal ions compared to the argon ions and reaches values of roughly 60% for the highest peak currents for both Al and Ti targets. The temporal behavior of these ion fractions follows rather well the discharge current evolution, as expected, since a large fraction of the discharge current is carried by the singly charged metal ions, as seen in Figs. 7.1 and 7.2. Concerning the twice ionized metal, the situation is quite different between the discharges with Al and Ti targets. In the case of Al, the Al2+ ion never reaches more than about Fdensity ≈ 1%, and Al2+ ions only play a minor role in the discharge operation, which is in line with the contribution of Al2+ ions to the discharge current (as seen in Fig. 7.1). This also means that the secondary electron emission due to aluminum ion bombardment is negligible, since singly charged Al+ ions have a secondary electron emission yield close to zero (see also Section 1.1.4), while very few Al2+ ions are present. However, for the Ar/Ti discharge, Fdensity for Ti2+ is about one third of Fdensity for Ti+ . Note that the second ionization energy of Ti is 13.58 eV, significantly lower than the second ionization en-

Physics of high power impulse magnetron sputtering discharges

269

ergy of Al, which is 18.8 eV, whereas the first ionization energy of argon is 15.76 eV. Thus we would expect a much higher density of Ti2+ ions when operating with a Ti target than that of Al2+ ions when operating with an Al target. In summary, there is a significant change in the ion current composition to the target when moving from dcMS-like to HiPIMS discharge currents, which is also reflected in the ion composition in the magnetic trap (ionization region) above the target. The composition also changes in time and gives rise to the observed discharge current variations during the pulse. However, we still need to identify the physical and chemical mechanisms operating at different stages of the discharge pulse and afterglow, which give rise to the observed compositional variations and ultimately the large HiPIMS discharge currents.

7.2 Discharge modes To define and explore the discharge modes in the HiPIMS discharge, we start by considering a schematic of various HiPIMS discharge current shapes presented in Fig. 7.3. These discharge current waveforms are typically observed for both non-reactive and reactive HiPIMS pulses when the applied peak power density is varied from about 0.1 kW/cm2 up to several kW/cm2 , that is, from the middle of the MPPMS range to the higher end of the HiPIMS range, as seen in Fig. 1.13. In the present example, this corresponds to peak current densities of approximately 0.1 – 1.6 A/cm2 averaged over the entire target area. For simplicity, here we assume square-shaped voltage pulses. The schematic discharge current waveforms of Fig. 7.3 are similar to the set of discharge current data presented in Fig. 7.1A – C for an Al discharge operated at various discharge voltages. In Fig. 7.3 the HiPIMS discharge current waveforms have been divided into five different phases during an approximately 300 µs-long pulse. The choice of a relatively long HiPIMS discharge pulse in the present example is based on the need to explore all the types of discharge regimes reported. The discharge current pulses in this example are shown to develop along different pathways generally characterized by an initial peak followed by a more or less stable current plateau (Fig. 7.1B and bottom current curves in Figs. 7.3) or by an initial peak followed by a second increase of the discharge current (Fig. 7.1C and top current curves in Figs. 7.3). Note that, for each of these different pathways, the discharge current amplitude, the point in time for reaching the peak current, current transitions, and so on are likely to change somewhat depending on discharge conditions, such as target material, target dimension, working gas pressure, gas composition, repetition frequency, magnetic field strength, and other factors (Anders et al., 2007, Magnus et al., 2011, ˇ Capek et al., 2012), and should therefore not be taken as exact values. We propose to suitably categorize these current curves according to the composition of the ion current at the target surface, which reflects the amount and type of ion recycling present in the discharge and which we will deal with in detail in Section 7.2.1. This description is followed by a discussion on the time-evolution of the discharge current in the volume in Section 7.2.2, and the physics involved in the various phases displayed in Fig. 7.3.

270

High Power Impulse Magnetron Sputtering

Figure 7.3 A schematic illustration of the HiPIMS discharge current density (averaged over the entire target) divided into five different phases: Phase 1 (ignition), Phase 2 (current rise to first maximum), Phase 3 (decay/transition from the first maximum to the next phase), Phase 4 (plateau/runaway), and Phase 5 (afterglow). The bottom two curves display an approximately 300 µs-long current pulse, where the current decays after an initial peak at around 80 µs, mainly due to rarefaction of the working gas, followed by a current plateau. The top two curves illustrate considerable ion recycling (working gas recycling and/or self-sputter recycling), where the current may reach a second maximum before the pulse is switched off. The middle curve displays an intermediate state with moderate ion recycling (sometimes denoted working gas-sustained self-sputtering). After Gudmundsson et al. (2012).

7.2.1 The discharge current amplitude We have already in Sections 6.3.3 and 7.1 seen that the discharge current waveforms ID (t) of the HiPIMS pulses show large variations with target material, pulse length, and applied power (Anders et al., 2007), whether operated in metal mode or poisoned mode (Magnus et al., 2012, Gudmundsson, 2016) and depending on the power supply used (as discussed in Section 2.2). With increasing discharge current amplitude, magnetron sputtering discharges have commonly been described (Gudmundsson et al., 2012) as gradually shifting character from working gas sputtering (Lundin et al., 2009), through working gas-sustained self-sputtering (SS) (Huo et al., 2014), and finally, for the highest currents, enter either self-sustained self-sputtering (Anders et al., 2007) or self-sputter runaway (Anders, 2008). An addition to this description is the concept of a working gas recycling trap proposed by Anders et al. (2012a), where working gas ions bombarding the substrate return during the HiPIMS pulse and are subsequently ionized and drawn back to the target to further amplify the discharge current. Anders et al. (2012a) argued that self-sputter recycling and working gas recycling can sometimes combine and lower the threshold for discharge current runaway, enabling this route to high discharge currents also for target materials with self-sputter yields YSS below unity. Definitions of these important discharge operating modes are summarized in Table 7.1.

Physics of high power impulse magnetron sputtering discharges

271

Table 7.1 A summary of the different types of discharge modes of the HiPIMS discharge and how they affect the discharge current. Process Working gas sputtering

Working gas sustained self-sputtering

Self-sustained self-sputtering

Self-sputter runaway

Working gas recycling

Description Atoms and molecules of the working gas, which are ionized and then sputter the target. This assumes no recycling of the working gas ions, i.e., no return of gas atoms from the target. Gas ion current is dominating ID (t). Ionized working gas is required for sputtering enough target atoms that are subsequently ionized and drawn back to the target starting a series of metal (target atom) recycling, which dominates the current. Working gas ion current, however, still provides an important contribution to ID (t). Significant ionization of the sputtered species, where a large fraction of these ions is attracted back to the target to sputter more target atoms, which are subsequently ionized. Through target atom recycling the discharge is maintained with sputtered species only, i.e., the discharge can run without working gas. ID (t) is completely dominated by the ions of the sputtered species. Self-sputtering amplifies itself, and the self-sputter parameter exceeds unity, so that there is a positive feedback, and the self-sputtering accelerates or runs away. Thus the current increases until the power supply reaches its limit. ID (t) is completely dominated by the ions of the sputtered species. Working gas ions are neutralized at the target, but a fraction returns to the discharge during the pulse. These returning gas neutrals are subsequently ionized and drawn back to the target, starting a series of gas-recycling. The working gas ions may carry a large fraction of the (high) discharge current.

Reference (Lundin et al., 2009)

(Huo et al., 2014)

(Anders et al., 2007)

(Anders, 2008)

(Brenning et al., 2017)

To understand the current evolution to high discharge currents, here we will mainly follow the ideas presented by Brenning et al. (2017), which involve analyzing and quantifying the individual contributions of the various ion fluxes to the target (carrying the discharge current), including recycling of ions via self-sputter recycling

272

High Power Impulse Magnetron Sputtering

(SS-recycling) and working gas-recycling (sometimes referred to as process gas recycling or gas-recycling). For the analysis of the combined processes of SS-recycling and working gas-recycling, the generalized recycling model (GRM) will be employed. The GRM was developed by Gudmundsson et al. (2016) for the analysis of a reactive (Ar/O2 ) HiPIMS discharge with a Ti target and later on expanded to other target materials (Al, C, Cu, Ti, and TiO2 ) by Brenning et al. (2017) to cover a wide range of current densities from the dcMS range to the HiPIMS range.

7.2.1.1

The generalized recycling model (GRM)

The basic idea of the GRM is focusing on the ion current at the target surface and neglecting the small electron fraction of the discharge current due to an effective secondary electron emission yield, which is commonly below 0.1 for typical voltages applied to the cathode in HiPIMS operation (as can be seen in Fig. 1.4 for argon ions), that is, it assumes that ID (t) ≈ Ii (t). In the GRM, the ions that hit the target are separated into three groups depending on their history: primary ions of the working gas, which are ionized for the first time, recycled ions of the working gas, and ions of the sputtered material. These components are all illustrated in Fig. 7.4 as parts of a causeand-effect chain of events, which goes from left to right in the figure. Note that the widths of all flow arrows in the figure are drawn consistent with the list of parameter values given in the caption, which is explained below and also used for a numerical example.

Figure 7.4 A schematic illustration of the combined processes of working gas recycling and self-sputter recycling to generate high discharge currents. The widths of the flow arrows are drawn to scale with a parameter combination αprim = 1, ξpulse = 1, αg = 0.7, βg = 0.7, Yg = 0.4, αt = 0.8, βt = 0.7, and YSS = 0.5. This combination is arbitrarily chosen as suitable to illustrate combined working gas-recycling and SS-recycling. Reprinted from Brenning et al. (2017). ©IOP Publishing. Reproduced with permission. All rights reserved.

Physics of high power impulse magnetron sputtering discharges

273

We start with the primary current Iprim , which is defined by those atoms and molecules of the working gas (index g) that are ionized for the first time with probability αprim (close to 1 in Fig. 7.4), then go to the target, and finally sputter with a sputter yield Yg . Thus Iprim acts as a seed for the entire discharge current. However, Iprim has an upper limit, corresponding to the case where all incoming gas atoms (often Ar gas) from the surrounding gas reservoir are ionized and drawn to the target. This upper limit was used by Huo et al. (2014) to derive a critical current Icrit . They assumed the thermal refill rate of ambient Ar to be given by the perpendicular thermal gas flux toward the active race track area SRT at pressure pg and gas temperature Tg . All incoming working gas atoms were then assumed to become singly ionized and drawn to the target. This gives   k B Tg 1 Icrit = eng SRT = epg SRT , (7.1) 2πMg 2πMg kB Tg where kB is Boltzmann’s constant, ng is the working gas density, and Mg is the mass of the working gas atom. For a gas temperature of 300 K, this gave an estimate of the maximum primary current given in practical units as Icrit = 0.38SRT pg ,

(7.2)

where SRT is the race track area in cm2 , and pg is the working gas pressure in Pa. In magnetron sputtering, it is often easier to use the average current density over the whole target area ST . For typical magnetron sputtering discharge parameters (T = 300 K, SRT = 0.5ST , and argon at pg = 1 Pa), this gives the critical current density Jcrit =

Icrit = 0.2 A/cm2 . ST

(7.3)

Conventional dcMS devices are operated well below this critical current density, and therefore there is no need for ion recycling, whereas for JD ≥ Jcrit , recycling is needed. This is the case for the HiPIMS discharge, where JD is commonly a factor 3 – 20 higher than Jcrit (see also Section 1.4.4). For example, the critical current for the discharge with Al target discussed in Section 7.1.1 is Icrit ≈ 7 A. Fig. 7.1 shows that the experiment with Al target is operated with discharge currents from far below Icrit to high above it, up to 36 A. Also, the discharge with the Ti target discussed in Section 7.1.1 is operated with peak discharge currents far above the critical current (up to 650 A while Icrit ≈ 19 A). So a significant fraction of the discharge current has to be recycled in both cases. From Fig. 7.4 we find that there are two ways to generate more ions going to the target and thereby to increase the discharge current ID (t) beyond Icrit : (i) recycling of working gas atoms from Iprim and (ii) recycling of sputtered target atoms. We start by looking at the possibility of working gas recycling. In this scenario the ions that constitute Iprim are neutralized at the target, and a fraction ξpulse returns to the discharge during the pulses. As discussed by Huo et al. (2014), embedded Ar atoms are most likely to leave the target when it is bombarded by ions. This corresponds to the

274

High Power Impulse Magnetron Sputtering

value ξpulse = 1, which will also be used here. The returning working gas atoms are subsequently ionized with probability αg and drawn back to the target with probability βg . The remaining fraction of the working gas ions (1 − βg ) goes to the surrounding volume. These steps constitute a first cycle in the working gas recycling loop (seen in the left-hand side of Fig. 7.4), where a recycled current Iprim πg is added to Iprim , and πg = αg βg ξpulse

(7.4)

is the working gas-sputtering parameter as defined by Gudmundsson et al. (2016). Each subsequent cycle adds yet another contribution to the working gas current by  n multiplying the recycled current with πg . Since ∞ n=1 a = a/(1 − a) for 0 < a < 1, it is possible to express the total current carried by recycled working gas ions in steady state (n → ∞) as a mathematical series of the form Igas-recycle = Iprim

πg . 1 − πg

The total current carried to the target by working gas ions therefore becomes   πg Ig = Iprim + Igas-recycle = Iprim 1 + . 1 − πg

(7.5)

(7.6)

This current can become much larger than Iprim if the denominator in the parenthesis approaches zero, that is, if πg approaches unity. We now turn to the possibility of recycling sputtered target atoms, referred to as self-sputter recycling (seen in the right-hand side of Fig. 7.4). Each ion of the working gas that constitutes Ig (Eq. (7.6)) sputters target atoms with a sputter yield Yg , which are subsequently ionized with probability αt and drawn back to the target with probability βt . This is the start of a self-sputter recycling process. It is almost identical to the working gas recycling, except that it relies on the self-sputter yield YSS , and it is therefore possible to apply the same way of reasoning for expressing the self-sputter current amplification. The total self-sputter current generated by Ig (acting as seed) with the subsequent SS-recycling added becomes (Gudmundsson et al., 2016)   Yg πSS , (7.7) ISS = Ig 1 + YSS 1 − πSS where the self-sputter parameter (Anders, 2008, Gudmundsson et al., 2016) is πSS = αt βt YSS .

(7.8)

Adding the currents given by Eqs. (7.6) and (7.7) gives the total ion current Ii . Thus the total discharge current can now be written as    πg Yg πSS 1+ ID ≈ Ii = Iprim + Igas-recycle + ISS = Iprim 1 + 1 − πg YSS 1 − πSS (7.9)

Physics of high power impulse magnetron sputtering discharges

275

Figure 7.5 The recycling map (slightly modified from Brenning et al. (2017)). The ion current mix of Iprim , Igas-recycle , and ISS to the target in a magnetron discharge is defined by a point. For ISS /ID > 0.5, we have the SS-recycle-dominated regime A and, for Igas-recycle /ID > 0.5, the gas-recycle-dominated regime B. As an example (described at the end of Section 7.2.1.1), the parameter combination used for Fig. 7.4 is represented by a filled circle inside the AB regime. Note that the value of Iprim /ID , 39% in this example, is read on the diagonal lines. Iprim /ID ≥ 0.85 defines the dcMS regime, whereas Iprim /ID < 0.5 defines the recycling regime (blue-shaded region (gray in print version)).

or ID ≡ Iprim gas-recycle SS-recycle .

(7.10)

The last step defines the two amplification factors gas-recycle and SS-recycle as the two parentheses in the step before, respectively. Note that there is an asymmetry in Eq. (7.9) between the two types of recycling. This is more clearly seen in Eq. (7.6), where the working gas ion current Ig is completely independent of how large the selfsputter current ISS is. The primary current Iprim , amplified by the first parentheses in Eq. (7.9), is therefore a one-way seed for the self-sputter process, without any feedback in the other direction, that is, from self-sputtering to working gas-recycling. The process can be seen as a food chain: the current Iprim acts as a seed for the working gas-recycling process, which enhances it with the factor gas-recycle . The resulting total current Ig of ionized working gas atoms then acts as the seed for the self-sputter process. If πSS > 1, then the discharge goes into runaway. If not, then the current is further amplified by the factor SS-recycle . Let us now see how the GRM framework, developed above, can be put to use in order to quantify the type and the amplitude of ion recycling. As a suitable tool to illustrate such an analysis, Brenning et al. (2017) proposed the use of a recycling map, similar to that shown in Fig. 7.5, which, for a given discharge, shows the fractions of Igas-recycle and ISS compared to the total discharge current ID on the x- and y-axes, respectively. If the ion mix bombarding the target in a discharge is known, then it can be represented on the recycling map by a point. Above a diagonal line where Iprim /ID < 0.5 in Fig. 7.5 (blue shaded region (gray in print version)), the discharges are dominated by ion recycling. This recycling regime is subdivided into an SS-recycle dominated regime A (ISS /ID > 0.5), a working gas-recycle dominated

276

High Power Impulse Magnetron Sputtering

regime B (Igas-recycle /ID > 0.5), and a mixed-recycling regime AB in between. The region where Iprim /ID ≥ 0.85 represents dcMS-like discharge currents, where little ion recycling is needed. As a demonstration of how to use the recycling map, we take as an example the discharge given in Fig. 7.4. By inserting the corresponding values αprim = 1, ξpulse = 1, αg = 0.7, βg = 0.7, Yg = 0.4, αt = 0.8, βt = 0.7, and YSS = 0.5 into Eq. (7.7) along with ID ≈ Ii = Iprim + Igas-recycle + ISS from Eqs. (7.6) and (7.9) and Igas-recycle = αg βg ξpulse Ig we find that Igas-recycle /ID = 0.37 and ISS /ID = 0.24, which is marked by a filled circle in Fig. 7.5. This discharge is found in the mixed-recycling regime AB, as expected, based on the widths of the flow arrows for the recycled currents in Fig. 7.4. In this case, the primary current Iprim is the seed for a considerably higher discharge current ID , since Iprim /ID = 1 − Igas-recycle /ID − ISS /ID = 0.39 by Eq. (7.9).

7.2.1.2

Discharge analysis

Analysis of several discharges using the generalized recycling model shows that the self-sputter yield YSS is the key parameter, which determines the type of ion recycling at high discharge currents. The starting point is the recycling map introduced in the previous section and here shown in Fig. 7.6 displaying discharges with five different targets. The five different discharges are based on TiO2 , C, Ti, Al, and Cu targets with self-sputter yields in the range from 0.1 (TiO2 ) to 2.6 (Cu) (Brenning et al., 2017). These discharges exhibit discharge current densities of JD ≈ 0.6 to 3.1 A/cm2 , averaged over the entire target surface, that is, in all cases well above the typical Jcrit ≈ 0.2 A/cm2 of Eq. (7.3). A summary of the discharge characteristics is provided in Table 7.2 to establish the necessary background for the following discussion on ion recycling. The required fractions of ISS /ID and Igas-recycle /ID needed to pinpoint these discharges on the recycling map in Fig. 7.6 were either extracted directly from modeling using the previously discussed IRM code (see Section 5.1.3) or assessed by analyzing the discharges by other means. The details can be found elsewhere (Brenning et al., 2017). From the combined results on ion recycling from these five different discharges displayed in Fig. 7.6 and described in Table 7.2 we see that a combination of working gas recycling and self-sputter recycling is generally involved at high discharge currents, beyond the critical current of Eq. (7.2) (all the discharges are in the blue-shaded region (gray in print version), in which the recycling current dominates over the primary current). Furthermore, high-YSS target materials result in discharges of type A (dominated by self-sputter recycling), whereas low-YSS materials give discharges either of type B (dominated by working gas recycling) or of mixed case AB. In type A discharges, large amounts of target material atoms are sputtered, which are easily ionized and can thereby achieve effective self-sputter recycling, which ultimately enables high discharge currents. Type A discharges with high YSS and operated with long pulses all saturate at steady-state plateau values (see Table 7.2) that can be gradually increased by increasing the discharge voltage, as earlier exemplified for a discharge with Al target and shown in Fig. 5.9 and discussed by Huo et al. (2014, 2017). The main reason

Physics of high power impulse magnetron sputtering discharges

277

Figure 7.6 A recycling map showing five discharges with typical HiPIMS discharge current densities of JD ≈ 0.6 – 3. A/cm2 taken over the whole target, and with self-sputter yields in the range from YSS ≈ 0.1 (TiO2 ) to 2.6 (Cu). Reprinted from Brenning et al. (2017). ©IOP Publishing. Reproduced with permission. All rights reserved.

Table 7.2 Overview of the five HiPIMS discharges investigated displaying the discharge voltage VD , the self-sputter yield YSS , the current density JD , and the pulse current evolution. The discharges are listed in order of decreasing self-sputter yield of the target material. The span in YSS for the TiO2 target is due to the various possible combinations of self-sputtering ions (Ti+ and O+ ) and sputtered atoms (Ti and O). The references point to the original works, where these discharges were first reported. Target

VD [V]

YSS

JD [A/cm2 ]

Cu

600

2.6

1.3

Al

600

1.1

0.6

Ti

630

0.7

0.6

C

1150

0.5

3.1

TiO2

600

0.04 – 0.25

1.6

Current evolution Stable plateau Stable plateau Stable plateau Current jump Triangular rising

Reference (Andersson and Anders, 2009) (Anders et al., 2007) (Magnus et al., 2012) (Anders et al., 2012a) (Magnus et al., 2012)

for such a stable current evolution with increasing discharge voltage was identified by Huo et al. (2014) as an increase in the self-sputter yield with increasing ion bombarding energy. They argued that a simplified relation between the sputter yield and the discharge current can be found from the expression for the total discharge current due to ion recycling, Eq. (7.9), with the assumption that the current above Icrit is mainly due to self-sputter recycling for type A discharges. The discharge current can then be simplified to ID ≈ Iprim

αt βt Yg . 1 − αt βt YSS

(7.11)

278

High Power Impulse Magnetron Sputtering

As long as the product αt βt YSS stays below 1 (no self-sputter runaway, described at the end of this section), the current can increase smoothly with increasing discharge voltage because YSS is a smooth function of the ion energy (see Section 1.1.7). The two cases with low YSS , that is, type AB and B discharges, exhibit a more complex current evolution. In one case (TiO2 ), there is no plateau (Magnus et al., 2012). Here the current increases with time during the whole pulse, with no sign of saturation (Gudmundsson et al., 2016). In the other case (carbon target), there are plateau currents, but they jump abruptly with increasing voltage, from a value below Icrit to a current high above Icrit (Anders et al., 2012a) (see also Table 7.2). These discharges do not sputter significant amounts of target material but instead rely on ionization of the working gas, which is mainly Ar. This implies a larger contribution of hot secondary electrons, since the secondary electron emission yield due to bombardment by Ar+ ions is γsee,Ar+ ≈ 0.1, whereas for singly charged metal ions, γsee,M+ ≈ 0. This important difference between type A and type AB/B discharges was quantified by Brenning et al. (2017), who investigated the trends in the fraction of secondary electron density to the total electron density (hot and cold thermal electrons eH and eC , respectively) neH /(neC + neH ), as well as the electron temperature Te . The data was taken from the discharges with TiO2 , Ti, Al, and Cu targets summarized in Table 7.2. In Fig. 7.7, this data is plotted versus self-sputter yield. The carbon case was not included due to lack of data. There is a clear trend with a less energetic electron population (both fewer hot secondary electrons and a lower electron temperature) with increasing self-sputter yield. The trend in hot electron density can be understood as follows: The TiO2 discharge is of type B and thereby dominated by working gas recycling. This discharge has the largest population of hot electrons because essentially all the bombarding ions (mainly Ar+ , but also O+ and Ti2+ toward the end of the pulse) contribute to the secondary electron emission, as verified by Gudmundsson et al. (2016). In the discharge with a pure Ti target, on the boundary between type AB and type A, only half of the ions contribute to the secondary electron emission (Ar+ and Ti2+ ), whereas the other half does not contribute at all (Ti+ with γsee,Ti+ ≈ 0) (Gudmundsson et al., 2016). This trend continues to the extreme type A discharges with Al and Cu targets, which are dominated by self-sputter recycling, and where the singly charged metal ions (Al+ and Cu+ ) carry almost all of the discharge currents (see Fig. 7.6). These ions release no secondary (hot) electrons, which leads to a low fraction of hot electrons in the EEDF of the type A discharges. That these discharges also have a lower electron temperature seems puzzling at a first glance. We might expect the discharge to compensate the lack of hot electrons with more efficient Ohmic heating, which would give a higher Te . However, this seems not to be needed, probably because type A discharges are dominated by the sputtered species, which are relatively easy to ionize. In contrast, type AB/B discharges can also reach high-current operation in HiPIMS, but they require a high-energy EEDF to enable the significant ionization of Ar needed for working gas-recycling (Brenning et al., 2017). In this scenario the sudden current jump with increasing discharge voltage of the investigated carbon discharge is due to working gas-recycling having a threshold behavior related to the requirement that returning Ar atoms from the target need to be ionized during one crossing time across the ionization region. For this to occur, a sufficiently high plasma density has to be

Physics of high power impulse magnetron sputtering discharges

279

Figure 7.7 Features of the EEDF versus the self-sputter yield. Black circles: the fraction of the secondary (hot) electron density to the total electron density. Red squares (gray in print version): electron temperature. Reprinted from Brenning et al. (2017). ©IOP Publishing. Reproduced with permission. All rights reserved.

reached at the beginning of the pulse to establish a loop in which a growing working gas-recycled current exceeds Icrit . For type AB/B discharges with low YSS , there is no stable operation at intermediate discharge currents, between Icrit and some much higher current, and hence the sudden current jump (Brenning et al., 2017) which has ˇ been observed experimentally (Anders et al., 2012a, Capek et al., 2012). It remains to discuss the cases with continuously increasing discharge currents during the pulse. In self-sputter dominated (type A) discharges, unlimited runaway, that is, an unlimited current increase at a fixed discharge voltage, is known to be possible (Anders et al., 2007), provided that the condition πSS = αt βt YSS > 1 is fulfilled. Physically, sputtering of new target atoms provides the source of new ions to the recycling loop that is needed for the current to increase in time. When YSS > 1 this is, in principle, an infinite source, and the current can therefore increase without a limit. The current rise limit is only imposed by the pulse cutoff. For a discharge where YSS < 1 (type AB and B), such as the TiO2 discharge, which also may exhibit an increasing current during the pulse, the situation is different. From Eq. (7.10) we see that self-sputter recycling gives a current amplification with a factor SS-recycle . This amplification is generally limited when YSS < 1. Working gas-recycling can give a separate amplification by a factor gas-recycle , but this factor never causes unlimited runaway for the reason that ξpulse ≤ 1, which (since also αg < 1 and βg < 1) gives πg = αg βg ξpulse < 1. In the TiO2 discharge, it was found that the reason for the continuously increasing (high) discharge current was due to a combination of high working gas ionization probability αg and high return probability βg (Gudmundsson et al., 2016). Then the current amplification factor gas-recycle of Eq. (7.10) can become very large. For the TiO2 discharge, the limiting factor in the product πg = αg βg ξpulse was identified as the ionization probability αg (Gudmundsson et al., 2016). At the end of the pulse, this probability was still a bit below 1, αg = 0.75, but had an increasing trend. The discharge was in a positive feedback loop: (higher αg ) → (higher ne ) → (higher ionization rate) → (higher αg ), and so on, and hence a continuously increasing current is observed. This behavior, applicable to type AB and B discharges, is defined as lim-

280

High Power Impulse Magnetron Sputtering

ited runaway, because the current increase can be large, but, for any fixed voltage, it still is limited by an upper bound (Brenning et al., 2017). It is also worth noting that the observed change in current shape from the stable plateau current for the pure Ti target to the continuously increasing triangular-shaped current seen with the oxidized Ti target (Magnus et al., 2012) has also been investigated experimentally in more detail by Layes et al. (2018) for a Cr target operated in an Ar/O2 mixture. They used in situ spatially resolved X-ray photoelectron spectroscopy (XPS) to measure the surface composition of the Cr target when operating in the entire range from metal to compound mode. Only when the target race track was completely covered by an oxide layer, they recovered the triangular pulse shape. In all other cases, a plateau current was observed. In fact, they found that if at least 20% of the target area is metallic, then metal atom recycling dominates despite the significant oxidation, and a plateau current is observed.

7.2.2 Temporal evolution of the discharge current We now address the time-evolution of the discharge current waveform, which involves discussing the physical mechanisms operating during the five phases shown in Fig. 7.3. We focus our discussion on experimental and modeling data from the commonly reported high-current pulses, represented by the middle and top curves in Fig. 7.3. However, also the low-current cases will be addressed where appropriate. Phase 1 (ignition) covers approximately the first 10 µs of the discharge pulse, which constitutes the ignition phase during which there is negligible plasma in the bulk volume of the discharge chamber. The discharge will likely ignite as a localized glow discharge at the target surface in the vicinity of the anode ring where the vacuum electric field is strongest. An example is seen in the current transport in Fig. 7.8A, where the initially small discharge current is mainly found being radially transported close to the target surface in the case of a circular magnetron target (Lundin et al., 2011). An obvious question is when can we expect to see the current rise in relation to the applied discharge voltage, as exemplified by the ∼ 10 µs-long delay to the current onset in Fig. 7.3. Experimentally it is known that the delay between the onset of the discharge voltage and the discharge current depends on the working gas pressure (Gudmundsson et al., 2002), working gas composition (Hála et al., 2010), target material (Hecimovic and Ehiasarian, 2011), and applied voltage (Yushkov and Anders, 2010). As was discussed in Section 2.2.5, the delay time increases with decreasing working gas pressure and can be in the range of a few µs to over 100 µs (Gudmundsson et al., 2002, Poolcharuansin et al., 2010). If the pressure is very low and the delay time is significant, then the plasma cannot fully develop within the pulse, and if the delay is longer than the actual pulse width, then the plasma will not ignite at all. To prevent this situation, Poolcharuansin et al. (2010) have demonstrated how a dc preionizer can be used to reduce or eliminate the time lag and thus the ignition delay time in a HiPIMS discharge when operating at pressures below 0.1 Pa (see also Section 2.2.4). By particle-in-cell modeling, the effect of pre-ionization has also been

Physics of high power impulse magnetron sputtering discharges

281

Figure 7.8 Analysis of the current transport in a HiPIMS discharge during (A) phase 1 – 2 (ignition and initial current rise), (B) phase 3 (decay/transition), and (C) phase 3 – 4 (decay/transition and plateau/runaway) above a 6” magnetron (7.6 cm radius) based on measured current densities in a Cu discharge with argon as the working gas at 0.53 Pa. The net current flow across the different boundaries of two cylindrical volumes in the discharge, between z coordinates 0 – 4 cm and 4 – 8 cm, respectively, is shown. The areas of the block arrows are drawn proportional to the currents, which are also given as a percentage of the discharge current. The ellipses above the target race track represent cross-sections of the dense plasma torus developing during the discharge pulse. The peak current was 145 A, which corresponds to a peak current density of 0.8 A/cm2 . The race track is centered at approximately r = 4.5 cm, z = 0 cm. The grounded anode ring is shown as a hatched rectangle above the edge of the target surface. Reprinted from Lundin et al. (2011). ©IOP Publishing. Reproduced with permission. All rights reserved.

demonstrated to lead to the rise of the discharge current by two orders of magnitude in ∼ 2 µs (Revel et al., 2018). The discharge characteristics of such a situation is shown in Fig. 5.2. During the ignition phase, time-resolved tunable diode-laser absorption spectroscopy measurements by Vitelaru et al. (2012) show that there is a very strong increase of the density of the metastable working gas atoms (Arm ) before the discharge current increases, as can be seen in Fig. 7.9. These results are consistent with the particle densities previously discussed in Section 4.2 and shown in Fig. 4.13B, where the Arm density starts to increase already within the first 5 µs, although the discharge current ID (t) is still very small (see Fig. 4.3 of Section 4.1.2). The sudden rise in the Arm density is due to the metastable density being built up practically without any losses during phase 1 (Stancu et al., 2015). This behavior is different from the temporal variation of the densities of the charged particles, since these carry the discharge current and therefore are continuously lost, electrons to the surrounding plasma volume and ions both to the target and the surrounding plasma volume. It should also be noted that the increase in the Arm density occurs before we can detect a significant density of sputtered material, since little sputtering can occur due to few ions impinging on the target (see also Section 4.1.2, where the spatio-temporal evolution of Ti+ ions is shown in Fig. 4.4, and Section 4.1.2, where the spatio-temporal evolution of Ti atoms is shown in Fig. 4.13A). As previously described in Section 3.2, Poolcharuansin and Bradley (2010) detected a short burst of hot electrons (70 – 100 eV) within the first 10 µs of the HiPIMS pulse, which would explain the great increase in the number of metastable Arm atoms observed as due to electron impact excitation. Also, a third very hot electron population has been observed during the first two microseconds of

282

High Power Impulse Magnetron Sputtering

Figure 7.9 Typical results of time resolved tunable diode-laser absorption spectroscopy in a HiPIMS discharge taken at 1 cm from the target surface at an Ar working gas pressure of 1.3 Pa. The full black curve displays the HiPIMS discharge current waveform ID (t) (corresponding to a peak current density of 0.5 A/cm2 ) during a 200 µs pulse, the red curve with circles (light gray in print version) is the temperature of the metastable working gas atoms Arm and the blue curve with squares (dark gray in print version) represents the Arm density. Reprinted from Vitelaru et al. (2012). ©IOP Publishing. Reproduced with permission. All rights reserved.

the pulse in PIC/MCC simulations and seen in Fig. 5.18 (Revel et al., 2018). Also, the neutral gas temperature starts to increase reaching values around 600 – 800 K, whereas the discharge current is still very low, as seen in Fig. 7.9 (Vitelaru et al., 2012). This is likely due the increasing amount of collisions with energetic sputtered atoms that are taking place. Using optical emission spectrometry, Hála et al. (2010) find that there is an initial strong increase in the emission from the neutral working gas atoms (Ar) before the discharge current starts to increase, as seen in Fig. 7.10. Phase 2 (current rise) displays the strong initial current increase, commonly seen after the bulk plasma breakdown, as seen in Fig. 7.3. Secondary electrons (hot electrons eH ) and electrons created in the ionization region close to the target (cold electrons eC ) are accelerated out along the magnetic field lines into the bulk volume and begin to ionize the neutral working gas resulting in a strong axial ion current (perpendicular to the target surface) (Lundin et al., 2011). The relative importance of eH and eC is of great interest for the energy balance of the discharge and will be discussed in more detail in Section 7.2.3. A dense plasma torus above the target race track is now also developing (Lundin et al., 2011), as indicated by ellipses in Fig. 7.8A. At this stage the metal atom and argon metastable densities build up, whereas working gas rarefaction sets in, mainly due to ionization losses (Huo et al., 2012), as previously discussed in Section 4.2.2. The metastable Arm density, which during phase 2 becomes coupled to the ground state Ar density, peaks and subsequently decreases (Stancu et al., 2015). The reason for this coupling is that Arm loss processes, such as Penning ionization of the sputtered atoms and electron impact ionization of neutral metastable gas atoms, have come into play (Vitelaru et al., 2012, Gudmundsson et al., 2015). However, the role of Penning ionization is small. Stancu et al. (2015)

Physics of high power impulse magnetron sputtering discharges

283

Figure 7.10 (A) Discharge current and voltage waveforms, where the discharge current peak corresponds

to a peak current density of approximately 2.5 A/cm2 , (B) optical emission from Cr, Cr+ , and Cr2+ , and + (C) optical emission from N2 , Ar, N+ 2 , and Ar for an HiPIMS discharge operated in an N2 /Ar (1/1) mixture at 1.3 Pa with Cr target. The three phases observed are by these authors denoted as the ignition phase (I), the high-current metal-dominated phase (M), and the transient phase (T). Reprinted from Hála et al. (2010), with the permission of AIP Publishing.

explain the decrease after the peak in the Arm density during this phase, which is seen in Fig. 7.9, as being due to gas rarefaction. At this time, there is a balance between the ongoing production (mainly electron impact excitation e + Ar −→ Arm + e) and loss mechanisms (mainly electron impact ionization e + Arm −→ Ar+ + 2e). Costin et al. (2011) used fast time-resolved 2D imaging to explore short pulses. They followed the emission of Ar and Al lines in an Ar/Al discharge looking at the Al target during a 4 µs pulse. After a 0.5 µs delay, they see a fast rise in the Ar emission lines to a peak at 1.2 µs into the pulse, which coincides with a rapid expansion of the torus. In contrast, the Al emission lines exhibit the same temporal behavior as the discharge current, a slow increase in the intensity to a maximum 2.8 µs into the pulse. Also, the optical emission spectrometry (OES) measurements reported by Hála et al. (2010) using a Cr target confirm these trends, where a fast increase in the Ar emission is detected before the peak in the discharge current is reached as well as a limited, but visible, increase in the density of the sputtered Cr during the same time, as seen in Fig. 7.10. Also, note that a first increase of the metal ion density occurs at this time, as earlier observed for Ti+ ions in Fig. 4.4 of Section 4.1.2. The occurrence of metal ions is slightly de-

284

High Power Impulse Magnetron Sputtering

layed vis-á-vis the sputtered neutrals (Hála et al., 2010) due to the time it takes to sputter and then ionize these species, also seen in the results from the time-dependent HiPIMS IRM studies (Gudmundsson et al., 2015) and described in Section 5.1.3. Furthermore, electron impact excitation and ionization of the sputtered target atoms will lower the effective electron temperature as the sputtered particle density grows during this early stage of the HiPIMS pulse, since the ionization potential of most sputtered elements is well below that of Ar. We typically find effective electron temperatures around Teff ≈ 2 – 5 eV, depending on the degree of self-sputter recycling, during the pulse (see Fig. 7.7 and Section 3.2 for more detail on the evolution of the electron temperature). As the peak in the discharge current is approached toward the end of phase 2, there is a strong decrease in the density of the metastable argon atoms, whereas the neutral argon temperature TAr begins to increase; see Fig. 7.9 (note that the authors assume that TAr ∼ TArm since Arm are produced by electron impact excitation from Ar and no great additional heating of the Arm is expected (Vitelaru et al., 2012)). Also, there is reported a strong increase in the emission from neutrals and ions of the sputtered material, which is often (but not always) found to dominate the discharge during phases 2 and 3. These trends are clearly shown in Fig. 7.10, where strong emission from neutral Cr atoms and Cr+ ions are detected by OES at the peak in the discharge current ID,peak when sputtering a Cr target in an Ar/N2 mixture (Hála et al., 2010). The same trends were also observed earlier when visualizing the particle densities in an Ar/Ti discharge shown in Figs. 4.13A and 4.4 for Ti atoms and Ti+ ions, respectively. In that case, short pulses were applied (20 µs), and the peak in the discharge current was reached at the end of the pulse, resulting in high Ti atom and Ti+ ion densities at that point in time. During phase 3 (current decay/transition), the bulk plasma density builds sufficiently to admit current closure across the magnetic field lines (i.e., cross-B electron drift toward the anode/ground): first, at larger distances from the target surface illustrated in Fig. 7.8B, but eventually the plasma density above the target race track is high enough so that this route is the easiest for the electron current to cross the magnetic field lines, which results in a more extended axial current, as shown in Fig. 7.8C (Lundin et al., 2011). The plasma potential has been found to be less negative compared to the ignition phase but might still reach down to −40 V close to the target surface (Mishra et al., 2010) (see also Section 3.3.2). At the time around the current peak, a strong reduction of the working gas atom density occurs, referred to as gas rarefaction and discussed in detail in Section 4.2.2. Gas rarefaction is mainly due to (i) electron impact ionization of the working gas and (ii) gas expansion. Electron impact ionization is dominant in the HiPIMS discharge due to the much higher electron densities during the peak discharge current as compared to, for example, dcMS (Raadu et al., 2011). Gas expansion is a result of heating due to momentum transfer in collisions between the background working gas and the increasing amount of sputter-ejected target atoms as well as reflected working gas atoms (Kadlec, 2007), as discussed in Section 4.2.2. Phase 3 begins with a discharge current decrease, which can sometimes be quite large, as shown in Fig. 7.9. When the discharge current decreases, the refill of argon

Physics of high power impulse magnetron sputtering discharges

285

from the surrounding gas reservoir becomes larger than the rarefaction rate, and therefore the Ar density increases again as shown in Fig. 5.13. This has the counterintuitive consequence that the metastable Arm density increases as the current decreases, as shown in Fig. 7.9 (Stancu et al., 2015). Phase 3 does not exhibit a steady state, as can be seen in Fig. 7.3, since it ends when the discharge either goes into the decay phase characterized by a decrease in the discharge current or an ion recycling regime (Brenning et al., 2017) characterized by yet another discharge current increase (or at least a sustained high-current mode), which will be addressed next. Phase 4 (plateau/runaway). This phase can exhibit very different current pathways, as seen in Fig. 7.3. It was discussed in detail in Section 7.2.1 concerning ion recycling to achieve high (or low) currents in long HiPIMS pulses. It is therefore not necessary to repeat the physical arguments as to why we achieve a certain current amplitude during this phase. However, it is worth spending some time looking at the time dynamics involved and connecting it to the general discharge modes presented in Table 7.1. During this phase, a dense plasma torus is now maintained above the target race track in essentially steady state (depending on the current evolution), which leads to considerable ionization in this region (Lundin et al., 2011). As shown in Fig. 7.8C, electrons are now transported across the magnetic field lines B, the entire way from close to the target surface and through the plasma volume until they reach the first grounded magnetic field line, which intersects the grounded anode ring. Axial crossB current transport is now the dominant fraction of the measured total current (88% in the Cu discharge illustrated in Fig. 7.8C), that is, a significant change compared to phases 1 – 2, where most of the discharge current crosses the B-field radially, and close to the target surface (as shown in Fig. 7.8A). Here we can have two scenarios depending on the discharge current amplitude. First, we discuss low discharge currents. In the case of a decaying discharge current (in the sense that the plateau current is lower than the peak current), such as the bottom current density curve in Fig. 7.3, the plasma density is during phase 4 decreased due to working gas rarefaction, which reduces the ionization of the working gas and of sputtered particles and thereby causes a reduced sputtering (i.e. decreasing metal flux) (Lundin et al., 2009). The low-current discharge characterized by Iprim /ID ≥ 0.85 as defined in Fig. 7.5 in Section 7.2.1, is dominated by the neutrals of the working gas and neutral sputtered species as in conventional dcMS. The overall effect on the gas dynamics is a modest gas heating (few collisions) and ultimately a gas rarefaction at the level expected in dcMS operation. Note that at low enough discharge currents the gas rarefaction is replaced by gas refill during this phase, as observed by Huo et al. (2012) and shown in Fig. 5.13. The increase of the working gas density is also consistent with the results of Vitelaru et al. (2012), where they find that the emission from the metastable working gas atoms (Arm ) increases during phases 3 – 4, as seen in Fig. 7.9. The reaction chain involving a replenished supply of Ar followed by an increase of Arm was later verified by Stancu et al. (2015) when modeling the same discharge; see Section 5.2.3.2. For the high-current regimes, the situation is quite different. Let us first consider moderate plateau currents like the middle current curve in Fig. 7.3. As already discussed in Section 7.2.1, this current evolution typically involves a combination of

286

High Power Impulse Magnetron Sputtering

working gas recycling and self-sputter recycling, which increases the discharge current ID (t) beyond the critical current Icrit and thereby leads to significantly higher current compared to the dcMS-like case (bottom curve, Fig. 7.3). Note that the discharge at such current amplitudes is neither defined as pure working gas sputtering nor self-sustained self-sputtering, but instead referred to as working gas-sustained selfsputtering (see also Table 7.1), where the working gas ion current acts as a seed for a stronger metal ion current (Huo et al., 2014). Hála et al. (2010) refer to this phase as the high-current metal-dominated phase since intense emission is observed from both neutrals and ions of the sputtered material. This emission dominates the discharge emission as seen in Fig. 7.10B (except in discharges dominated by working gas recycling (see Section 7.2.1.2)). Huo et al. (2014, 2017) studied a set of discharge voltage–current curves for an Al discharge operated in pure Ar using the previously discussed IRM code (see also Section 7.1.1). For high discharge voltage (VD > 750 V), the metal ion current is about one order of magnitude higher than the working gas ion current during phases 3 and 4 (Huo et al., 2014), which is defined as a type A discharge in Section 7.2.1.2. The authors found that there is a faster and stronger rarefaction of the neutral argon gas with increasing peak-current during phase 3, which affects the amplitude of the following plateau-current in phase 4. If the discharge had remained in the working gas-sustained self-sputtering mode throughout the remainder of the pulse, then the total current should not have increased again. Instead, for VD > 750 V, the discharge current ID (t) increased after a narrow minimum (see Fig. 7.1C) and finally settled at a steady-state plateau that, depending on the discharge voltage, could be even higher than the initial discharge current peak (Huo et al., 2014) (see Fig. 5.13). This was clearly a transition away from the working gas-sustained self-sputtering. By artificially turning off the argon working gas supply in the IRM code during phase 4 the authors found that the discharge had now transitioned into the self-sustained self-sputtering mode for the highest discharge voltage (∼ 1000 V), which roughly corresponds to the second top-most current curve in Fig. 7.3. However, this did not occur for the lower discharge voltages investigated, where instead the discharge died out when the working gas supply was turned off. Furthermore, it ˇ should be noted that Capek et al. (2012) have demonstrated stable sputtering operation for a number of target materials and were able to control the current plateau level in the range of 14 – 105 A by varying the magnetic field strength. By decreasing the magnetic field strength the plateau current can be lowered. It remains to investigate the possibility of self-sputter runaway illustrated by the continuously increasing (highest) current curve in Fig. 7.3, which requires that the self-sputter parameter fulfills πSS = αt βt YSS > 1 (Anders, 2008), as already touched upon in Section 7.2.1.2. Since αt and βt are always ≤ 1, self-sputter runaway requires YSS > 1. Self-sputter runaway can indeed occur for copper and other high-yield materials, including silver and zinc, as pointed out by Anders (2011). However, YSS > 1 does not guarantee self-sputter runaway, since the product πSS = αt βt YSS still has to be greater than 1, hence the onset of runaway at a well-defined (high enough) threshold power, which is set by the discharge voltage. Furthermore, in the seminal work of Anders et al. (2007), where the discharge current waveforms are measured for a number of target materials over a wide range of discharge voltages, sudden and irre-

Physics of high power impulse magnetron sputtering discharges

287

producible current increases up to 5 A/cm2 for both Ti and Nb targets were reported, which indicate the onset of self-sputter runaway. This behavior was observed for a discharge voltage of 600 V, where the self-sputter yields of both Ti+ and Nb+ ions are roughly 0.7 – 0.8, that is, too low for self-sputter runaway. In the Ti case the amplitude of the current was shown to be directly correlated to the Ti2+ ion count in a mass spectrometer. The physical mechanisms involved can be understood directly from the self-sputter parameter πSS = αt βt YSS . The effect of doubly charged ions on πSS is double. First, their impact energy on the target is twice that of Ti+ ions, giving a higher YSS . Second, in contrast to singly charged ions, they release secondary (hot) electrons that add to the ionization rate and increase αt . At some discharge power, these two effects can combine to make πSS > 1, resulting in a rapid current increase and self-sputter runaway. Phase 5 (afterglow). This stage is reached as the HiPIMS pulse is switched off and is characterized by a sharp drop of the discharge current. During the afterglow, Poolcharuansin and Bradley (2010) detect an initial fast decrease of the electron density with a time constant of about 30 µs followed by a much slower decay rate (3500 µs). The effective electron temperature Teff also quickly decays reaching values around 0.2 eV, which is sustained during several milliseconds (Poolcharuansin and Bradley, 2010). In addition, we see in Fig. 7.9 that the density and temperature of Arm are rapidly decreasing as the sputtered flux disappears and the plasma species are lost through recombination and diffusion toward the chamber walls (Vitelaru et al., 2012). The decay of the Arm density is characterized by an initial fast decrease followed by a more slow decay which is due to diffusion of the metastables out of the ionization region. The reason for the initial fast decay is a rapid disappearance of the most energetic electrons that constitute the EEDF. This reduces the rate of electron-impact population of metastable Arm from the Ar ground state while the loss mechanisms are still active: the sum of electron impact ionization (e + Arm −→ Ar+ + 2e, dominating) and electron impact quenching loss to the ground state (e + Arm −→ Ar + e, a smaller contribution) (Stancu et al., 2015). For discharge current evolutions that are characterized by a current peak ID,peak at the end of the pulse, there is commonly also a peak observed in the density of the ionized sputtered material in the immediate afterglow. For example, we found in Fig. 4.4 that the Ti+ ion density peaked about 5 – 10 µs after pulse-off, which was followed by a rather slow decay. On the other hand, if ID,peak was reached much earlier during the pulse followed by a current decrease, such as seen in Fig. 7.10, then low ion densities are expected during phase 5, which is also in agreement with the results seen in Fig. 7.10B. It is worth bearing in mind that the HiPIMS discharge plasma can survive for a long time during the off-time, where a weak electron density was detected for up to 10 ms after the pulse was switched off (Poolcharuansin and Bradley, 2010). Also Hecimovic and Ehiasarian (2009, 2011) have found that working gas ions and various metal ions are long-lived in the HiPIMS discharge and in some cases present during the entire pulse-off time (up to 10 ms), which is described in more detail in Section 4.1.3.2.

288

High Power Impulse Magnetron Sputtering

7.2.3 Ohmic heating versus sheath acceleration As discussed in Section 1.1.1, the dc glow discharge is maintained through secondary electron emission from the cathode surface. These secondary electrons and new electrons created by the onset of electron-impact ionization avalanches within the sheath are accelerated by the electric field within the sheath and gather the energy needed for these (hot) electrons to participate in the ionization processes that maintain the discharge. Sheath acceleration of electrons is important also in the magnetron sputtering discharge but with one important difference: here the ionization mean free path is typically longer than the thickness of the cathode sheath, and electron avalanches cannot begin to develop within the sheath. Therefore, ionization within the sheath is taken into account by multiplying the secondary electron emission coefficient γsee with a factor m that accounts for secondary electrons ionizing in the sheath, as described in Section 1.2.4. Early on, sheath acceleration was believed to be the main source of electron energy also within the magnetron sputtering discharge (Thornton, 1978). However, recently it has been demonstrated that sheath acceleration alone cannot sustain the magnetron sputtering discharge at typical discharge voltages (Huo et al., 2013, 2017, Brenning et al., 2016). As seen in Fig. 1.8, sheath energization, already in dc magnetron sputtering, provides only 30 – 70% of the electron energization. Fig. 1.8 also shows that this fraction depends in a natural way on the secondary electron emission coefficient: a higher γsee gives a larger fraction of sheath energization, and vice versa. In the HiPIMS discharge, sheath energization plays an even smaller role, sometimes almost negligible as recently demonstrated (Huo et al., 2013, 2017). Also, here the general rule holds: a lower secondary electron emission coefficient gives a lower fraction of the total energy spent in sheath acceleration. However, this connection is less strong in the HiPIMS discharges, where the importance of sheath energization is mainly determined by the self-sputter yield YSS of the target. Fig. 7.7 shows an example of this: higher values of YSS are correlated to low densities of hot (i.e. sheathaccelerated) electrons in the discharge. This connection between sheath energization and self-sputter yield can be understood as follows. The value of γsee in a HiPIMS discharge depends mainly on the composition of the ions that hit the target. This, in turn, is determined by the type of ion recycling that dominates in the discharge, which was discussed in Section 7.2.1.1. Fig. 7.6 shows that a HiPIMS discharge with an aluminum target, which is of type A, is dominated (close to 100%) by self-sputter recycled Al+ ions. These have γsee ≈ 0, and therefore the role of sheath energization is practically negligible. In the other extreme, the type B discharge with a TiO2 target is dominated by working-gas recycling. Here 57% of the ion current to the target is due to Ar+ ions with γsee ≈ 0.1 (see Fig. 7.6), which gives significant sheath energization. The “missing electron heating”, the part that is supplied outside the cathode sheath, is commonly called Ohmic heating. This concept was introduced by Huo et al. (2013) and was briefly touched upon in Sections 1.2.4 and 5.1.3. Ohmic heating is a simplified concept based on two time-averaged macroscopic features in the plasma outside the sheath. First, there is an electric field E due to the potential difference across the plasma outside the sheath, in Section 1.2.4 denoted as VIR , which (as discussed in Section 1.2.4) in both dc magnetron sputtering discharges and in HiPIMS discharges is of

Physics of high power impulse magnetron sputtering discharges

289

the order of 50 – 100 V, or 10 – 20% of the applied discharge voltage VD . This is also consistent with 2D PIC simulation results reported by Revel et al. (2018). Second, the electrons carry a fraction Je of the discharge current, a fraction which is small close to the target, but which increases with the distance from the target, so that the electron current dominates at the boundary between the ionization region and the diffusive plasma outside the ionization region. The rate of Ohmic heating of electrons is simply defined by the scalar product Je · E, in analogy with the heating by electric energy dissipation when a current is led through a resistive medium. Provided that the electrons can be assumed to carry typically half of the current in the ionization region, this gives the total Ohmic heating power as POhm = 12 ID VIR (see e.g. Huo et al. (2013)). This is used as a standard assumption in the IRM (see Section 5.1.3). It is important to realize that the concept of Ohmic heating implicitly involves two assumptions: first, that the time-averaged values of E and Je give the correct energy dissipation through the product Je · E and, second, that the electron population is collectively heated and therefore retains a thermal (Maxwellian) energy distribution. The strength of the Ohmic heating concept is that it gives a simple first-approximation physical picture of the electron energy gain outside the sheath; for refined results, the specific mechanism(s) that enable the electron transport across B and in the direction of E (a condition that excludes the Hall drift, which is perpendicular to E) need to be considered. We will return to this issue in Section 7.3.1.2. Further evidence of the differences between the discharges with Al and Ti targets introduced in Section 7.1.1 is found when comparing the fraction of the Ohmic heating (Huo et al., 2013, Brenning et al., 2016) for the Al and Ti targets. For the Al target, the fraction of the total electron heating that is attributable to Ohmic heating is found to be of the order of 99% in the HiPIMS operation regime. This particular result has previously been discussed by Huo et al. (2013), who demonstrated that for a HiPIMS discharge with Al target operated at typical high discharge voltages, almost all of the electron heating is of Ohmic nature and located within the ionization region. The energetic secondary electrons accelerated in the cathode sheath, as well as the twice ionized Al2+ , play very small roles in line with our discussion earlier in this section. For the discharge with Ti target, we instead find a mix of Ohmic heating and sheath energization, which is a result both of the presence of more Ar+ ions and of the ionization degree of Ti2+ being at least an order of magnitude larger than the ionization degree of Al2+ . When operating with a Ti target, the fraction of the total electron heating that is attributable to Ohmic heating is about 92% in the HiPIMS operation regime (Huo et al., 2017).

7.3

Transport of charged particles

It is not straightforward to analyze the motion of charged particles in HiPIMS discharges due to a rather complex nature of the plasma. Still, we can try to find various ways to illustrate the plasma dynamics by studying some simple cases of particle motion. One such example was already given in Section 1.2.2, where it was shown

290

High Power Impulse Magnetron Sputtering

that the Hall drift and the diamagnetic drift give rise to an azimuthal current flowing above the target race track. However, we need to go further in our studies of transport of charged particles to also understand other phenomena, such as the reported backattraction of ionized sputtered species (Christie, 2005), ion azimuthal rotation along the race track (Lundin et al., 2008b, Poolcharuansin et al., 2012, Yang et al., 2015), fast electron transport across magnetic field lines, which carries the discharge current (Lundin et al., 2008a, 2011), and rotating dense plasma structures often referred to as spokes (Hecimovic and von Keudell, 2018). The motion of charged particles is one of the most challenging problems in the physics of the HiPIMS discharge. As discussed in Section 1.2.2, only the electrons are confined by the magnetic field. The electrons gyrate around the magnetic field lines and recoil at the sheath edge. However, local electric fields may be established and consequently drive instabilities, which weaken the magnetic confinement. The key parameters that determine the macroscopic flow speeds ve and vi of electrons and ions, respectively, in the plasma are: the magnetic field B, the gradient in electron pressure ∇pe , the electric field, which here is split up into a “quasi-dc” part denoted by E (which varies on the time scale of the HiPIMS pulse), and a high frequency Ehf part associated with waves, turbulence, and anomalous resistivity and transport, the classical elastic mean free path λcoll for collisions with charged and neutral working gas particles, and the characteristic length scale c of the device. In magnetron sputtering discharges the inequalities rce c rci generally hold, as discussed in Section 1.2.2, meaning that the electrons are magnetized while the ions are practically unmagnetized. Ion-neutral mean free paths are found in ranges from λcoll c to λcoll > c , depending on apparatus size and working gas pressure. However, for the electron flow and transport, classical collisions are usually less important than “anomalous collisions” mediated by the high frequency Ehf fields, which we will return to in Section 7.3.2. In a fluid description, these can be represented by an anomalous effective ion–electron momentum exchange time constant τeff , which, however, only applies to the cross-B component of the electron–ion relative motion (alternatively expressed as resistivity, a tensor η¯ with a small field-aligned component). Often, τeff is referred to as the effective collision time. Hence both species, the electrons and the ions, exhibit an anomalous transport discussed in Sections 7.3.2.1 and 7.3.2.2, respectively. Strongly related to the anomalous resistivity and the related instabilities is the phenomenon of spokes in the HiPIMS discharges (Hecimovic and von Keudell, 2018), which will be addressed in detail in Section 7.4. One way to look at the spoke structures is that they are large-scale versions of two-stream driven microinstabilities, and like these give anomalous transport and azimuthal electron–ion drag and also are involved in the important mechanism(s) of electron heating outside the sheath. The fundamental difference is that the spokes have scale sizes comparable to the plasma characteristic length scale c . An important common feature of both instabilities and spokes is that if they enable cross-B electron transport needed for the electrons to carry the discharge current, then they will also transmit the macroscopic azimuthal Je × B force, which is associated with that current, from the electrons to the ions. We attempt to introduce the mechanisms involved in such a way that they appear in a natural sequence of increasing complexity. Three types of mechanisms need to be

Physics of high power impulse magnetron sputtering discharges

291

considered in HiPIMS discharges: (i) The classical cross-B mobility through collisions between electrons and neutrals, or Coulomb collisions between electrons and ions, (ii) anomalous cross-B mobility through the wave structure in instabilities with length scales c , and (iii) electron cross-B motion in spokes, which have length scales c . In all these scenarios, electrons exchanging momentum with ions or neutrals lead to a shift of the electron guiding centers and a drift across magnetic field lines (recall that the electron is moving in circles around a guiding center in a plane perpendicular to the magnetic field, as discussed in Section 1.2.2). Three types of charged species will be treated: working gas ions, denoted as G+ , ions of the sputtered material, denoted as M+ , and electrons e. For the following discussion, we define z = 0 at the target surface, and the +z-direction is perpendicularly away from the target surface. Also, the most interesting plasma region is above the race track, where B is parallel to the target.

7.3.1 Classical ion and neutral species transport 7.3.1.1

Ion transport

We start by looking at the ions. In Section 7.2.1.2, we saw that a high return probability of the working gas ions βg to the target was beneficial to sustain of the discharge due to a nonzero secondary electron emission. The bombardment of the target by the ions of the working gas provides the discharge with hot secondary electrons for continued ionization. Due to a large cross section for resonant charge exchange collisions, the ion motion of G+ for the simplest case with zero E field (which applies in the afterglow plasma when the pulsed potential is switched off) can, in the first approximation, be treated as diffusion through the background gas. The ion flux is then given by Fick’s law (Lieberman and Lichtenberg, 2005, p. 134) diff = −Ddiff ∇nG+ ,

(7.12)

where Ddiff , for ions, is the ambipolar diffusion coefficient (Chen, 2016). However, both the neutral working gas and the working gas ions are, in addition to the diffusion flux, moving away from the target under the action of the sputter wind (Hoffman, 1985), which also includes fast recombined working gas ions reflected from the target surface (Lundin et al., 2009, Huo et al., 2012), as discussed in Section 4.2.2. This gas flow speed must be added to the diffusion flow speed. Such a situation is, for example, described by the IRM code (Huo et al., 2012) discussed in Section 5.1.3. In the case of significant gas rarefaction, the problem becomes more complicated because the assumption of a collision-dominated regime might no longer be valid. In the zero E field case, the uncollided M+ ion population does not return to the target, whereas the collided population behaves as the G+ ions in the zero E field treated earlier, moving according to the combined mechanisms of diffusion and rarefaction flow. A simple estimate of returning M+ ions in the zero E field can be extracted from the results of Lundin et al. (2013), who used a 3D Monte Carlo code for studying transport of sputtered neutral Ti atoms in Ar gas. From their published velocity distributions of Ti, it is found that about 9% of the sputtered Ti has a velocity directed

292

High Power Impulse Magnetron Sputtering

Figure 7.11 A sketch of back-attraction of ionized sputtered species due to a finite E field extending into the plasma and directed toward the target (−Ez ), which is here displayed as a potential drop (E = −∇V ). The figure is inspired by measurements using an emissive probe in dcMS with Ti target by Bradley et al. (2001).

toward the target (−vz ) at a typical working gas pressure of 0.4 Pa when sampling a small volume above the target race track at z = 1 cm. However, Van Aeken et al. (2008) noted a considerable redeposition on a circular planar magnetron target when simulating sputtering of Al at an Ar working gas pressure of 0.3 Pa, that is, when using a lighter target material compared to the process gas. Rossnagel (1988) also reported a similar trend with higher redeposition when using lighter target materials by experimentally trying to estimate the probability of redeposition on the target using either Al or Cu in an Ar atmosphere. For typical working gas pressures around 0.7 – 1.0 Pa, he found that about 5 – 10% of the sputtered neutrals were redeposited. Based on these results, we might think that return of sputtered material to the target is of limited importance. However, as already discussed in Section 3.3.2, there is usually a nonzero (timeaveraged) E field extending into the plasma and directed toward the target, as seen in Fig. 7.11. This finite E field is a key to understanding the high return probability βt of M+ ions to the target, which is crucial when describing the deposition rate loss (discussed in Section 7.5.1) and when modeling the HiPIMS discharge by the material pathway and the ionization region models (discussed in Section 5.2.1), and a key to Ohmic heating (discussed in Section 7.2.3). Consider the following: Each M+ ion has, at the time and place of ionization, the same initial velocity ui0 as the neutral had (we distinguish here between individual particle velocities u and flow velocities v). After ionization and until the next collision, the ions follow ballistic orbits where the particle acceleration dui /dt (i.e. not ui0 ) is determined by the local electric fields E. Notice that a fluid description cannot accurately describe such a motion. However, a few observations can be made. First, let us consider the consequence of a potential uphill in the z direction as seen in the time-averaged measurements. The collided, thermal, part of the M+ ion distribution is expected to return to the target already at potentials of a few volts, as seen in Fig. 7.11. Uncollided M+ ions, on the other hand, start with ui0 directed away from the target and with the energy distribution of sputtered

Physics of high power impulse magnetron sputtering discharges

293

material given by Eq. (1.28) (Section 1.1.8). Their point of ionization is furthermore determined by their velocity: those with low initial velocity uz spend more time close to the target and are therefore on average ionized closer to the target. These slow ions have both a lower directed kinetic energy in the +z-direction and a larger average potential hill qi U to climb, which creates a high-energy-pass filtering effect. The average point of ionization also depends on time during the pulse: as the discharge current peaks, the plasma density is higher, and ionization occurs closer to the target as the mean free path for electron impact ionization changes from several centimeters to a very small value. As an example, we consider the situation depicted in Fig. 7.11. Take a sputtered atom and let it be ionized 20 mm from the target (left vertical dashed line in the figure). If it has a directed kinetic energy of 5 eV in the +z (axial) direction, gained in the sputtering process, it will be drawn back after less than 10 mm of further flight due to the potential hill (right vertical dashed line). Only atoms that are ionized beyond 40 mm have a chance to escape. Most ions are created in the ionization region next to the target with a potential slope of VIR = 50 – 100 V (Rauch et al., 2012) (see also Section 3.3.2). This is sufficient to draw most of these ions back to the target, and the back-attraction probability is typically found to be in the range 0.8 ≤ βt ≤ 1 (Huo et al., 2013), which is considerably higher than the ∼10% we found earlier for zero E field. We will return to this topic in Section 7.5.1 when discussing loss of deposition rate in HiPIMS. If we instead look at the working gas ion dynamics in a finite E field, where we consider only the component Ez , then we can identify two simple extreme cases. In the collision-free extreme the G+ ions move in ballistic orbits and will end up on the target if, at their point of ionization, their kinetic energy in the +z direction (away from the target) is lower than the remaining potential hill qi U they have to climb in the +z-direction. In the collision-dominated case the electric mobility drift uz = μi Ez is added to (and directed against) the outward flow speeds from the diffusion and the rarefaction flows treated earlier. The G+ ions will move toward the target if they become ionized in a region where this total drift has a negative sign. Revel et al. (2018) have carried out detailed PIC/MCC simulations on the working gas Ar+ ion dynamics, which reveal two different ion groups coexisting during the HiPIMS pulse. The first population is composed of ions created at the boundary between the cathode sheath and the ionization region (see also Section 5.2.3.4), of which a fraction is accelerated toward the target with a high-energy tail corresponding to the potential drop in the cathode sheath only. The second population contains ions created in the ionization region volume. A fraction of these ions are accelerated toward the target by the combined potential drops in the ionization region and in the cathode sheath. In summary, the ion transport speeds can generally be expected to be very complicated functions of both the local parameters and the time histories of the individual particles. In any case, it is important to emphasize that ions reaching the cathode or the substrate are far from a monokinetic flux of particles. Even if the electric potential profile U (r, t) were known, calculations of the ion transport velocity would require PIC simulations or at least Monte Carlo simulations for longer pulses. As an example, Fig. 5.14 shows the 2D maps of the electric field and the plasma potential in front of the target (Revel et al., 2018).

294

High Power Impulse Magnetron Sputtering

7.3.1.2

Classical electron transport

We now turn to the electron motion, starting from the simplest case, the transport along the magnetic field B. The magnetic-field-aligned component ve of the electron drift speed ve is not determined by the local plasma parameters. The reason is that electrons, with their light mass, easily respond by motions along B which minimize departures from the equilibrium state in which the pressure gradient is balanced by the electric volume force ∇pe = ene E .

(7.13)

If there is a loss (or gain) of charge in one part of a flux tube, then electrons are redistributed along it and modify the electric field (through Poisson’s equation) so that Eq. (7.13) is maintained. The component ve is therefore driven by the global cross-B current pattern, which gives the loss (or gain) of charges on different parts of the magnetic field line that drives the redistribution. The collisional parallel resistivity can generally be neglected in this process. In a homogeneous plasma, ∇pe = 0, giving E = 0, and the magnetic field lines are equipotentials. However, in the dynamic and inhomogeneous HiPIMS pulses the full expression given by Eq. (7.13) might be needed, particularly in the region penetrated by high-energy secondary electrons accelerated across the sheath. More interestingly from a magnetron sputtering (HiPIMS) discharge point of view is the component of the electron transport across B, which is in the z-direction above the race track, since this component both carries the discharge current and contributes to Ohmic heating. The cross-B part of ve is split up into two parts depending on the direction with respect to the net cross-B force Fe⊥ = (−∇pe − ene E)⊥ .

(7.14)

Let us consider a circular planar magnetron with azimuthal symmetry, where Fe⊥ lies in the (r, z) plane. In the Fe⊥ × B direction, there is an azimuthal drift speed veφ =

Fe⊥ ωe2 τc2 , ene B 1 + ωe2 τc2

(7.15)

where τc is the classical collision time due to electron–ion (Coulomb) and electron– neutral collisions, and ωe is the electron cyclotron angular frequency (given by Eq. (1.31)). The dimensionless cross-B transport parameter ωe τc is often referred to as the Hall parameter. The Hall parameter is common for electric conductivity, electron diffusion, diamagnetic drift, electron mobility, and the magnetic field diffusion into a plasma (Brenning et al., 2009). In the collision free limit (ωe τc → ∞) the sum of the Hall drift, Eq. (1.33), and the diamagnetic drift, Eq. (1.34), are recovered from Eqs. (7.14) and (7.15). Since the ions are unmagnetized, they have no corresponding drift motion, and the electron drift gives the azimuthal current density Je,φ = −ene veφ .

Physics of high power impulse magnetron sputtering discharges

295

In the direction along Fe⊥ the electron drift component is given by ve (r, z) =

Fe⊥ ωe τc . ene B 1 + ωe2 τc2

(7.16)

This is the drift component that carries the discharge current and contributes to Ohmic heating. An important relation, first proposed by Rossnagel and Kaufman (1987a), can be derived for the case where the pressure term in Fe⊥ is negligible. In that case the currents (i.e. the electron drifts in the ion rest frame) across B are given by the classical Hall and Pedersen conductivities, which can be obtained from the generalized Ohm’s law as functions of the Hall parameter ωe τc . In the plasma bulk the electrons have to move across the magnetic field lines to arrive at a magnetic field line that is in contact with the anode. The electric-field-driven part of the cross-B discharge current density and the electric field are related through the generalized Ohm’s law (Chen, 2016), which in this case gives  −1 JD⊥ ω e τc ene = JD⊥ , E⊥ = σP B 1 + (ωe τc )2

(7.17)

where σP is the Pedersen conductivity. In the parts of the plasma where the current is carried mainly by electrons, we can write (Lundin et al., 2008b) ω2 τ 2

ene e c Je,φ E⊥ σH E⊥ B 1+(ωe τc )2 = = = ω e τc , ωe τc e JD⊥ E⊥ σP E⊥ en B 1+(ω τ )2

(7.18)

e c

where Je,φ is the azimuthal current density, JD⊥ is the discharge current density, and σH is the Hall conductivity. Thus the Hall parameter can be obtained from a measurement of the current density ratio Je,φ /JD⊥ . An important consequence of the interaction between electrons, ions, and neutrals is the constant transfer of momentum (or energy). A somewhat simplified picture is that “friction” arises when groups of different species drift with respect to each other. The strength of the friction is quantified by the resistivity tensor η. The cross-B component of the tensor can be expressed using the Hall parameter as η⊥ =

me B = , 2 τc e ne ωe τc ene

(7.19)

where the last step is made using the electron angular gyro frequency ωe = eB/me . We can therefore sum up the results so far by concluding that a low current ratio Je,φ /JD⊥ corresponds to a low Hall parameter ωe τc and a high cross-B resistivity (Eq. (7.19)), and has a high momentum transfer between electrons and ions. Counter-intuitively, a higher cross-B resistivity η⊥ increases the Pedersen conductivity, making it easier to transport electrons across B in the direction of an applied electric fields (Chen, 2016).

296

High Power Impulse Magnetron Sputtering

7.3.2 Anomalous transport1 7.3.2.1

Anomalous electron transport

Classical theory of diffusion and electrical conductivity, where collisions move electrons across the magnetic field lines, results in values of cross-B diffusion and mobility that scale as B−2 . Electrons do not always follow this classical picture, but instead work out new ways of diffusing in the plasma. Several plasma experiments on diffusion during the first half of the 20th century were not able to confirm the B−2 dependence expected from classical theory of collisions. Notable is the helium plasma experiment by Hoh and Lehnert (1960), who investigated the cross-B diffusion of electrons when varying the magnetic field strength. They found that the experiments followed the expected classical diffusion closely up to a critical point in the magnetic field strength when suddenly the cross-B diffusion started to depart from the classical prediction with further increasing magnetic field. Soon the first theories of this anomalous transport were presented by Kadomtsev and Nedospasov (1960), who had discovered that a plasma instability developed at high magnetic field strengths. The presence of plasma instabilities in HiPIMS will be dealt with in some detail in the present section, but first we need to look into the widely accepted Bohm diffusion, commonly seen in many magnetron sputtering experiments (Rossnagel and Kaufman, 1987a,b, Bradley, 1998), where the measured cross-B diffusion of plasmas scales as B−1 leading to a faster than classical transport of charged particles. This more rapid or anomalous loss of plasma across magnetic field lines is caused by microinstabilities and is referred to as Bohm diffusion. It was first discovered by Bohm et al. (1949), who suggested the semiempirical formula (Chen, 2016, Section 5.10) DB =

1 k B Te . 16 eB

(7.20)

Bohm diffusion can be formally ascribed to anomalous collisions with an effective collision time τeff . The empirically found constant 16 in Eq. (7.20) is, in this description, the anomalous Hall parameter (ωe τeff )Bohm = 16. This approach has been generalized to include conductivity, mobility, and magnetic field diffusion (Rossnagel and Kaufman, 1987a, Lundin et al., 2008a, Brenning et al., 2009), wherein the relation given by Eq. (7.18) has been shown to apply also for pressure driven (i.e. diamagnetic) currents. Thus, a determination of the ratio Je,φ /JD⊥ , where Je,φ is the azimuthal current density, and JD⊥ is the discharge current density, gives a direct measure of ωe τeff , and thereby all the transport parameters needed for fluid modeling: μ⊥ , η⊥ , σH , σP , D⊥ , and the magnetic field diffusion constant. For definitions and relations to ωe τeff of these parameters, see Brenning et al. (2009). The azimuthal drift currents in dcMS have been measured for a range of discharge parameters. For a dcMS discharge, the values of the Hall parameter were found close to the Bohm value, that is, (ωe τeff )Bohm = 16 within a factor 2 (Rossnagel and Kaufman, 1987a, Bradley et al., 2001). The drift current for any given discharge was found 1 We will here not restrict ourselves only to collisions, since we will see in the next section that we can

transfer momentum in a plasma instability.

Physics of high power impulse magnetron sputtering discharges

297

Figure 7.12 Measured values of Je,φ /JD⊥ ≈ ωe τeff above the race track at 30, 60, 85, 100, and 130 µs into the pulse versus the distance from the cathode surface. The curve marked (A) shows the average of the experimental data. For reference, two values of classical Je,φ /JD⊥ are also given: classical electron– neutral collisions (B) and combined electron–neutral and Coulomb collisions (C), as well as the Bohmvalue Je,φ /JD⊥ = 16 (dashed). The Bohm region 8 < Je,φ /JD⊥ < 30 and the faster-than-Bohm region (super-Bohm) 1.5 < Je,φ /JD⊥ < 5.5 appear as shaded areas. Reprinted from Lundin et al. (2011). ©IOP Publishing. Reproduced with permission. All rights reserved.

to vary roughly linearly with the discharge current. None or only a weak dependence on the gas species or the cathode target material was observed in the dcMS case (Rossnagel and Kaufman, 1987a). Surprisingly, it turns out that electron cross-B transport in the HiPIMS discharge is much faster than classically predicted through collisions and also faster than Bohm diffusion given by Eq. (7.20). We will further also see that ωe τeff changes with distance from the target z in the HiPIMS discharge. Brenning et al. (2009) show that the diffusion coefficient is roughly a factor of 5 greater than predicted by the Bohm diffusion, and the empirically found parameter is now in the range 1.5 < Je,φ /JD⊥ < 5.5. Early measurements by Bohlmark et al. (2004) indicated that the ratio between the azimuthal current density Je,φ and the discharge current JD⊥ in that HiPIMS discharge was Je,φ /JD⊥ ∼ 2. More recently the spatial and temporal variation of the internal current densities Je,φ and JD⊥ (z) have been measured by a Rogowski coil (Lundin et al., 2011). These measurements indicate a variation of the transport parameter Je,φ /JD⊥ over time and space. The low values of Je,φ /JD⊥ ≈ 2 are observed at distances 7 – 8 cm from the target surface. Closer to the target, Je,φ /JD⊥ increases with decreasing distance approaching the values expected for Bohm diffusion. There are small variations in Je,φ /JD⊥ with time; however, the values stay within a factor of two from the average value. These results are shown in Fig. 7.12, which shows Je,φ /JD⊥ above the race track at 30, 60, 85, 100, and 130 µs from the pulse initiation (pulse length 200 µs). The low value of Je,φ /JD⊥ observed for a HiPIMS discharge indicates a much more efficient electron transport across the magnetic field lines than for a conventional dcMS, which can be formally described as being the result of increased cross-B resistivity η⊥ and thereby increased cross-B conductivity in the direction of E and increased diffusion of electrons. However, as will be discussed in Section 7.4, it is

298

High Power Impulse Magnetron Sputtering

now known that spokes, azimuthally limited electron current channels with enhanced ionization, are involved and complicate this picture.

7.3.2.2

Anomalous ion transport

The high-energy tails observed in the IEDF from the HiPIMS discharge, with measured energies sometimes exceeding 100 eV (see Fig. 4.7), are a desirable feature for film growth, but the acceleration of these ions is at present not entirely understood, and any model for ion transport that does not include this feature must be regarded as incomplete. Lundin et al. (2008b) argued that this ion energization is associated with the anomalous resistivity effect that gives the efficient cross-B electron transport. This claim was supported by Lundin et al. (2008b) by experimental data, where a mass spectrometer showed a much more pronounced high-energy tail in the IEDF in the expected azimuthal direction, as seen in Fig. 7.13, which is indicated as position S1 in Fig. 7.14. The proposed mechanism is also shown in Fig. 7.14 and is based on results from PIC simulations of the wave structure in the modified two-stream instability (MTSI) (Hurtig, 2004, Hurtig et al., 2005). The instability, when driven by an azimuthal current Je,φ , sets up a wave structure with the wave vector kφ , in which the wave electric field Ew and the density perturbations (δne = δni due to quasineutrality) are correlated in such a fashion that there is a net azimuthal force Fei = ± ene Ew  between ions and electrons. The force is directed along Je,φ and gives an anomalous resistivity effect. However, besides the action on the electrons that facilitates the radial transport, there must be an equal and opposite reaction on the ions, that is, a net average drag in the direction of the electron Hall drift, i.e., against the direction of Je,φ . The MTSI is driven by the relative drifts between electrons ve and ions vi in the plasma, that is, vrel = vi − ve , in the presence of a magnetic field component perpendicular to this relative drift. The MTSI can give rise to acceleration of the charged plasma species and thus give a net transport of electrons across the magnetic field lines. This is the case for the circulating azimuthal current in the magnetic field trap of a magnetron sputtering discharge above the target in a HiPIMS discharge (Bohlmark et al., 2004). Because the ion gyro radii in magnetron sputtering discharges are typically larger than the spatial dimension of the plasma, only the electrons are magnetized and take part in this azimuthal drift. Lundin et al. (2008a) estimated the individual contributions of the various drift terms on the total azimuthal current. They found that the Hall drift (Eq. (1.33)) and the diamagnetic drift (Eq. (1.34)) are oriented in the same direction and combine to an azimuthal drift speed exceeding the MTSI threshold. This approach was further developed by Poolcharuansin et al. (2012), who added a drag force term, accounting for the azimuthal anomalous-resistive drag force, to the ion equation of motion, which was solved numerically. It was shown that a fraction of the circulating ion flux, which does not suffer from collisions, can then overcome a radial electric field and leave the discharge volume in the tangential direction. The results obtained for elevated pressures indicate that the sideway transport of ions is increasingly influenced by scattering of ions out of the discharge volume. Previous investigations of the MTSI have shown that the result will be large oscillations in the electric field, which are often correlated with oscillations in the plasma

Physics of high power impulse magnetron sputtering discharges

299

Figure 7.13 A comparison between IEDFs of Ti+ ions originating from (mainly) two opposite sides of the target race track and recorded at positions S1 and S2, as indicated in Fig. 7.14. The measurements were carried out at an Ar working gas pressure of 0.80 Pa and z = 0.01 m using 500 V discharge pulses resulting in a peak current density of 5.9 A/cm2 . Reprinted from Lundin et al. (2008b). ©IOP Publishing. Reproduced with permission. All rights reserved.

Figure 7.14 Azimuthal ion acceleration and the mechanism proposed by Lundin et al. (2008b). The dashed arrows show the deflection of ions sideways toward a mass spectrometer placed at either position S1 or S2. Fiφ is the ion force, vi is the ion velocity, and n symbolizes the neutral background gas. Ew is the oscillating electric wave field (oscillations are indicated by gray and white stripes) found in the anomalous transport, and L is the length scale, which is approximately 0.05 m. Reprinted from Lundin et al. (2008b). ©IOP Publishing. Reproduced with permission. All rights reserved.

density, resulting in a net transport of electrons perpendicular to both Je,φ and B, whereas the ions are too heavy to follow this motion (Hurtig, 2004). Measurements and simulations that indicate oscillating electric fields in the MHz range in magnetron sputtering devices (Bultinck et al., 2010, Lundin et al., 2008a) are also consistent with the MTSI as discussed previously. Lundin et al. (2008a) applied electric field probe arrays to explore oscillating electric fields in the megahertz range in a HiPIMS discharge. They demonstrated that the frequency dependence on the ion mass and the magnetic field strength correspond to lower hybrid oscillations when the fraction of the ions of the sputtered material is roughly 80% of the total ion density. Winter et al. (2013) also report on oscillations at around 2.4 MHz detected by a Langmuir probe biased into the ion saturation regime and connect this phenomenon to electron beams ejected from the cathode target radially. In agreement with Lundin et al. (2008a), they relate these oscillations to MTSI. These findings are also in line with the

300

High Power Impulse Magnetron Sputtering

numerical time-dependent results by Pseudo-3D PIC/MCC simulation (Revel et al., 2016), which underline the presence of electron instabilities at high frequency (MHz range). Besides the MTSI, also other frequency ranges and instabilities have been observed. Oscillations or instabilities have been observed in dcMS discharges (Martines et al., 2001, 2004) and in HiPIMS discharges (Kouznetsov et al., 1999, DeKoven et al., 2003, Winter et al., 2013) and sometimes are put in the context of fast electron transport (Martines et al., 2004, Sheridan and Goree, 1989). A recent example is the work by Tsikata and Minea (2015), who report on a MHz, mm-scale instability in a HiPIMS discharge identified as the electron cyclotron drift instability (ECDI). The ECDI has some similarities to the previously described MTSI in that it is driven by the difference in electron and ion velocities and also plays a role in enhancing electron current. However, this drift instability is believed to be of smaller scale compared to the larger wavelength MTSI (∼ cm). It is worth noting that reports of MTSI and ECDI in HiPIMS discharges also report on oscillations in the kHz range (Lundin et al., 2008a, Tsikata and Minea, 2015) consistent with observations of larger scale rotating dense plasma structures, spokes, which is the topic of the following section.

7.4

Plasma Instabilities

Plasmas are practically never uniform and steady. They are sustained by adding energy to an open system, which then inherently tends to develop nonuniformities and selforganized patterns. Self-organization implies the evolution of the plasma into more or less ordered structures, which can be dynamic, periodic, or chaotic. Self-organized patterns in the form of the striations of the positive column were observed already in the early investigations of direct current (dc) discharges (de la Rue and Müller, 1878). Since then, plasma structures have been observed in many different discharge configurations (Hayashi et al., 1999). The development of structures and patterns in plasma discharges is generally associated with a feedback mechanism (e.g. stream interaction, wave coupling, etc.). In an active discharge, neighboring charged particles are coupled via the Coulomb force affecting their position and motion. The motion of charged particles, in turn, will change their distances and strengths of coupling. A charged particle in a plasma interacts with many neighboring particles at the same time, causing the ensemble of charged particles to exhibit a common collective behavior. This collective behavior of charged particles is a general plasma phenomenon. A variation of the plasma density, for example, will propagate via the collective coupling. The feedback forces turn a density variation into an oscillation; a propagating oscillation is called a wave. When energy is supplied by a current driven by an applied voltage, a positive (amplifying) feedback can cause the wave amplitude to grow until large macroscopic variations or patterns appear: the wave becomes an instability. The instability is characterized by strong variations of the local plasma quantities including particle density, particle temperature, potential, and pressure. This section focuses on instabilities observed in magnetron sputtering discharges and in particular HiPIMS discharges, since

Physics of high power impulse magnetron sputtering discharges

301

instabilities can have a profound effect on particle transport, especially across magnetic field lines, already touched upon in Section 7.3. Magnetron sputtering discharges belong to the group of E × B discharges. The most investigated such devices are Hall thrusters studied for electric propulsion of spacecraft since the 1960s (Janes and Lowder, 1966, Mazouffre, 2016, Boeuf, 2017). In Hall thrusters, instabilities in the form of moving regions of enhanced ionization are generally referred to as spokes (McDonald and Gallimore, 2011, Ellison et al., 2012, Boeuf, 2017). This nomenclature has been adopted by the HiPIMS community and will be used in the following discussion.

7.4.1 Spokes and breathing instabilities in magnetron sputtering discharges Early observations of electrostatic fluctuations in dcMS discharges operated at nominal power densities in the range 0.5 – 6 W/cm2 lead to the discovery of plasma patterns or coherent modes corresponding to waves propagating in the direction of the electron diamagnetic drift (Martines et al., 2001, 2004). Martines et al. (2001, 2004) found that the presence of waves or modes is influenced by the discharge power and by the neutral working gas pressure. By increasing the neutral working gas pressure to several Pa a progressive transition toward a turbulent state was observed, expressed by nonregular amplitude modulation similar to the behavior of coupled oscillators. Such modes have been interpreted as electron drift waves destabilized by the combined effect of density gradient and electric field. Exploring HiPIMS discharges, using fast cameras, Ehiasarian (2008) showed images of HiPIMS plasmas as early as 2008 with nonuniform light emission, which suggested the presence of instabilities in HiPIMS discharges. Confirmation came in 2011 – 12 from three different laboratories, all using fast imaging techniques, which also allowed researchers to quantify properties of “ionization zones” or “spokes” in terms of their number, velocity, and propagation direction (Kozyrev et al., 2011, Anders, 2012, Ehiasarian et al., 2012). Commonly spokes are observed by probes or by fast ICCD cameras. Time-resolved imaging and probe techniques are the main diagnostic techniques to study spokes (Hecimovic and von Keudell, 2018). Typically, two types of spoke shapes are found when HiPIMS discharges are operated in noble gases, as illustrated in Fig. 7.15. On one hand, it is diffuse as observed for Ti and Nb targets, and on the other hand, it is triangular as observed for Al, Cu, Mo, Cr targets (Hecimovic et al., 2014). A more recent study of a discharge with Ti target suggests, however, that the appearance of various spoke shapes depends on the discharge current density, working gas pressure and magnetic field strength rather than the target material (Hnilica et al., 2018). The addition of a reactive gas leads to compound formation on the target surface (poisoned surface) with profound consequences for many parameters of the magnetron sputtering discharge such as the secondary electron emission yield and the plasma composition near the target. Consequently, the fluxes of atoms and ions leaving the target toward a substrate are also changed, together with film composition, microstructure, and deposition rate, as discussed in Chapter 6. Investigation of several target/reactive gas combinations showed that in

302

High Power Impulse Magnetron Sputtering

Figure 7.15 Spoke appearance in a HiPIMS discharge at Ar working gas pressure of 0.2 Pa. The pulse power density varied from 1 kW/cm2 (Mo, Cr, Cu) to 45 kW/cm2 (Al and Ti). From Hecimovic et al. (2014). ©IOP Publishing. Reproduced with permission. All rights reserved.

the poisoned mode, the spoke shape becomes more diffuse (Hecimovic et al., 2017b), that is, similar to the Ar/Ti and Ar/Nb discharges shown in Fig. 7.15. For the conditions of these experiments, the discharge voltage decreased, which can be correlated with an increase in the secondary electron emission (Depla and Mahieu, 2008, Marcak et al., 2015). Note that spokes occur on all kinds of magnetron targets, including rectangular or linear magnetron targets, where the race track has not only curved but also straight sections (Preissing, 2016, Anders and Yang, 2017, 2018). In addition to plasma instabilities that propagate along the race track (i.e. spokes), the plasma may also exhibit other instabilities. In particular, the plasma can oscillate in a direction normal to the target surface, which has been termed “breathing instability” (Yang et al., 2016) in analogy to a similar phenomenon in Hall thrusters (Young et al., 2015). Spokes and the breathing instability usually superimpose, which is shown in Fig. 7.16 (Yang et al., 2016). However, it should be mentioned that the breathing instability in Hall thrusters is linked to almost complete ionization of the neutral gas, whereas in the HiPIMS discharge, the neutral species are continuously injected in the ionization region via working gas and metal recycling (discussed in Section 7.2.1.1), and therefore strongly depends on the working gas pressure and the target material.

Physics of high power impulse magnetron sputtering discharges

303

Figure 7.16 Floating potential characteristic period contour for Au target (76 mm diameter) at Ar pressures from 0.13 Pa to 2.7 Pa and current from 10 mA to 300 A. Modes are indicated as regions separated by white dashed lines. Reprinted from Yang et al. (2016), with the permission of AIP Publishing.

For some target materials, especially for those with high self-sputter yield, the spoke patterns disappear when the applied power density is above 5 kW/cm2 , as indicated for the highest discharge currents in Fig. 7.16. Then the plasma emission becomes homogeneous along the race track, as shown, for example, for chromium in Fig. 7.17 (Hecimovic et al., 2016) and also for copper (Yang et al., 2015). Such transition can be clearly observed during current rise (Fig. 7.17C) within a single HiPIMS pulse. The triangular spoke shape (seen in Fig. 7.17A, left) is present at low discharge current, and its presence is related to an oscillating plasma potential (Fig. 7.17B shows the recorded floating potential). After increase of the power density above a threshold, the plasma becomes homogeneous (seen in Fig. 7.17A, right) and the floating potential value becomes constant in time, as seen in Fig. 7.17B. For high power, the system exhibits high impedance associated with a high rate of collisions within the discharge, and we can deduce that the collision rate is high enough to eliminate the need of instabilities for charged particle transport. When entering the spoke free regime, we can observe an increased ion flux toward the substrate (de los Arcos et al., 2013, 2014, Andersson and Anders, 2009). So far, the transition to a spoke-free mode has only been observed for a limited number of target/gas combinations (in Ar gas: Cr, Au, Cu, Al, Ta, Mo; in Kr gas: Al; and in gasless environment: Cu) although further combinations may be discovered in the future. The transition to spoke-free plasma in reactive HiPIMS discharges has so far not been observed for any target/gas combinations. The velocity of a spoke along the race track exhibits a dependence on power density, working gas pressure, and target material. Below 25 W/cm2 , spokes move in the retrograde direction (i.e. opposite to the general E × B direction) with a velocity

304

High Power Impulse Magnetron Sputtering

Figure 7.17 (A) ICCD images showing the transition from a spoke mode (left image) to a spoke-free mode (right image). (B) Floating potential oscillations corresponding to the images above. (C) Discharge current waveform. The transition to an azimuthally uniform plasma occurs when the nominal power density exceeds 5 kW/cm2 for Cr HiPIMS. Reprinted from Hecimovic et al. (2016). ©IOP Publishing. Reproduced with permission. All rights reserved.

approximately proportional to the power density. They reach, as shown in Fig. 7.18, values of order 103 m/s. Comparison of the spoke velocity for three different target materials (Al, Cr, Ti) shows that, for a given power density, the velocity is independent of the target material and determined by the background working gas, which is not surprising given that the plasma is primarily composed of background working gas. This changes when the power density exceeds about 25 W/cm2 : the spoke velocity becomes dependent on the target material. We could argue that the observed threshold itself is related to the power density needed to change the plasma composition from being dominated by the working gas to become target material dominated. The spoke velocity and even the direction changes with power. At high power, spokes propagate in the E × B direction and can reach velocities up to one order of magnitude faster than in dcMS mode, that is, ∼ 104 m/s. The number of spokes also changes with HiPIMS plasma parameters. Under some conditions of working gas pressure and power, spokes appear well defined: we can observe a specific small number of spokes, which often are more or less regularly spaced from each other. The most regular appearance can be found in dcMS discharges, where we can set discharge conditions such as, for example, to have exactly 1, 2, or 3 spokes. This regularity has been exploited to determine the potential structure of spokes using probes (Panjan and Anders, 2017) (see Section 7.4.2). At higher power, like in HiPIMS operations, the situation is more complicated. Under many conditions, at any given moment, we can usually observe a discrete and finite number of spokes; however, the spokes are not of the same intensity (brightness, plasma density, etc. (Yang et al., 2015)). Even under nominally the same discharge conditions, the number of

Physics of high power impulse magnetron sputtering discharges

305

Figure 7.18 Spoke angular velocity for Al, Cr and Ti targets as a function of discharge current at an Ar working gas pressure of 0.5 Pa. The half-filled symbols at the very left stand for spoke velocity for alternating mode at lowest discharge currents. Negative velocities represent retrograde E × B motion. From Hecimovic et al. (2016). ©IOP Publishing. Reproduced with permission. All rights reserved.

spokes can vary. In some cases, an assignment of a distinct number of spokes is not even possible as these regions of enhanced ionization and excitation amplify and decay, and their intensity varies on a more gradual scale. Furthermore, using optical and probe techniques, we can observe spoke splitting (Anders and Yang, 2018) and spoke merging (Hecimovic et al., 2015, Klein et al., 2017). Merging and splitting of spokes can readily be observed in Fig. 7.19. This figure was recorded using a streak camera by aligning the entrance slit of the camera with a linear section of the race track (Anders and Yang, 2017). Also here, the local character of spokes indicates a local character of electron energization, which can be associated with the local structure of the spoke plasma potential, as discussed in Section 7.4.3. The use of bandpass interference filters allows looking at spokes in the light of selected spectral lines associated with plasma species of interest such as ions or neutrals of the working gas or target ions or neutrals. A direct way to analyze the spokes evolution was performed by following the spatial distribution of light emission from the different species in the spoke by using interference bandpass filters in front of an ICCD camera. The results from such an investigation are shown in Fig. 7.20. This technique is even more powerful when using four ICCD cameras, each with a different bandpass filter, triggered simultaneously because one can record the emission from ionic species, both working gas ion species (Ar+ ) and sputtered metal ion species (Al+ ), and show that the atomic species are completely depleted in the spoke. This emphasizes the understanding that a spoke is an ionization zone (Anders et al., 2012b, Hecimovic, 2016) in agreement with the modeling results dis-

306

High Power Impulse Magnetron Sputtering

Figure 7.19 Spokes in a HiPIMS discharge with an applied voltage of 547 V (leading to a 900 A peak in the discharge current at the end of the pulse), with a 240 × 120 mm2 Al target in 0.4 Pa Ar with 16 mPa N2 added. We see an example of spoke splitting at about 8 µs into the image. The horizontal brightness modulations correlate with oscillations of discharge current, which often occur near the end of each pulse. Reprinted from Anders and Yang (2017), with the permission of AIP Publishing.

cussed at the end of this section. Also, spectral filters offer to study optical emission from different energy levels. This approach provides an opportunity to learn something about the excitation conditions, that is, about localized electron heating and the presence of energetic electrons. Light emission from increasingly higher energy levels, especially from ions, is concentrated in ionization zones: the higher the energy level from which the optical transition originates, the more spatially localized the optical emission (see Fig. 7.20). This indicates that, in the presence of spokes, the heating or energization of electrons responsible for the excitation and ionization is localized, as opposed to being evenly distributed (Anders, 2014, Hecimovic et al., 2017a). Since the spokes move, the location of the most intense electron heating is moving. The spokes have also been modeled using the Pseudo-3D PIC/MCC simulation approach introduced in Section 5.1.4.2 (Revel et al., 2016). The model shows that the number of spokes increases with increased discharge current for relatively low power density (< 100 W/cm2 ). In addition, the model gives access to the microscopic events occurring in the plasma including the electron motion, as shown in Fig. 7.21. The spoke ionization zone appears to be confined close to the target at the border between the sheath and the IR (z < 1.5 mm), as can be seen in Fig. 7.21C, consistent with OES measurements by Andersson et al. (2013). Moreover, the Pseudo-3D PIC/MCC approach can also reproduce plasma flares that travel in the axial direction (Ni et al., 2012), as shown in Fig. 7.21A (Revel et al., 2016) which is addressed in Section 7.4.3.2.

Physics of high power impulse magnetron sputtering discharges

307

Figure 7.20 Spatial distribution of light-emission from different species. The shape of a spoke is determined by the light that is observed, indicative of local electron heating and locally different excitation of the upper levels of optical transitions (the light intensity is in false colors, with the camera image intensifier optimized for the spectral line observed). Reprinted from Andersson et al. (2013), with the permission of AIP Publishing.

308

High Power Impulse Magnetron Sputtering

Figure 7.21 2D projection of the electron density (A) and (B) and ionization (C) maps for the dc operation regime of a planar magnetron sputtering discharge, as simulated by Pseudo-3D PIC/MCC. An illustrative trajectory of a trapped electron is shown by the black line. Note that the electron trajectory is obtained in time whereas 2D maps show instant structures. Input parameters: discharge voltage 600 V, mean secondary electron current 0.1 A, discharge current 1 A, and Ar working gas pressure 0.4 Pa. Reproduced from Revel et al. (2016), with the permission of AIP Publishing.

7.4.2 The potential structure Measurements using electrical probes (e.g. Panjan and Anders (2017)), ion energy analyzers (e.g. Yang et al. (2015)), and spectrally selective imaging (e.g. Andersson et al. (2013)) provide ample evidence that ionization zones (spokes) are locations of locally enhanced potential. Such potential structures can explain the disruption of closed electron drift, formation of plasma flares, and formation of energetic ions, especially considering the differences of ion energies in E × B and −E × B directions (Yang et al., 2015). Each spoke represents a potential hump relative to its surroundings. Each is enclosed by an electric double layer, creating a local electric field (denoted Es ) that affects the local direction of electron drift and can give rise to local acceleration of ions. Electrons arriving at a spoke, enter the potential hump, reach a region of higher potential, and are thus energized, enabling them to cause localized excitation and ionization, as illustrated in Fig. 7.20. In that sense, images of spokes are approximate images of the potential distribution (Anders, 2014). For potential measurements, it is highly desirable to utilize conditions that are regular and reproducible. Such conditions have been found at certain power and pressure conditions in dcMS. Using closely spaced cold and hot emissive probes (see Section 3.1.2) has allowed researchers to derive the potential distribution, the local electric fields, and the energy gain of electrons.

Physics of high power impulse magnetron sputtering discharges

309

Figure 7.22 Plasma potential (color) and electric field (vector) distributions in the azimuthal-radial (ξ − r) plane for different axial (z) distances from the target surface (z from 2.5 mm to 40 mm). In the right bottom corner: a corresponding fast-camera image of the spoke, correlating the potential distribution to the image as seen in visible light (the light intensity is in false color for better presentation). Reprinted from Panjan and Anders (2017), with the permission of AIP Publishing.

The potential difference between the spoke and its surroundings can reach 70 V, and therefore the energy gain was found to be far in excess of the ionization energies (Panjan and Anders, 2017). Fig. 7.22 illustrates this point. The plasma potential distribution, as recorded by the floating potential of an emitting probe, can be mapped in an elegant way using a stationary probe with exactly one spoke moving along the race track. The spoke passes the probe, and the time dependence of the probe potential can readily be converted to a spatial distribution knowing the position and speed of the spoke. Through axial and radial changes of the probe position, the entire axial (z, distance from target surface), radial (r, distance from target center), and azimuthal (ξ , coordinate along the race track) space is mapped as shown in Fig. 7.22. The measured spoke field was Es = 8 × 103 V/m (Panjan and Anders, 2017), which is slightly below the maximum Es found by Pseudo-3D PIC/MCC modeling (3 × 104 V/m) (Revel et al., 2016), but the discharge used in the experiment was operated in dcMS (lower power), whereas the model results were for a HiPIMS discharge. Modeling provides at least two scenarios to explain the electron movement and their organization in spokes. In the first scenario the electron movement is driven by a combination of at least three drifts, all of the type E×B. In addition to (i) the widely known

310

High Power Impulse Magnetron Sputtering

Figure 7.23 A phenomenological depiction of electron motion across spokes based on the Pseudo-3D PIC/MCC simulation results. In (A): the spoke electric field Es is shown with the spoke main azimuthal velocity vs ; v2 is the electron velocity in the azimuthal-axial plane. In (B): v3 is the electron velocity in the azimuthal-radial plane; the trajectory of an isolated electron is shown with a dotted line. The color levels illustrate qualitatively the observation of higher electron densities at the leading edges of the spokes. Input parameters: discharge voltage 600 V, mean secondary electron current of 0.1 A, discharge current of 1 A, and argon working gas pressure of 0.4 Pa. Reproduced from Revel et al. (2016), with the permission of AIP Publishing.

Hall drift v1 = Ez × B /B 2 , (Eq. (1.33)), with Ez being the macroscopic discharge field normal to the target, two other drifts have been identified (Revel et al., 2016): (ii) a drift v2 = Es × B /B 2 involving the locally developed electric field Es due to the spoke itself and the magnetic field component parallel to the target surface, and (iii) a drift v3 = Es × Bz /B2 due to the axial (Bz ) component of the magnetic field, which changes sign when crossing the target surface (the center and edge magnets have opposite polarity). These two latter drifts are represented in Fig. 7.23, where v2 acts in the vertical plane of the race track. It pushes the electrons up and down making them “surf on” the moving spokes because Es always points toward the center of the spoke, whereas B stays unchanged (B = Bx in Fig. 7.23). The third drift v3 does not change sign because both Es and Bz change sign when electrons bounce on each side of the race track (see Fig. 7.23B). In the second modeling scenario, spokes form due to wave coupling (wave coupling model (WCM) introduced in Section 5.1.6.3.2) driven by the Doppler-shifted electron Bernstein (DSEB) wave and the ion sound (IS) wave (Luo et al., 2018). If their respective frequencies are close, then they couple to each other, and the electric field experiences a faster oscillation with the sum frequency (SF) and its amplitude modulated by the difference frequency (DF). Analogous modulations of the electron electric field have been experimentally observed in dcMS and HiPIMS discharges (Tsikata and Minea, 2015), identified as an electron cyclotron drift instability discussed in Section 7.3.2.2. The WCM can explain the spoke split initiated when the local spoke field exceeds the amplitude of the DF wave field, as experimentally recorded by Anders and Yang (2017) (Fig. 7.19). This can explain the lack of coherence observed sometimes in the movement of the spokes. In addition, the WCM predicts the same number

Physics of high power impulse magnetron sputtering discharges

311

of spokes as experimentally recorded (Hecimovic, 2016) with increasing pulse discharge current. This model allows a collisionless energy transfer from electrons to ions and thus provides a mechanism for anomalous ion heating (as discussed in Section 7.3.2.2). As the electrons are magnetized, they keep their trajectory close to the race track, whereas the ions are not trapped by the magnetic field. If they gain a tangential velocity component, then they can leave the spoke, as found by Lundin et al. (2008b) (Fig. 7.14). Analogous to this mechanism, the energetic ions could be pushed away, normal to the target, leaving behind only low-energy ions inside the spoke. No azimuthal ion movement has been detected in spokes.

7.4.3 Effect of spokes on charged particle transport The appearance of spokes, as well as other instabilities, is related to the need to close the electrical circuit and provide conditions allowing the electrical current to flow. The magnetron’s E × B configuration is an electron trap. Electrons are confined in a closed drift until they escape through collisions (“classical transport” in Section 7.3.1.2) or via instability-facilitated processes (“anomalous transport” in Section 7.3.2.1). The spoke instability can be seen as a modulation of the high-frequency instabilities discussed in Section 7.3.2. This section summarizes the physics of the cross-B motion of charged particles due to spokes, which has been identified as the third mechanism for electron transport in HiPIMS. Since only electrons are magnetized, we can focus on the issue of how electrons manage to move across the magnetic field line structure.

7.4.3.1

Transport near the target

Using a segmented target, the current densities at the target associated with spokes in a HiPIMS discharge have shown that spokes can be identified as more or less regular perturbations of the local discharge current density with about 25% modulation induced by the traveling spokes. The plasma density at the target between the spokes never decreases to zero (Poolcharuansin et al., 2015, Hecimovic et al., 2017b, Lockwood Estrin et al., 2017). The plasma density within the spokes is of order 1019 m−3 and generally increases approximately linearly with increasing power density (Hecimovic et al., 2017b). Ionized sputtered atoms in the presheath will be accelerated toward the target by the local electric field. Target ions are subplanted (shallow implantation) and thus (re)deposited at the target. Due to the direction of the local electric field and the motion of the spokes, target ions may arrive at the target somewhat displaced relative the location of the origin (Layes et al., 2017a,b). Layes and coworkers investigated the distribution of sputtered material from a small disk embedded in the circular target at the race track position in two configurations, a small Cr disk inserted into an Al target and a small Al disk inserted into a Cr target. The target surface composition was characterized using in vacuo XPS (the target was not exposed to air but analyzed in the same vacuum chamber). The target redeposition of sputtered species was more effective for Cr atoms than for Al atoms at all powers. The region of redeposition of target material was larger than the source region. Deposition did not occur symmetrical

312

High Power Impulse Magnetron Sputtering

relative to the source area but somewhat displaced in the E × B direction irrespective of the presence of spokes. When spokes were present, an enhanced transport in the −E × B direction was also observed. This can be explained by the large electric field at the trailing edge of each spoke, affecting the direction of ions after they have been produced.

7.4.3.2

Transport in the bulk plasma

As discussed in Section 7.3.2.1, cross-B transport of electrons is for many systems approximately 5 times greater than Bohm diffusion, an empirical scaling often used to benchmark transport and given by Eq. (7.20). The anomalous cross-B transport in HiPIMS discharges has been correlated to the appearance of spokes. This implies that transport is not just based on diffusion but facilitated by collective processes governed by the local electric fields, which can significantly deviate from the average electric field (e.g. see Fig. 7.22). Our current understanding of spoke dynamics is still incomplete, but it is clear that ions formed in the spoke volume (where a potential hump is observed) are accelerated by the electric field of the double layer surrounding the spoke. This acceleration is displacing ions in all directions (Hecimovic, 2016) and preferentially in the spoke-forward direction (Panjan et al., 2014), suggesting the picture of a propeller acting on ions (Anders et al., 2013). Using a triple probe 15 mm above the target, Lockwood Estrin et al. (2017) determined that each spoke has a dense but relatively “cool” leading edge (ne ∼ 2.0 × 1019 m−3 , Te ∼ 2.1 eV) and a relatively hotter but more rarefied trailing edge (ne ∼ 1 × 1019 m−3 , Te ∼ 3.9 eV). We should keep in mind, though, that the temperature is an expression related to the width of a Maxwellian distribution, whereas there may be hot, non-Maxwellian electrons present that are not well represented by Te . Furthermore, at 15 mm from the target, the potential inside is about 8 V more positive than the potential of the inter-spoke regions, giving rise to an azimuthal electric field of ∼1 kV/m (Lockwood Estrin et al., 2017). Their result is in qualitative agreement with observations made on dcMS discharges (Panjan and Anders, 2017). The reason for the higher electron temperature at the trailing edge can be qualitatively understood keeping in mind that drifting electrons arrive first at the trailing edge, get energized by entering the region of higher potential, keep drifting and produce ion–electron pairs, and thereby loosing energy. This picture also offers a clue why HiPIMS spokes move in the E × B direction. Namely, ions and electrons leave the location of highest plasma density on different time scales: electrons with drift velocity (∼ 105 m/s) and ions much slower, depending on their mass and local electric field. Hence, the location of highest plasma density becomes the location of highest charge imbalance or electric field, which is the trailing edge; the trailing edge shifts to the location of highest ionization. This was qualitatively described in the early spoke reports (Anders et al., 2012b, Anders, 2012) and is now supported by experimental findings. However, much more needs to be done to fully describe spoke formation and displacement processes. Spokes are also the origin of plasma flares, that travel axially out into the plasma volume (Ni et al., 2012, Anders et al., 2012b), which have been illustrated by numerous fast camera images, of both the frame and the streak type (see e.g. Fig. 7.24).

Physics of high power impulse magnetron sputtering discharges

313

Figure 7.24 Flares from HiPIMS spokes, operated with an Nb target with argon at 0.27 Pa as the working gas; z is the distance from the target surface. Top: as observed with a fast frame camera, 10 ns exposure time. Bottom: same discharge pulse observed with a streak camera. Reprinted from Anders et al. (2012b), with the permission of AIP Publishing.

Flares have been associated with large changes of local electric field, which can redirect electron drift and produce ionization far from the target. Flares are likely the most effective process disrupting the electron trap of the magnetron E × B configuration. In addition to the observed electric field structures associated with spokes, magnetic fluctuations have also been detected using miniature magnetic pickup-coils (Spagnolo et al., 2016). The magnetic fluctuations are in the frequency range of 100 kHz and correlate well with the electrostatic oscillations detected with probes. Spagnolo et al. (2016) concluded that spokes are not purely electrostatic but of electromagnetic nature, at least when the power level is high and the βkm parameter, the ratio of kinetic to magnetic pressure, reaches a few percent.

314

7.4.3.3

High Power Impulse Magnetron Sputtering

Transport near the substrate

Film growth occurs on the scale of minutes or even hours for thick coatings. Therefore the effects of spokes “smear out” in time and space but are still relevant since particle fluxes and energies change. The most relevant effects of the spokes are in changes induced in the ion energy distribution functions (IEDFs) as measured at the substrate position. In HiPIMS discharges, when the spokes are dominated by sputtered metal or recycled working gas species and the plasma densities in the spoke reach up to 8 × 1019 m−3 (Hecimovic et al., 2017), the IEDF of metal ions comprise a low-energy peak and an additional broad peak at high energies. It is generally assumed that the high-energy ions originate from the potential hump of the spoke, where the ions are accelerated away from the target toward the substrate (Maszl et al., 2014a,b). At high power densities, when metal-dominated spokes are present, an additional peak at energies in the range 15 – 25 eV is observed with the position of the second peak shifting to higher energy when the power density is increased. Additionally, it was found that doubly charged ions have approximately twice the energy of singly charged ions, indicating an electric acceleration mechanism as provided by a potential hump (Panjan et al., 2014, Anders et al., 2013). However, the absolute energy values are somewhat higher than the simple hump argument allows, and future research is needed to clarify and quantify the origin of the energy, for example, by considering the contribution of the breathing instability. An interesting question is what happens to the IEDF when the power density is increased beyond the threshold where the plasma becomes azimuthally homogeneous. Breilmann et al. (2015) determined that the high-energy part of the metal ion IEDF, measured normal to the target, does not change but the low energy peak shifts by several eV to higher energies. Therefore a change of plasma behavior from a spoke mode to the spoke-free mode is not of concern in terms of energy effects on films deposited using the ion flux normal to the target. When looking from the side, however, the situation is different. The low-energy peak is smaller, and the high-energy tail of the distribution is always higher when measured tangentially in the E × B direction than when measuring the flux in the opposite, −E × B direction, as seen in Fig. 7.25 (Panjan et al., 2014, Yang et al., 2015, Franz et al., 2016). Similar results were already shown in Fig. 7.14. The same asymmetry was found under dcMS conditions, suggesting that the same ion acceleration mechanisms may be at work when the discharge is continuously operating, even though the motion of spokes in dcMS is in the −E × B direction. When the HiPIMS power level goes beyond the threshold to an azimuthally homogeneous plasma, the ions going sideways are generally of lower energy, and the pronounced azimuthal asymmetry disappears when ionization zones are absent as seen in Fig. 7.25 (Yang et al., 2015). Estimates of neutral working gas and metal atom flux from the target suggest that a rarefaction of neutrals does not occur, but rather the density of neutrals becomes high enough to enable a collision rate sufficiently high for cross-field transport without the need of instabilities. Measuring sideway IEDFs is one way to determine the presence or absence of spokes (Yang et al., 2015).

Physics of high power impulse magnetron sputtering discharges

315

Figure 7.25 Energy distribution functions for argon and copper ions emitted “sideways” from a magnetron sputtering discharge. This experiment was designed to test if the presence of spokes matters for ion acceleration: Spokes are present at 40 A but not at 400 A. Reprinted from Yang et al. (2015), with the permission of AIP Publishing.

7.5

Deposition rate

Before moving on to deposition of thin films by HiPIMS in Chapter 8, we would first like to discuss the much-debated topic of deposition rate. The deposition rate depends on the sputter rate, which was discussed in Section 1.1.7. For dcMS, the deposition rates are practically found to be directly proportional to the power applied to the target (Waits, 1978). The deposition rates are thus determined by the power density, target material, size of the erosion area, target-to-substrate distance, and discharge pressure. In the HiPIMS regime the situation is somewhat more complex due the pulsed nature of the discharge. For example, for certain discharge conditions, the absolute deposition rate can increase almost linearly with increasing (time-averaged) applied power (Ross et al., 2011). However, the applied power can be increased by increasing the amplitude of the voltage and current pulses, but we can equally well maintain the pulse amplitudes and instead increase the pulse frequency (or pulse length), and the resulting deposition rates will not be the same. Samuelsson et al. (2010) compared the deposition rates of various metals (Ti, Cr, Zr, Al, Cu, Ta, Pt, Ag) with pure argon as the working gas for both dcMS and HiPIMS discharges applying the same average power. They observed that the HiPIMS deposition rates are in the range of 30 – 85% of the dcMS deposition rates depending on target material. These results are shown in Fig. 7.26. However, the reduction in the deposition rate was not more pronounced for materials with low sputter yield as had earlier been concluded from measured data (Helmersson et al., 2005). In addition, Konstantinidis et al. (2006a) found that the deposition rate depends on the pulse length

316

High Power Impulse Magnetron Sputtering

Figure 7.26 Deposition rates for dcMS and HiPIMS discharges plotted as bars for the different target materials used (left axis). The ratio of the deposition rate of HiPIMS over dcMS deposition rate is shown as a scatter plot (right axis). The average power was kept constant at 125 W for both deposition methods, except in the case of Pt and Ta, where the average power was slightly lower. Reprinted from Samuelsson et al. (2010), with permission from Elsevier.

and increases from 20% to 70% of the dcMS values as the pulse length is decreased from 20 to 5 µs for the same average power of 300 W when sputtering a Ti target with argon as the working gas at 1.33 Pa. Similar trends are also reported by (Leroy et al., 2011) using a rotating cylindrical magnetron, where the deposition rate is found to be up to 75% lower for HiPIMS compared to dcMS when sputtering Ti in Ar at 0.7 Pa, and the decrease in deposition rate becomes more pronounced with increased pulse length (5 – 20 µs were investigated).

7.5.1 Physics of deposition rate loss There have been several suggestions on the cause of the lower deposition rate observed in non-reactive HiPIMS. The most common explanation to the reduction in deposition rate stems from a work by Christie (2005), who argued that back-attraction of the ions of the sputtered material M+ to the target followed by self-sputtering causes a reduction in the amount of sputtered particles reaching the substrate. The idea is as follows. After the sputtering event the target neutrals are transported out into the plasma, where they may undergo an ionizing collision. The probability of an ionizing collision is denoted by αt and depends on the plasma conditions, as discussed in Section 7.2.1.1. In agreement with our discussion on ion transport in Section 7.3.1.1, a fraction of those ions will be close enough to the cathode fall and also have a low enough kinetic energy as to be back-attracted to the target surface, thereby causing a reduction in the amount of sputtered particles reaching the substrate. This means that by using predominantly ions instead of neutrals in the deposition process the electric potential applied to the target and the resulting electrical field Ez (directed toward the target) can reduce the deposition rate significantly if these fields extend outside the cathode sheath and into the dense plasma, where most of the ionization occurs. In Christie-type models (Christie, 2005, Vlˇcek and Burcalová, 2010, Andersson and Anders, 2009) (previously

Physics of high power impulse magnetron sputtering discharges

317

discussed in Section 5.1.2) a key variable is the return fraction βt of ionized sputtered target atoms. An electric field Ez in the plasma can turn such ions around, increase βt , and decrease the deposited fraction of ions of the target material M+ . Spatial measurements of the plasma potential in HiPIMS discharges (Sigurjónsson, 2008, Mishra et al., 2010, Rauch et al., 2012, Liebig and Bradley, 2013) have shown that there commonly is a potential uphill, from the cathode sheath edge and reaching far outside the ionization region (several cm), which can vary at least in the range 7 – 100 V, as discussed in Sections 3.3.2 and 7.3.1.1. Stronger Ez and higher potentials VIR across the ionization region are generally observed closer to the target, as well as for stronger magnetic field, for higher applied power, and during the early stage of the HiPIMS pulses (the latter particularly for lower pressure) (Mishra et al., 2010). In Fig. 7.27A, we see one example from Mishra et al. (2010) of how the plasma potential varies with axial distance from the target z when weakening the absolute magnetic field strength |B| at the target by 33%. Profile A corresponds to the weakest |B|, and profile C to the strongest |B|. All the measurements were taken at peak discharge current. Using this data along with a typical energy distribution of sputtered Ti shown in Fig. 7.27B (Lundin et al., 2013) and assuming that ionization of sputtered atoms is distributed with some unknown probability, depending mainly on the plasma density, over the whole range of potential profiles shown in Fig. 7.27A, we can make the following observations (Brenning et al., 2012): Consider ions that are created at a distance of 30 mm from the cathode and for simplicity assume that they have the more or less preserved energy distribution from the sputtering event at the target. From 30 to 90 mm (∼ substrate position), the potential differences in Fig. 7.27A are VA − VA ≈ 1 V, VB − VB ≈ 5 V, and VC − VC ≈ 10 V. With a sputter energy distribution as seen in Fig. 7.27B at z = 30 mm, only a small fraction would be back-attracted in potential profile A (< 10%), about half in B, and the majority in C (∼ 90%). This is consistent with measured variations in deposition rates (Mishra et al., 2010), which for profile A was a factor of 6 higher than for profile C at a typical substrate location (z = 100 mm); see Fig. 7.28. Note also that if the sputtered energy distribution in Fig. 7.27B is taken as typical for HiPIMS, then a high deposition rate is unlikely when the potential drop extending into the plasma is significantly higher than ≈ 10 V; or, conversely expressed, significant escape of ionized sputtered material is quite possible, provided that the potential is well below ≈ 10 V. Therefore, controlling and optimizing the potential profile in the cathode region will greatly affect the number of metal ions incident on the target surface (Poolcharuansin and Bradley, 2010), which so far has not been fully explored. In addition, we note that it is not only the return probability of ionized sputtered species βt that determines the reduction of deposition rate in the described scenario. It is also closely connected to previously discussed discharge modes, where we saw in Section 7.2 a transition from gas-sputtering to self-sputtering as the discharge begins to create and attract M+ ions back to the target. First, the curves for sputter yield versus ion energy for Ar+ ions and self-ion sputtering for various target materials are very similar; however, they are not identical, and the self-sputter yield is typically 10 – 15% lower (Anders, 2010), which will also have a negative influence on the total deposition rate. Second, discharges that are prevented from transiting into significant

318

High Power Impulse Magnetron Sputtering

Figure 7.27 (A) The plasma potential versus axial distance z from the cathode measured at current maximum. Results for three different B-field configurations are shown: profiles A (weakest |B|), B, and C (strongest |B|), and with parts marked A-A’, B-B’, and C-C’. The measurements were carried out at an average discharge power of 750 W, an Ar working gas pressure of 1.08 Pa, and above the race track of a planar circular magnetron equipped with a Ti target, 15 cm in diameter. Data from Mishra et al. (2010) and Brenning et al. (2012). (B) Typical sputter energy distribution of Ti calculated using a modified Thompson distribution from Stepanova and Dew (2004) using a cutoff energy of 17 eV. The vertical lines show the threshold energies for escaping back-attraction after ionization at z = 30 mm (at the marks A, B, and C) in the potential profiles in (A). Data from Lundin et al. (2013).

self-sputtering, such as when applying short HiPIMS pulses (t ≤ 50 µs), are dominated by G+ ions for sputtering, which means that the effective sputter rate can be kept high. This latter point is likely one reason for the reported higher deposition rates for shorter pulses discussed earlier. However, the risk with short pulses is that the increase in deposition rate is accompanied by a decrease in ionization fraction (Konstantinidis et al., 2006a). There are also other processes affecting the deposition rate in HiPIMS. In Section 4.2.2, we saw that gas rarefaction leads to lower density of the working gas in front of the target and thus a reduction in the number of ions available for sputtering. This subsequently leads to a reduction in the deposition rate, in particular, for long pulses (t > 100 µs), although we are not aware of any reports quantifying this contribution. In addition, Emmerlich et al. (2008) argue that the nonlinear scaling of

Physics of high power impulse magnetron sputtering discharges

319

Figure 7.28 The deposition rate measured using a QCM at different axial positions above the race track for the three different B-field configurations shown in Fig. 7.27A. The measurements were carried out at an average discharge power of 750 W and an Ar gas pressure of 1.08 Pa using a planar circular magnetron equipped with a Ti target, 15 cm in diameter. Data from Mishra et al. (2010).

√ the sputter yield with the applied voltage is not taken into account (often Y ∝ VD ) when comparing dcMS and HiPIMS discharges operated at the same average power. This would reduce the sputter rate since in HiPIMS operation the target voltage is significantly higher than for a conventional dcMS discharge. It is therefore not reasonable to compare the two at the same average power. In the case of Cu sputtering the authors estimated a relative HiPIMS-to-dcMS deposition rate between 43% and 76%, depending on the fraction of Ar+ to Cu+ ions sputtering the target (Emmerlich et al., 2008). These results were benchmarked against experiments, where the relative deposition rate based on thickness measurements was determined to be 32%, and thus the difference in sputter yields cannot fully explain the difference in deposition rates. Also, Alami et al. (2006) address the difference in discharge voltage and current between dcMS and HiPIMS and suggest that the lower deposition rate in HiPIMS is at least partially due to a lower average target current during HiPIMS deposition when the same average power is applied due to higher voltage necessary for HiPIMS operation. They conclude that comparison should be made for the same average discharge current. Another possible reason for the deposition rate loss is linked to the previously discussed anomalous transport of charged particles in Section 7.3.2.2. Lundin et al. (2008b) show that a significant fraction of the sputtered metal species is deposited sideways. This enhanced radial transport (across the magnetic field lines) increases the deposition rates perpendicular to the target surface but decreases the amount of sputtered vapor that reaches a substrate in front of the target. The authors investigated Cr and Ti deposition in Ar on samples located outside the edge of a circular planar magnetron, which were placed perpendicular to the target surface. The measured deposition rates were normalized to a reference sample on the standard substrate holder. By combining results on the sideways deposition rate for various distances z, they found a 25% and 10% higher sideways deposition rate in HiPIMS for Cr and

320

High Power Impulse Magnetron Sputtering

Ti, respectively. Leroy et al. (2011) carried out similar investigations using a rotating cylindrical magnetron. However, they did not observe an increase in sideways deposition and suggest that anomalous transport might work differently in these devices or that the sideways deposited material is transported in a different direction compared to the angular range investigated (Leroy et al., 2011).

7.5.2 Increasing the deposition rate There have been some attempts to increase the deposition rate in the HiPIMS discharge. In the previous section, we already identified that a reduction of the magnetic field strength resulted in both a reduction of the back-attracting electric field (reduction of the plasma potential) and an increase in the deposition rate (Mishra et al., 2010). The deposition rate profiles above the target race track are shown in Fig. 7.28 for the three different B-field configurations displayed in Fig. 7.27. As one possible reason for the deposition rate increase, Mishra et al. (2010) proposed a reduced βt due to the weaker electric field, which would increase the ion flux to the substrate in line with our general explanation on ion back-attraction. However, the situation is not quite clear. In a later analysis of the same experimental data (Bradley et al., 2015), it was argued that there was also a lower ionization probability αt at the weaker magnetic fields. This gives an alternative explanation for the increased deposition rate: at lower αt , ions are replaced by neutrals, which are not back-attracted. Whatever the main reason for the increased deposition rate is, however, decreases of the magnetic field strength is a promising way to increase the deposition rate. Furthermore, Raman et al. (2016) modified the magnetic field topology of a HiPIMS discharge, which increased the deposition rate (Raman et al., 2016, McLain et al., 2018). In the cited studies the modified magnet pack had a high magnetic field region over three concentric race track regions but fell off more steeply than for a conventional magnet pack as we move away from the target surface. Such a configuration, with open field lines toward the substrate region, which allows electrons to escape the magnetic trap more easily, is suggested to reduce the effect of self-sputter recycling (lower discharge current) and thus reduce βt . The authors benchmarked the deposition rates to dcMS using the same magnetron configuration and found that the HiPIMS rates were up to 25% higher with a Ti target, about equal with a carbon target, and 25% lower with an Al target compared to the dcMS rates (Raman et al., 2016). Similar trends were found by making the same modifications to a rectangular magnetron, where McLain et al. (2018) report an increased deposition rate in HiPIMS mode compared to a standard magnet pack (commercial magnetron assembly). There are also reports of a deposition rate increase related to guiding the ionized flux using external magnetic fields (Bugaev et al., 1996, Bohlmark et al., 2006b). In conventional magnetron sputtering, we saw in Section 1.2.2 that ions are not magnetized by the relatively weak static magnetic field. However, Bohlmark et al. (2006b) demonstrated that a sufficiently strong B-field (|B| ∼mT) can be created with a current-carrying coil placed in front of the magnetron target. When current was drawn through the coil, it generated a magnetic field opposing the field from the center pole of the magnetron. An increase of 80% in deposition rate was observed for

Physics of high power impulse magnetron sputtering discharges

321

the sample placed in the central position (right in front of the target center i.e. typical substrate position), and the deposition rate was strongly decreased on samples placed to the side of the target. The measurements were also performed using dcMS, but no major effect of the magnetic field was observed in that case probably due to the low ionized flux fraction. For another possibility to reduce βt , Butler et al. (2018) investigated the number of Ti+ ions that are in the ionization region at the end of a HiPIMS pulse. Since the back-attracting electric field disappears at pulse end, these ions will experience an abruptly lowered βt . In a 100 µs-long reference pulse the authors found that the time-integrated number of Ti+ ions going from the ionization region and out into the volume plasma is approximately ten times the number of Ti+ ions that are left in the ionization region at pulse end. If these “afterglow ions” retain their directed velocity from the sputtering process, then they are all directed away from the target. For the case of such an effective βt = 0 after the pulse, about 10% of the time-integrated (pulse + afterglow) ion flow to the volume plasma would come from the afterglow. However, if we instead consider a shorter 10 µs-long pulse with the same current at the pulse end, then the number of ions that experience high βt during the pulse would be reduced by a factor of 10 (probably more, keeping in mind that the ion production rate is lower during the beginning of a pulse), whereas the same amount of ions would be released at the end of the pulse with low βt (Butler et al., 2018). The average βt could be shifted down considerably. One scenario built on this approach is chopped HiPIMS (Barker et al., 2013, Antonin et al., 2015) discussed in Section 2.4.3. Butler et al. (2018) also point out that concepts such as modulated pulse power magnetron sputtering (MPPMS) (Liebig et al., 2011) and deep oscillation magnetron sputtering (DOMS) (Ferreira et al., 2014) could have similar effects. Both of these methods are based on a train of micropulses (∼ µs) that constitutes a macropulse (∼ ms). The key parameter is the value of the voltage after the individual micropulses in which the ionization occurs. This voltage has to go down to zero, or at least become very low, to release the produced ions. In another attempt to reduce back-attraction of ionized sputtered species, Konstantinidis et al. (2006b) added a secondary discharge by placing an inductive coil to create an inductively coupled discharge, halfway between the target and the substrate to increase the conductivity of the interelectrode volume plasma. They demonstrated increased ion collection at the substrate with increased rf power to the inductive coil and claim that this effect could be used to minimize the decrease in deposition rate due to self-sputtering as it would make it easier for the metal ions to leave the magnetic trap (reduced βt ). Also, the use of bipolar HiPIMS, where a positive voltage pulse is applied after the conventional negative HiPIMS pulse, have been claimed to increase the deposition rate. Wu et al. (2018) report a rate increase of up to 19% when sputtering Cu target in argon at 1.07 Pa using 100 µs long HiPIMS pulses followed by a 100 µs positive pulse with amplitude of maximum Vreverse ≤ 150 V. The HiPIMS discharge current peaked at about 40 A corresponding to a peak current density of 0.12 A/cm2 , that is, a rather weak HiPIMS discharge. The authors propose that the observed rate increase is due to

322

High Power Impulse Magnetron Sputtering

the creation of a positive sheath at the target during the positive pulse, which pushes more positive ions to the substrate. The situation is not clear, however, since other investigations using the same approach do not observe an increase in deposition rate when sputtering Cu (Nakano et al., 2013) or Ti (Britun et al., 2018, Keraudy et al., 2019) with argon as the working gas. Keraudy et al. (2019) state that no deposition rate increase is to be expected, since the positive pulse does not primarily create an ion-reflecting sheath between the plasma and the target, as previously suggested. Instead, the main effect of the reversed pulse is that it raises the plasma potential in the whole magnetic trap (the ionization region), which the authors define as the region where both ends of the magnetic field lines are connected to the target. The reservoir of ions that are inside the magnetic trap at the end of the HiPIMS pulse therefore do not react on the application of the positive pulse. However, the IEDF indicates that as the ions leave the magnetic trap they are uniformly accelerated, and gain an energy qVreverse given by the applied reversed potential. The result is a uniform addition of the same amount of energy to all the ions that leave the cathode plasma during the time of the application of the positive pulse. In addition, Vlˇcek et al. (2009) have demonstrated an increase in the deposition rate (up to 1.9 times) by increasing the target surface temperature (up to 1700◦ C) for a Ti target. It was also shown that the required discharge voltage to maintain the same discharge current was decreased when heating the target, which resulted in an even greater power-normalized deposition rate (deposition rate/time-averaged discharge power) by a factor close to 2.9 at a pulse current density of 0.33 A/cm2 . They point out that the target temperature can be controlled over a wide range in HiPIMS operation. It is likely that at these temperatures the surface of the target, and in particular the race track zone, may be heated to such degree that sublimation (from a solid) or evaporation (from a liquid) takes place. A more detailed study of the target melting, including the spatial and temporal variation of the target surface temperature for various discharge conditions, was reported by Tesaˇr et al. (2011). It should be noted that Anders (2010) carried out a literature survey of hot target effects and argued that the deposition rate increase reported by Bohdansky et al. (1986) under these conditions is related to evaporation rather than to sputtering. This conclusion was supported by Behrisch and Eckstein (1993, 2007), who also acknowledged that the surface binding energy has a nonlinear effect on the sputter yield. Although the heat of sublimation decreases with increasing temperature, evaporation is still dominating at high temperatures by a wide margin (Behrisch and Eckstein, 1993). Indirectly related to the deposition rate is target utilization. Among the early claims about the HiPIMS technique, target utilization was improved (Kouznetsov et al., 1999). Indeed, Liebig et al. (2010) have shown using 2D OES that the sputter distribution of the target is wider for a HiPIMS discharge than for dcMS. Similar findings have been reported by Clarke et al. (2009). This is consistent with empirical observations that show that the width of the ion current density distribution in the target vicinity and thus the erosion width increases with increased discharge current and voltage (Wendt and Lieberman, 1990), both of which are significantly higher for HiPIMS than for dcMS.

Physics of high power impulse magnetron sputtering discharges

323

7.5.3 Deposition rates in reactive HiPIMS Last, we address the situation in reactive HiPIMS discussed in Chapter 5. From the discussion on hysteresis in Section 6.3 we conclude that reactive HiPIMS differs significantly from reactive dcMS due to a less abrupt transition to the poisoned (compound) mode and an eliminated, or at least significantly reduced, hysteresis. The combination of these two factors lead to higher deposition rates and the mechanisms were discussed in Section 6.3.1. For example, investigations of the process characteristics during reactive HiPIMS deposition of Al2 O3 (Wallin and Helmersson, 2008, Aiempanakit et al., 2011), ZrO2 (Sarakinos et al., 2008), and CeO2 (Aiempanakit et al., 2011) have shown that these processes can exhibit a hysteresis-free and stable transition zone at deposition conditions, which in the case of dcMS result in hysteresis and an unstable transition zone (see Fig. 6.10 for Al2 O3 ). The stabilization of the transition zone allows for deposition of stoichiometric films at a lower target compound coverage when compared to the compound mode in dcMS (Wallin and Helmersson, 2008, Aiempanakit et al., 2011, Sarakinos et al., 2008). This has been shown to result in deposition rates similar (Wallin and Helmersson, 2008) or up to two times higher (Sarakinos et al., 2008) than those obtained by dcMS.

References Aiempanakit, M., Kubart, T., Larsson, P., Sarakinos, K., Jensen, J., Helmersson, U., 2011. Hysteresis and process stability in reactive high power impulse magnetron sputtering of metal oxides. Thin Solid Films 519 (22), 7779–7784. Alami, J., Sarakinos, K., Mark, G., Wuttig, M., 2006. On the deposition rate in a high power pulsed magnetron sputtering discharge. Applied Physics Letters 89 (15), 154104. Anders, A., 2008. Self-sputtering runaway in high power impulse magnetron sputtering: the role of secondary electrons and multiply charged metal ions. Applied Physics Letters 92 (20), 201501. Anders, A., 2010. Deposition rates of high power impulse magnetron sputtering: physics and economics. Journal of Vacuum Science and Technology A 28 (4), 783–790. Anders, A., 2011. Discharge physics of high power impulse magnetron sputtering. Surface and Coatings Technology 205, S1–S9. Anders, A., 2012. Self-organization and self-limitation in high power impulse magnetron sputtering. Applied Physics Letters 100 (22), 224104. Anders, A., 2014. Localized heating of electrons in ionization zones: going beyond the Penning–Thornton paradigm in magnetron sputtering. Applied Physics Letters 105 (24), 244104. Anders, A., Andersson, J., Ehiasarian, A., 2007. High power impulse magnetron sputtering: current–voltage–time characteristics indicate the onset of sustained self-sputtering. Journal of Applied Physics 102 (11), 113303. ˇ Anders, A., Capek, J., Hála, M., Martinu, L., 2012a. The ‘recycling trap’: a generalized explanation of discharge runaway in high-power impulse magnetron sputtering. Journal of Physics D: Applied Physics 45 (1), 012003.

324

High Power Impulse Magnetron Sputtering

Anders, A., Ni, P., Rauch, A., 2012b. Drifting localization of ionization runaway: unraveling the nature of anomalous transport in high power impulse magnetron sputtering. Journal of Applied Physics 111 (5), 053304. Anders, A., Panjan, M., Franz, R., Andersson, J., Ni, P., 2013. Drifting potential humps in ionization zones: the “propeller blades” of high power impulse magnetron sputtering. Applied Physics Letters 103 (14), 144103. Anders, A., Yang, Y., 2017. Direct observation of spoke evolution in magnetron sputtering. Applied Physics Letters 111 (6), 064103. Anders, A., Yang, Y., 2018. Plasma studies of a linear magnetron operating in the range from DC to HiPIMS. Journal of Applied Physics 123 (4), 043302. Andersson, J., Anders, A., 2009. Self-sputtering far above the runaway threshold: an extraordinary metal-ion generator. Physical Review Letters 102 (4), 045003. Andersson, J., Ehiasarian, A.P., Anders, A., 2008. Observation of Ti4+ ions in a high power impulse magnetron sputtering plasma. Applied Physics Letters 93 (7), 071504. Andersson, J., Ni, P., Anders, A., 2013. Spectroscopic imaging of self-organization in high power impulse magnetron sputtering plasmas. Applied Physics Letters 103 (5), 054104. Antonin, O., Tiron, V., Costin, C., Popa, G., Minea, T.M., 2015. On the HiPIMS benefits of multi-pulse operating mode. Journal of Physics D: Applied Physics 48 (1), 015202. Barker, P.M., Lewin, E., Patscheider, J., 2013. Modified high power impulse magnetron sputtering process for increased deposition rate of titanium. Journal of Vacuum Science and Technology A 31 (6), 060604. Behrisch, R., Eckstein, W., 1993. Sputtering yield increase with target temperature for Ag. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 82 (2), 255–258. Behrisch, R., Eckstein, W., 2007. Introduction and overview. In: Behrisch, R., Eckstein, W. (Eds.), Sputtering by Particle Bombardment: Experiments and Computer Calculations from Threshold to MeV Energies, vol. 110. Springer Verlag, Berlin–Heidelberg, Germany, pp. 1–10. Chapter 1. Boeuf, J.-P., 2017. Tutorial: physics and modeling of Hall thrusters. Journal of Applied Physics 121 (1), 011101. Bohdansky, J., Lindner, H., Hechtl, E., Martinelli, A.P., Roth, J., 1986. Sputtering yield of Cu and Ag at target temperatures close to the melting point. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 18 (1–6), 509–514. Bohlmark, J., Helmersson, U., VanZeeland, M., Axnäs, I., Alami, J., Brenning, N., 2004. Measurement of the magnetic field change in a pulsed high current magnetron discharge. Plasma Sources Science and Technology 13 (4), 654–661. Bohlmark, J., Lattemann, M., Gudmundsson, J.T., Ehiasarian, A.P., Gonzalvo, Y.A., Brenning, N., Helmersson, U., 2006a. The ion energy distributions and ion flux composition from a high power impulse magnetron sputtering discharge. Thin Solid Films 515 (5), 1522–1526. Bohlmark, J., Östbye, M., Lattemann, M., Ljungcrantz, H., Rosell, T., Helmersson, U., 2006b. Guiding the deposition flux in an ionized magnetron discharge. Thin Solid Films 515 (4), 1928–1931. Bohm, D., Burhop, E.H.S., Massey, H.S.W., 1949. The use of probes for plasma exploration in strong magnetic fields. In: Guthrie, A., Wakerling, R.K. (Eds.), The Characteristics of Electrical Discharges in Magnetic Fields, Number I. In: National Nuclear Energy Series – Manhattan Project Technical Section, vol. 5. McGraw-Hill, New York, pp. 13–76. Chapter 2.

Physics of high power impulse magnetron sputtering discharges

325

Bradley, J.W., 1998. Study of the plasma pre-sheath in magnetron discharges dominated by Bohm diffusion of electrons. Plasma Sources Science and Technology 7 (4), 572–580. Bradley, J.W., Mishra, A., Kelly, P.J., 2015. The effect of changing the magnetic field strength on HiPIMS deposition rates. Journal of Physics D: Applied Physics 48 (21), 215202. Bradley, J.W., Thompson, S., Gonzalvo, Y.A., 2001. Measurement of the plasma potential in a magnetron discharge and the prediction of the electron drift speeds. Plasma Sources Science and Technology 10 (3), 490–501. Breilmann, W., Eitrich, A., Maszl, C., Hecimovic, A., Layes, V., Benedikt, J., von Keudell, A., 2015. High power impulse sputtering of chromium: correlation between the energy distribution of chromium ions and spoke formation. Journal of Physics D: Applied Physics 48 (29), 295202. Brenning, N., Gudmundsson, J.T., Lundin, D., Minea, T., Raadu, M.A., Helmersson, U., 2016. The role of Ohmic heating in dc magnetron sputtering. Plasma Sources Science and Technology 25 (6), 065024. Brenning, N., Gudmundsson, J.T., Raadu, M.A., Petty, T.J., Minea, T., Lundin, D., 2017. A unified treatment of self-sputtering, process gas recycling, and runaway for high power impulse sputtering magnetrons. Plasma Sources Science and Technology 26 (12), 125003. Brenning, N., Lundin, D., Raadu, M.A., Huo, C., Vitelaru, C., Stancu, G.D., Minea, T., Helmersson, U., 2012. Understanding deposition rate loss in high power impulse magnetron sputtering: I. Ionization-driven electric fields. Plasma Sources Science and Technology 21 (2), 025005. Brenning, N., Merlino, R.L., Lundin, D., Raadu, M.A., Helmersson, U., 2009. Faster-thanBohm cross-B electron transport in strongly pulsed plasmas. Physical Review Letters 103 (22), 225003. Britun, N., Michiels, M., Godfroid, T., Snyders, R., 2018. Ion density evolution in a high-power sputtering discharge with bipolar pulsing. Applied Physics Letters 112 (23), 234103. Bugaev, S.P., Koval, N.N., Sochugov, N.S., Zakharov, A.N., 1996. Investigation of a highcurrent pulsed magnetron discharge initiated in the low-pressure diffuse arc plasma. In: Proceedings of the XVIIth International Symposium on Discharges and Electrical Insulation in Vacuum. Berkeley, California, July 21–26, 1996. IEEE, Piscataway, New Jersey, pp. 1074–1076. Bultinck, E., Mahieu, S., Depla, D., Bogaerts, A., 2010. The origin of Bohm diffusion, investigated by a comparison of different modelling methods. Journal of Physics D: Applied Physics 43 (29), 292001. Butler, A., Brenning, N., Raadu, M.A., Gudmundsson, J.T., Minea, T., Lundin, D., 2018. On three different ways to quantify the degree of ionization in sputtering magnetrons. Plasma Sources Science and Technology 27 (10), 105005. ˇ Capek, J., Hála, M., Zabeida, O., Klemberg-Sapieha, J.E., Martinu, L., 2012. Steady state discharge optimization in high-power impulse magnetron sputtering through the control of the magnetic field. Journal of Applied Physics 111 (2), 023301. Chen, F.F., 2016. Introduction to Plasma Physics and Controlled Fusion, 3 ed. Springer Verlag, Cham, Switzerland. Christie, D.J., 2005. Target material pathways model for high power pulsed magnetron sputtering. Journal of Vacuum Science and Technology A 23 (2), 330–335. Clarke, G., Mishra, A., Kelly, P.J., Bradley, J.W., 2009. Cathode current density distributions in high power impulse and direct current magnetron sputtering modes. Plasma Processes and Polymers 6 (S1), S548–S553. Costin, C., Tiron, V., Popa, G., 2011. Fast imaging investigation on pulsed magnetron discharge. IEEE Transactions on Plasma Science 39 (11), 2482–2483.

326

High Power Impulse Magnetron Sputtering

de la Rue, W., Müller, H.W., 1878. Experimental researches on the electric discharge with the chloride of silver battery. Philosophical Transactions of the Royal Society of London 169, 155–241. de los Arcos, T., Layes, V., Aranda Gonzalvo, Y., Schulz-von der Gathen, V., Hecimovic, A., Winter, J., 2013. Current–voltage characteristics and fast imaging of HPPMS plasmas: transition from self-organized to homogeneous plasma regimes. Journal of Physics D: Applied Physics 46 (33), 335201. de los Arcos, T., Schröder, R., Gonzalvo, Y.A., Schulz-von der Gathen, V., Winter, J., 2014. Description of HiPIMS plasma regimes in terms of composition, spoke formation and deposition rate. Plasma Sources Science and Technology 23 (5), 054008. DeKoven, B.M., Ward, P.R., Weiss, R.E., Christie, D.J., Scholl, R.A., Sproul, W.D., Tomasel, F., Anders, A., 2003. Carbon thin film deposition using high power pulsed magnetron sputtering. In: Society of Vacuum Coaters 46th Annual Technical Conference Proceedings. San Francisco, California, May 3–8, 2003. Society of Vacuum Coaters, Albuquerque, New Mexico, pp. 158–165. Depla, D., Mahieu, S. (Eds.), 2008. Reactive Sputter Deposition. Springer Series in Materials Science, vol. 109. Springer-Verlag, Berlin–Heidelberg, Germany. Ehiasarian, A.P., 2008. Fundamentals and applications of HIPIMS. In: Wei, R. (Ed.), Plasma Surface Engineering Research and Its Practical Applications. Research Signpost, Kerala, India, pp. 35–86. Ehiasarian, A.P., Hecimovic, A., de los Arcos, T., New, R., Schulz-von der Gathen, V., Böke, M., Winter, J., 2012. High power impulse magnetron sputtering discharges: instabilities and plasma self-organization. Applied Physics Letters 100 (11), 114101. Ellison, C.L., Raitses, Y., Fisch, N.J., 2012. Cross-field electron transport induced by a rotating spoke in a cylindrical Hall thruster. Physics of Plasmas 19 (1), 013503. Emmerlich, J., Mráz, S., Snyders, R., Jiang, K., Schneider, J.M., 2008. The physical reason for the apparently low deposition rate during high power pulsed magnetron sputtering. Vacuum 82 (8), 867–870. Ferreira, F., Serra, R., Oliveira, J.C., Cavaleiro, A., 2014. Effect of peak target power on the properties of Cr thin films sputtered by HiPIMS in deep oscillation magnetron sputtering (DOMS) mode. Surface and Coatings Technology 258, 249–256. Franz, R., Clavero, C., Kolbeck, J., Anders, A., 2016. Influence of ionisation zone motion in high power impulse magnetron sputtering on angular ion flux and NbOx film growth. Plasma Sources Science and Technology 25 (1), 015022. Gudmundsson, J.T., 2016. On reactive high power impulse magnetron sputtering. Plasma Physics and Controlled Fusion 58 (1), 014002. Gudmundsson, J.T., Alami, J., Helmersson, U., 2002. Spatial and temporal behavior of the plasma parameters in a pulsed magnetron discharge. Surface and Coatings Technology 161 (2–3), 249–256. Gudmundsson, J.T., Brenning, N., Lundin, D., Helmersson, U., 2012. The high power impulse magnetron sputtering discharge. Journal of Vacuum Science and Technology A 30 (3), 030801. Gudmundsson, J.T., Lundin, D., Brenning, N., Raadu, M.A., Huo, C., Minea, T.M., 2016. An ionization region model of the reactive Ar/O2 high power impulse magnetron sputtering discharge. Plasma Sources Science and Technology 25 (6), 065004. Gudmundsson, J.T., Lundin, D., Stancu, G.D., Brenning, N., Minea, T.M., 2015. Are the argon metastables important in high power impulse magnetron sputtering discharges? Physics of Plasmas 22 (11), 113508.

Physics of high power impulse magnetron sputtering discharges

327

Hála, M., Viau, N., Zabeida, O., Klemberg-Sapieha, J.E., Martinu, L., 2010. Dynamics of reactive high-power impulse magnetron sputtering discharge studied by time- and spaceresolved optical emission spectroscopy and fast imaging. Journal of Applied Physics 107 (4), 043305. Hayashi, T., Sato, T., the Complexity Simulation Group, 1999. Self-organizing plasmas. Plasma Physics and Controlled Fusion 41 (3A), A229–A238. Hecimovic, A., 2016. Anomalous cross-B field transport and spokes in HiPIMS plasma. Journal of Physics D: Applied Physics 49 (18), 18LT01. Hecimovic, A., Böke, M., Winter, J., 2014. The characteristic shape of emission profiles of plasma spokes in HiPIMS: the role of secondary electrons. Journal of Physics D: Applied Physics 47 (10), 102003. Hecimovic, A., Britun, N., Konstantinidis, S., Snyders, R., 2017a. Sputtering process in the presence of plasma self-organization. Applied Physics Letters 110 (1), 014103. Hecimovic, A., Corbella, C., Maszl, C., Breilmann, W., von Keudell, A., 2017b. Investigation of plasma spokes in reactive high power impulse magnetron sputtering discharge. Journal of Applied Physics 121 (17), 171915. Hecimovic, A., Ehiasarian, A.P., 2009. Time evolution of ion energies in HIPIMS of chromium plasma discharge. Journal of Physics D: Applied Physics 42 (13), 135209. Hecimovic, A., Ehiasarian, A.P., 2011. Temporal evolution of the ion fluxes for various elements in HIPIMS plasma discharge. IEEE Transactions on Plasma Science 39 (4), 1154–1164. Hecimovic, A., Held, J., Schulz-von der Gathen, V., Breilmann, W., Maszl, C., von Keudell, A., 2017. Probing the electron density in HiPIMS plasmas by target inserts. Journal of Physics D: Applied Physics 50 (50), 505204. Hecimovic, A., Maszl, C., Schulz-von der Gathen, V., Böke, M., von Keudell, A., 2016. Spoke rotation reversal in magnetron discharges of aluminium, chromium and titanium. Plasma Sources Science and Technology 25 (3), 035001. Hecimovic, A., Schulz-von der Gathen, V., Böke, M., von Keudell, A., Winter, J., 2015. Spoke transitions in HiPIMS discharges. Plasma Sources Science and Technology 24 (4), 045005. Hecimovic, A., von Keudell, A., 2018. Spokes in high power impulse magnetron sputtering plasmas. Journal of Physics D: Applied Physics 51 (45), 453001. Helmersson, U., Lattemann, M., Alami, J., Bohlmark, J., Ehiasarian, A.P., Gudmundsson, J.T., 2005. High power impulse magnetron sputtering discharges and thin film growth: a brief review. In: Proceedings of the 48th Society of Vacuum Coaters Annual Technical Conference. Denver, Colorado, April 23–28, 2005. Society of Vacuum Coaters, Albuquerque, New Mexico, pp. 458–464. Hippler, R., Cada, M., Stranak, V., Helm, C.A., Hubicka, Z., 2019. Pressure dependence of singly and doubly charged ion formation in a HiPIMS discharge. Journal of Applied Physics 125 (1), 013301. Hnilica, J., Klein, P., Šlapanská, M., Fekete, M., Vašina, P., 2018. Effect of magnetic field on spoke behaviour in HiPIMS plasma. Journal of Physics D 51, 095204. Hoffman, D.W., 1985. A sputtering wind. Journal of Vacuum Science and Technology A 3 (3), 561–566. Hoh, F.C., Lehnert, B., 1960. Diffusion processes in a plasma column in a longitudinal magnetic field. Physics of Fluids 3 (4), 600–607. Huo, C., Lundin, D., Gudmundsson, J.T., Raadu, M.A., Bradley, J.W., Brenning, N., 2017. Particle-balance models for pulsed sputtering magnetrons. Journal of Physics D: Applied Physics 50 (35), 354003.

328

High Power Impulse Magnetron Sputtering

Huo, C., Lundin, D., Raadu, M.A., Anders, A., Gudmundsson, J.T., Brenning, N., 2013. On sheath energization and ohmic heating in sputtering magnetrons. Plasma Sources Science and Technology 22 (4), 045005. Huo, C., Lundin, D., Raadu, M.A., Anders, A., Gudmundsson, J.T., Brenning, N., 2014. On the road to self-sputtering in high power impulse magnetron sputtering: particle balance and discharge characteristics. Plasma Sources Science and Technology 23 (2), 025017. Huo, C., Raadu, M.A., Lundin, D., Gudmundsson, J.T., Anders, A., Brenning, N., 2012. Gas rarefaction and the time evolution of long high-power impulse magnetron sputtering pulses. Plasma Sources Science and Technology 21 (4), 045004. Hurtig, T., 2004. Plasma Cloud Penetration Across Magnetic Barriers. Ph.D. thesis. KTH Royal Institute of Technology, Stockholm, Sweden. Hurtig, T., Brenning, N., Raadu, M.A., 2005. The role of high frequency oscillations in the penetration of plasma clouds across magnetic boundaries. Physics of Plasmas 12 (1), 012308. Janes, G.S., Lowder, R.S., 1966. Anomalous electron diffusion and ion acceleration in a lowdensity plasma. Physics of Fluids 9 (6), 1115–1123. Jouan, P.-Y., Le Brizoual, L., Cardinaud, C., Tricot, S., Djouadi, M.A., 2010. HiPIMS ion energy distribution measurements in reactive mode. IEEE Transactions on Plasma Science 38 (11), 3089–3094. Kadlec, S., 2007. Simulation of neutral particle flow during high power magnetron impulse. Plasma Processes and Polymers 4 (S1), S419–S423. Kadomtsev, B.B., Nedospasov, A.V., 1960. Instability of the positive column in a magnetic field and the ‘anomalous’ diffusion effect. Journal of Nuclear Energy. Part C 1 (4), 230–235. Keraudy, J., Viloan, R.P.B., Raadu, M.A., Brenning, N., Lundin, D., Helmersson, U., 2019. Bipolar HiPIMS for tailoring ion energies in thin film deposition. Surface and Coatings Technology 359, 422–437. Klein, P., Lockwood Estrin, F., Hnilica, J., Vašina, P., Bradley, J.W., 2017. Simultaneous electrical and optical study of spoke rotation, merging and splitting in HiPIMS plasma. Journal of Physics D: Applied Physics 50 (1), 015209. Konstantinidis, S., Dauchot, J.P., Ganciu, M., Hecq, M., 2006a. Influence of pulse duration on the plasma characteristics in high-power pulsed magnetron discharges. Journal of Applied Physics 99 (1), 013307. Konstantinidis, S., Dauchot, J.P., Ganciu, M., Hecq, M., 2006b. Transport of ionized metal atoms in high-power pulsed magnetron discharges assisted by inductively coupled plasma. Applied Physics Letters 88 (2), 021501. Kouznetsov, V., Macák, K., Schneider, J.M., Helmersson, U., Petrov, I., 1999. A novel pulsed magnetron sputter technique utilizing very high target power densities. Surface and Coatings Technology 122 (2–3), 290–293. Kozyrev, A.V., Sochugov, N.S., Oskomov, K.V., Zakharov, A.N., Odivanova, A.N., 2011. Optical studies of plasma inhomogeneities in a high-current pulsed magnetron discharge. Plasma Physics Report 37 (7), 621–627. Layes, V., Monje, S., Corbella, C., Trieschmann, J., de los Arcos, T., von Keudell, A., 2017a. Species transport on the target during high power impulse magnetron sputtering. Applied Physics Letters 110 (8), 081603. Layes, V., Monje, S., Corbella, C., von der Gathen, V.S., von Keudell, A., de los Arcos, T., 2017b. Composite targets in HiPIMS plasmas: correlation of in-vacuum XPS characterization and optical plasma diagnostics. Journal of Applied Physics 121 (17), 171912. Layes, V., Roca, C.C., Monje, S., Schulz-von der Gathen, V., von Keudell, A., de los Arcos, T., 2018. Connection between target poisoning and current waveforms in reactive high power

Physics of high power impulse magnetron sputtering discharges

329

impulse magnetron sputtering of chromium. Plasma Sources Science and Technology 27 (8), 084004. Leroy, W.P., Konstantinidis, S., Mahieu, S., Snyders, R., Depla, D., 2011. Angular-resolved energy flux measurements of a dc- and HIPIMS-powered rotating cylindrical magnetron in reactive and non-reactive atmosphere. Journal of Physics D: Applied Physics 44 (11), 115201. Lieberman, M.A., Lichtenberg, A.J., 2005. Principles of Plasma Discharges and Materials Processing, 2 ed. John Wiley & Sons, New York. Liebig, B., Bradley, J.W., 2013. Space charge, plasma potential and electric field distributions in HiPIMS discharges of varying configuration. Plasma Sources Science and Technology 22 (4), 045020. Liebig, B., Braithwaite, N.St.J., Kelly, P.J., Bradley, J.W., 2010. Spatial and temporal investigation of high power pulsed magnetron discharges by optical 2D-imaging. Thin Solid Films 519 (5), 1699–1704. Liebig, B., Braithwaite, N.St.J., Kelly, P.J., Chistyakov, R., Abraham, B., Bradley, J., 2011. Time-resolved plasma characterisation of modulated pulsed power magnetron sputtering of chromium. Surface and Coatings Technology 205, S312–S316. Lockwood Estrin, F., Karkari, S.K., Bradley, J.W., 2017. Triple probe interrogation of spokes in a HiPIMS discharge. Journal of Physics D: Applied Physics 50 (29), 295201. Lundin, D., Brenning, N., Jadernas, D., Larsson, P., Wallin, E., Lattemann, M., Raadu, M.A., Helmersson, U., 2009. Transition between the discharge regimes of high power impulse magnetron sputtering and conventional direct current magnetron sputtering. Plasma Sources Science and Technology 18 (4), 045008. Lundin, D., Helmersson, U., Kirkpatrick, S., Rohde, S., Brenning, N., 2008a. Anomalous electron transport in high power impulse magnetron sputtering. Plasma Sources Science and Technology 17 (2), 025007. Lundin, D., Larsson, P., Wallin, E., Lattemann, M., Brenning, N., Helmersson, U., 2008b. Cross-field ion transport during high power impulse magnetron sputtering. Plasma Sources Science and Technology 17 (3), 035021. Lundin, D., Sahab, S.A., Brenning, N., Huo, C., Helmersson, U., 2011. Internal current measurements in high power impulse magnetron sputtering. Plasma Sources Science and Technology 20 (4), 045003. Lundin, D., Vitelaru, C., de Poucques, L., Brenning, N., Minea, T., 2013. Ti–Ar scattering cross sections by direct comparison of Monte Carlo simulations and laser-induced fluorescence spectroscopy in magnetron discharges. Journal of Physics D: Applied Physics 46 (17), 175201. Luo, H., Minea, T., Gao, F., Billard, A., 2018. The spoke origin based on the coupling-induced wave model in high-power impulse magnetron sputtering plasma. Plasma Sources Science and Technology 27 (11), 115003. Magnus, F., Sveinsson, O.B., Olafsson, S., Gudmundsson, J.T., 2011. Current–voltage–time characteristics of the reactive Ar/N2 high power impulse magnetron sputtering discharge. Journal of Applied Physics 110 (8), 083306. Magnus, F., Tryggvason, T.K., Olafsson, S., Gudmundsson, J.T., 2012. Current–voltage–time characteristics of the reactive Ar/O2 high power impulse magnetron sputtering discharge. Journal of Vacuum Science and Technology A 30 (5), 050601. Marcak, A., Corbella, C., de los Arcos, T., von Keudell, A., 2015. Ion-induced secondary electron emission from oxidized metal surfaces measured in a particle beam reactor. Review of Scientific Instruments 86 (10), 106102.

330

High Power Impulse Magnetron Sputtering

Martines, E., Cavazzana, R., Serianni, G., Spolaore, M., Tramontin, L., Zuin, M., Antoni, V., 2001. Electrostatic fluctuations in a direct current magnetron sputtering plasma. Physics of Plasmas 8 (6), 3042–3050. Martines, E., Zuin, M., Antonia, V., Cavazzana, R., Serianni, G., Spolaore, M., Nakashima, C., 2004. Experimental investigation of low frequency waves propagating in a direct planar magnetron plasma. Physics of Plasmas 11 (5), 1938–1946. Maszl, C., Breilmann, W., Benedikt, J., von Keudell, A., 2014a. Origin of the energetic ions at the substrate generated during high power pulsed magnetron sputtering of titanium. Journal of Physics D: Applied Physics 47 (22), 224002. Maszl, C., Breilmann, W., Berscheid, L., Benedikt, J., von Keudell, A., 2014b. Fast time resolved techniques as key to the understanding of energy and particle transport in HPPMSplasmas. IEEE Transactions on Plasma Science 42 (10), 2812–2813. Mazouffre, S., 2016. Electric propulsion for satellites and spacecraft: established technologies and novel approaches. Plasma Sources Science and Technology 25 (3), 033002. McDonald, M.S., Gallimore, A.D., 2011. Rotating spoke instabilities in Hall thrusters. IEEE Transactions on Plasma Science 39 (11), 2952–2953. McLain, J., Raman, P., Patel, D., Spreadbury, R., Uhlig, J., Shchelkanov, I., Ruzic, D.N., 2018. Linear magnetron HiPIMS high deposition rate magnet pack. Vacuum 155, 559–565. Mishra, A., Kelly, P.J., Bradley, J.W., 2010. The evolution of the plasma potential in a HiPIMS discharge and its relationship to deposition rate. Plasma Sources Science and Technology 19 (4), 045014. Nakano, T., Hirukawa, N., Saeki, S., Baba, S., 2013. Effects of target voltage during pulse-off period in pulsed magnetron sputtering on afterglow plasma and deposited film structure. Vacuum 87, 109–113. Ni, P.A., Hornschuch, C., Panjan, M., Anders, A., 2012. Plasma flares in high power impulse magnetron sputtering. Applied Physics Letters 101 (22), 224102. Panjan, M., Anders, A., 2017. Plasma potential of a moving ionization zone in DC magnetron sputtering. Journal of Applied Physics 121 (6), 063302. Panjan, M., Franz, R., Anders, A., 2014. Asymmetric particle fluxes from drifting ionization zones in sputtering magnetrons. Plasma Sources Science and Technology 23 (2), 025007. Poolcharuansin, P., Bradley, J.W., 2010. Short and long-term plasma phenomena in a HiPIMS discharge. Plasma Sources Science and Technology 19 (2), 025010. Poolcharuansin, P., Liebig, B., Bradley, J.W., 2010. Plasma parameters in a pre-ionized HIPIMS discharge operating at low pressure. IEEE Transactions on Plasma Science 38 (11), 3007–3015. Poolcharuansin, P., Liebig, B., Bradley, J.W., 2012. More evidence for azimuthal ion spin in HiPIMS discharges. Plasma Sources Science and Technology 21 (1), 015001. Poolcharuansin, P., Lockwood Estrin, F., Bradley, J.W., 2015. The use of segmented cathodes to determine the spoke current density distribution in high power impulse magnetron sputtering plasmas. Journal of Applied Physics 117 (16), 163304. Preissing, P., 2016. Investigation of HiPIMS Plasmas by Absorption Spectroscopy. Master’s thesis. Ruhr Universität Bochum, Bochum, Germany. Raadu, M.A., Axnäs, I., Gudmundsson, J.T., Huo, C., Brenning, N., 2011. An ionization region model for high power impulse magnetron sputtering discharges. Plasma Sources Science and Technology 20 (6), 065007. Raman, P., Shchelkanov, I., McLain, J., Cheng, M., Ruzic, D., Haehnlein, I., Jurczyk, B., Stubbers, R., Armstrong, S., 2016. High deposition rate symmetric magnet pack for high power pulsed magnetron sputtering. Surface and Coatings Technology 293, 10–15.

Physics of high power impulse magnetron sputtering discharges

331

Rauch, A., Mendelsberg, R.J., Sanders, J.M., Anders, A., 2012. Plasma potential mapping of high power impulse magnetron sputtering discharges. Journal of Applied Physics 111 (8), 083302. Revel, A., Minea, T., Costin, C., 2018. 2D PIC-MCC simulations of magnetron plasma in HiPIMS regime with external circuit. Plasma Sources Science and Technology 27 (10), 105009. Revel, A., Minea, T., Tsikata, S., 2016. Pseudo-3D PIC modeling of drift-induced spatial inhomogeneities in planar magnetron plasmas. Physics of Plasmas 23 (10), 100701. Ross, A.E., Sanginés, R., Treverrow, B., Bilek, M.M.M., McKenzie, D.R., 2011. Optimizing efficiency of Ti ionized deposition in HIPIMS. Plasma Sources Science and Technology 20 (3), 035021. Rossnagel, S.M., 1988. Deposition and redeposition in magnetrons. Journal of Vacuum Science and Technology A 6 (6), 3049–3054. Rossnagel, S.M., Kaufman, H.R., 1987a. Charge transport in magnetrons. Journal of Vacuum Science and Technology A 5 (4), 2276–2279. Rossnagel, S.M., Kaufman, H.R., 1987b. Induced drift currents in circular planar magnetrons. Journal of Vacuum Science and Technology A 5 (1), 88–91. Samuelsson, M., Lundin, D., Jensen, J., Raadu, M.A., Gudmundsson, J.T., Helmersson, U., 2010. On the film density using high power impulse magnetron sputtering. Surface and Coatings Technology 202 (2), 591–596. Sarakinos, K., Alami, J., Klever, C., Wuttig, M., 2008. Process stabilization and enhancement of deposition rate during reactive high power pulsed magnetron sputtering of zirconium oxide. Surface and Coatings Technology 202 (20), 5033–5035. Sheridan, T.E., Goree, J., 1989. Low-frequency turbulent transport in magnetron plasmas. Journal of Vacuum Science and Technology A 7 (3), 1014–1018. Sigurjónsson, P., 2008. Spatial and Temporal Variation of the Plasma Parameters in a High Power Impulse Magnetron Sputtering (HiPIMS) Discharge. Master’s thesis. University of Iceland, Reykjavik, Iceland. Spagnolo, S., Zuin, M., Cavazzana, R., Martines, E., Patelli, A., Spolaore, M., Colasuonno, M., 2016. Characterization of electromagnetic fluctuations in a HiPIMS plasma. Plasma Sources Science and Technology 25 (6), 065016. Stancu, G.D., Brenning, N., Vitelaru, C., Lundin, D., Minea, T., 2015. Argon metastables in HiPIMS: validation of the ionization region model by direct comparison to time resolved tunable diode-laser diagnostics. Plasma Sources Science and Technology 24 (4), 045011. Stepanova, M., Dew, S.K., 2004. Anisotropic energies of sputtered atoms under oblique ion incidence. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 215 (3–4), 357–365. Tesaˇr, J., Martan, J., Rezek, J., 2011. On surface temperatures during high power pulsed magnetron sputtering using a hot target. Surface and Coatings Technology 206 (6), 1155–1159. Thornton, J.A., 1978. Magnetron sputtering: basic physics and application to cylindrical magnetrons. Journal of Vacuum Science and Technology 15 (2), 171–177. Tsikata, S., Minea, T., 2015. Modulated electron cyclotron drift instability in a high-power pulsed magnetron discharge. Physical Review Letters 114 (18), 185001. Van Aeken, K., Mahieu, S., Depla, D., 2008. The metal flux from a rotating cylindrical magnetron: a Monte Carlo simulation. Journal of Physics D: Applied Physics 41 (20), 205307. Vitelaru, C., Lundin, D., Stancu, G.D., Brenning, N., Bretagne, J., Minea, T., 2012. Argon metastables in HiPIMS: time-resolved tunable diode-laser diagnostics. Plasma Sources Science and Technology 21 (2), 025010.

332

High Power Impulse Magnetron Sputtering

Vlˇcek, J., Burcalová, K., 2010. A phenomenological equilibrium model applicable to highpower pulsed magnetron sputtering. Plasma Sources Science and Technology 19 (6), 065010. Vlˇcek, J., Zustin, B., Rezek, J., Brucalova, K., Tesar, J., 2009. Pulsed magnetron sputtering of metallic films using a hot target. In: Proceedings of the 52nd Annual Technical Conference Society of Vacuum Coaters. Santa Clara, California, May 9–14, 2009. Society of Vacuum Coaters, Albuquerque, New Mexico, pp. 219–223. Waits, R.K., 1978. Planar magnetron sputtering. Journal of Vacuum Science and Technology 15 (2), 179–187. Wallin, E., Helmersson, U., 2008. Hysteresis-free reactive high power impulse magnetron sputtering. Thin Solid Films 516 (18), 6398–6401. Wendt, A.E., Lieberman, M.A., 1990. Spatial structure of a planar magnetron discharge. Journal of Vacuum Science and Technology A 8 (2), 902–907. Winter, J., Hecimovic, A., de los Arcos, T., Böke, M., Schulz-von der Gathen, V., 2013. Instabilities in high-power impulse magnetron plasmas: from stochasticity to periodicity. Journal of Physics D: Applied Physics 46 (8), 084007. Wu, B., Shchelkanov, I.H.I., McLain, J., Patel, D., Uhlig, J., Jurczyk, B., Leng, Y., Ruzic, D.N., 2018. Cu films prepared by bipolar pulsed high power impulse magnetron sputtering. Vacuum 150, 216–221. Yang, Y., Tanaka, K., Liu, J., Anders, A., 2015. Ion energies in high power impulse magnetron sputtering with and without localized ionization zones. Applied Physics Letters 106 (12), 124102. Yang, Y., Zhou, X., Liu, J.X., Anders, A., 2016. Evidence for breathing modes in direct current, pulsed, and high power impulse magnetron sputtering plasmas. Applied Physics Letters 108 (3), 034101. Young, C.V., Fabris, A.L., Cappelli, M.A., 2015. Ion dynamics in an E × B Hall plasma accelerator. Applied Physics Letters 106 (4), 044102. Yushkov, G.Y., Anders, A., 2010. Origin of the delayed current onset in high power impulse magnetron sputtering. IEEE Transactions on Plasma Science 38 (11), 3028–3034.