High power impulse magnetron sputtering (HiPIMS) discharges with a zirconium target are studied experimentally and by applying the ionization region model (IRM). The measured ionized flux fraction lies in the range between 25% and 59% and increases with increased peak discharge current density ranging from 0.5 to 2 A/cm 2 at a working gas pressure of 1 Pa. At the same time, the sputter rate-normalized deposition rate determined by the IRM decreases in accordance with the HiPIMS compromise. For a given discharge current and voltage waveform, using the measured ionized flux fraction to lock the model, the IRM provides the temporal variation of the various species and the average electron energy within the ionization region, as well as internal discharge parameters such as the ionization probability and the back-attraction probability of the sputtered species. The ionization probability is found to be in the range 73%–91%, and the back-attraction probability is in the range 67%–77%. Significant working gas rarefaction is observed in these discharges. The degree of working gas rarefaction is in the range 45%–85%, higher for low pressure and higher peak discharge current density. We find electron impact ionization to be the main contributor to working gas rarefaction, with over 80% contribution, while kick-out by zirconium atoms and argon atoms from the target has a smaller contribution. The dominating contribution of electron impact ionization to working gas rarefaction is very similar to other low sputter yield materials.

The magnetron sputtering discharge1–3 is a highly successful and widely used thin film deposition technique that belongs to the group of physical vapor deposition methods.4 The source of the film-forming material is a solid target out of which the atoms are released by ion bombardment. The magnetron sputtering discharge is based on forming a dense plasma in the target vicinity by a static magnetic field that traps the electrons.1,2,5 This dense plasma is easily observable and appears as a brightly glowing torus located adjacent to the target surface. This brightly glowing region is referred to as the ionization region (IR).6 Ions accelerated from this dense plasma sputter the film-forming material from the cathode target.

When operated as a dc magnetron sputtering (dcMS) discharge, the ions of the working gas bombard the target and the sputtered species that reach the substrate are mostly neutral atoms. The ions bombarding the substrate are ions of the working gas. By applying high voltage pulses of low duty cycle to the cathode target, the discharge current density in the pulse can become high, and therefore, a high electron density is created in the IR.7–12 Consequently, a significant fraction of the sputtered atoms coming off the target becomes ionized as they pass through the dense plasma of the ionization region. In this case, ions of both the working gas and the target material bombard the target. This also makes ions of the film-forming material available for deposition onto the substrate. This variant of magnetron sputtering is referred to as high power impulse magnetron sputtering (HiPIMS).7,10 It is one approach to create a highly ionized flux of the film-forming material.7,13 When the atoms of the film-forming material in the deposition flux are ionized, the energy and direction of the ions bombarding the substrate can be controlled by biasing the substrate.13–15 Control of the ion bombarding energy means that the need for external substrate heating can be significantly reduced or even eliminated.16–18 Furthermore, selective microstructural texturing is made possible.18–20 

Zirconium (Zr([Kr]4d 2s 2)) is a group-IV transition metal element. The stable crystalline state of zirconium at room temperature and ambient pressure is a hexagonal close-packed (hcp) structure ( α-Zr phase). With increased temperature, it transforms martensitically into the body-centered cubic (bcc) structure ( β-Zr phase) at 1136 K.21 In comparison with other elemental metals, zirconium in solid form exhibits good thermal conductivity, high melting point, low thermal expansion, and good mechanical strength. Furthermore, zirconium has a very low neutron scattering cross section and a high solid solubility of oxygen and hydrogen. Therefore, zirconium and its alloys in bulk and thin film forms are widely used in the nuclear industry.22,23 Furthermore, as zirconium has excellent corrosion resistance and acceptable biocompatibility, titanium–zirconium (Ti–Zr) binary alloys have been proposed for biomedical applications.24,25

Zirconium thin films with hexagonal close packed crystal structure ( α-Zr) have been deposited by dc magnetron sputtering,26–28 asymmetric bipolar pulsed magnetron sputtering,29,30 and HiPIMS.19,20 Noteworthy is the work of Fankhauser et al.28 which deposited epitaxial Zr(0001) thin films onto Al 2O 3(0001) using dc magnetron sputtering. When deposited by HiPIMS, at substrate temperature in the range 300–873 K, Kuo et al.20 find zirconium films to be polycrystalline and exhibit predominantly [0 0 0 1] texture. The crystallite size is found to increase with increasing substrate temperature during deposition.29,30 Kuo et al.20 also explored the influence of the pulse width and substrate bias on the properties of zirconium films deposited by HiPIMS and showed that the predominant texture can become [1 0 1 ¯ 1] by synchronizing bias on the substrate and longer pulse lengths. Lustosa et al.25 deposited Ti-Zr alloy using HiPIMS, exploring how the hardness varied with pulsing frequency. The hardness decreased and lower contact angles and better hydrophilic properties were observed when the alloy was deposited at lower pulsing frequencies.

Here, we develop an ionization region model (IRM) of a HiPIMS discharge with argon as the working gas and a zirconium target. The model provides insights into the discharge physics and chemistry, notably the temporal evolution of the species densities and the discharge current composition, a voltage drop across the IR, the ionization probability, as well as the back-attraction probability of the sputtered species.31 Earlier, the IRM has been applied to study discharges with graphite,32 aluminum,31,33 titanium,31,34 copper,35 and tungsten36,37 targets. These studies indicate that the process that dominates working gas rarefaction depends strongly on the sputter yield and/or self-sputter yield,38 with little dependence on the mass of the target atoms, contrary to reports by other authors.39,40 For example, rarefaction in a discharge with a tungsten target, having a high atomic mass and a moderate sputter yield, behaves very similar to a discharge using an aluminum target, having a low atomic mass and a similar sputter yield to tungsten.38 Similarly, the back-attraction probability appears to depend on the sputter yield of the target material.35 To fully disentangle the effect of mass and sputter yield, we here develop a model of a HiPIMS discharge with a zirconium target and apply it to a few discharges with experimentally determined discharge voltage and current waveforms and measured ionized flux fraction. Zirconium has a moderate atomic mass, lower than tungsten and higher than copper, and a low sputter yield. Therefore, it is important to understand a HiPIMS discharge with a zirconium target to provide a piece of the puzzle on how working gas rarefaction, the deposition rate, and the back-attraction probability depend on the atom mass and the sputter yield of the target material.

The paper is structured as follows: In Sec. II A, we discuss the experimental setup. The basics of the ionization region model and the addition of the zirconium reaction set are reviewed in Sec. II B. Section III A discusses the experimental findings and Sec. III B the results of the model studies. The findings of this work are summarized in Sec. IV.

The sputter target was a 2 in. zirconium disk mounted on an unbalanced magnetron assembly. The base pressure was maintained below 2 × 10 4 Pa by a turbomolecular pump backed by a roughing pump. The working gas pressure was set to 0.5 and 1 Pa by regulating the argon gas flow. A dc power supply together with a HiPSTER 6 pulsing unit (Ionautics, Sweden) was used to apply voltage pulses to the cathode target. The peak discharge current was kept fixed and an average discharge power P D was maintained at 60 W by varying the repetition frequency. The pulse was kept at a constant length of either 50 or 100  μs. For comparison, measurements were also made for a dcMS discharge at the same pressures and average power and a discharge voltage of V D , dcMS = 255 V.

The flux parameters were determined using an ion meter, which consisted of a magnetic schielding, a grounded casing, and a quartz crystal micro-balance (QCM) sensor which could be biased to achieve charge selectivity. The ion meter could measure either the deposition rate from ions and neutrals or from neutrals only by varying the voltage applied to the biased top QCM electrode. The ion meter (or gridless QCM/m-QCM) and its design and operation principles are described in detail elsewhere.41,42 For the measurements, the ion meter was placed at distances of 3, 4, 6, 8, and 10 cm above the racetrack and facing the target surface.

The IRM of a high power impulse magnetron sputtering discharge is a volume-averaged plasma chemistry model that provides the temporal variation of the various species densities and the electron energy. It is a semi-empirical model that requires experimentally determined discharge voltage and current waveforms, the working gas pressure, the target and its dimensions, and the dimensions of the ionization region as input. The IRM only covers the target and the ionization region, which is defined as an annular cylinder of width w RT = r c 2 r c 1 positioned above the racetrack, and a length L = z 2 z 1, extending from z 1 to z 2 axially away from the target.

The IRM, originally described by Raadu et al.43 in 2011, has been under constant development ever since, and its main features are summarized by Huo et al.31 In the IRM, the temporal development of the species densities and electron temperature is defined by a set of ordinary differential equations.31,43 The electron density is found by applying the quasineutrality condition. The details of the IRM, including the reaction rates for the various surface and volume processes that are taken into account, are summarized by Huo et al.31 More recent modifications concerning the treatment of the afterglow44 and updated reaction rates45 have been made, as well as a modification to the term that describes the kick-out by the sputtered species and contributes to working gas rarefaction as discussed by Barynova et al..38 This last modification is needed to analyze the contributions from electron impact ionization and kick-out to working gas rarefaction. The updated IRM is applied for this current study.

There are three free parameters or fitting parameters that are adjusted in the IRM: (i) the ion back-attraction probability for the metal ions β t , pulse and gas ions β g , pulse; (ii) the potential drop across the IR, V IR; and (iii) the electron recapture probability r. In practice, V IR is determined using the ratio f = V IR / V D, where V D is the discharge voltage.31 For the cases presented here, we assume r = 0.7, since it has been suggested by Buyle et al.,46 based on a Monte Carlo model calculations, that the electron recapture probability is typically between 65% and 75% for a planar magnetron sputtering discharge. Note that for a metal target, the value of the electron recapture probability r does not influence the model results significantly. Furthermore, we assume β t , pulse = β g , pulse as in previous studies.31,36,43 It has been argued, based on the direct simulation Monte Carlo calculation, that this may be a rough approximation and that the back-attraction probability for the ions of the working gas is close to unity.47 This will not have much influence on the overall findings reported in this current work.

We can lock the model and confine the two fitting parameters, using the experimentally measured discharge current waveform and the measured ionized flux fraction as discussed by Butler et al..48 The ionized flux fraction onto a given surface facing the discharge is related to the time-integrated total number of metal atoms and metal ions leaving the IR for the diffusion region (DR) during the discharge pulse through
F flux = ( 1 + ( ξ tn ξ ti ) T Γ ~ M DR ( t ) d t T Γ ~ M + DR ( t ) d t ) 1 ,
(1)
where Γ ~ M ( t ) is the total flux of metal neutrals and Γ ~ M + ( t ) is the total flux of metal ions into the diffusion region, T is the pulse period, and the collection of metal neutrals and ions on the given surface is described through the ratio of the transport parameters ξ tn / ξ ti, where ξ ti is the transport parameter for ions, and ξ tn is the transport parameter for neutrals, of the sputtered species49,50 (see, in particular, Fig. 1 of Rudolph et al.34). The transport parameter ratio has been determined experimentally for a HiPIMS discharge with a titanium target to be roughly ξ tn / ξ ti 1.25 for a substrate located 3 cm from the target surface and ξ tn / ξ ti 2 for a substrate located 7 cm from the target surface.50 We use these values and assume a value of 2 for flux measurements made in the range 7–10 cm from the target surface and use a linear fit to determine values for 4 and 6 cm distance.
As discussed above, the model results include the back-attraction probability during the pulse from a potential drop across the IR, V IR. This potential barrier prevents some of the ions in the IR from reaching the substrate, lowering the deposition rate. This potential barrier is eliminated when the pulse is shut off. Therefore, we assume β t to be zero in the afterglow and consequently the back-attraction probability is defined as44 
β t ( t ) = { β t , pulse during the pulse , 0 in the afterglow .
(2)
After the pulse is switched off, the metal ions are assumed to have a velocity that is similar to that of the sputtered metal species.

1. Species considered and reactions involving zirconium

The discharge formed is composed of the argon working gas atoms and ions, the sputtered zirconium species and their ions, as well as electrons. The working gas species included in the model for the argon discharge are cold argon atoms in the ground state Ar C, metastable argon atoms [both Ar(4s[3/2] 2) and Ar(4s’[1/2] 0)], Ar + and Ar 2 + ions, and warm Ar W and hot Ar H argon atoms. The latter two populations of argon atoms originate from argon ions that bombard the target and then return to the discharge as neutrals. The hot argon population represents reflected argon atoms at the target.51,52 They are assumed to have an average energy of 2 eV as motivated by Raadu et al.43 The warm population Ar W, which is assumed to have energy similar to the thermal energy of the surface, with about 0.1 eV ( 1000 K),53 is due to argon ions that penetrate the target surface and then slowly diffuse back as atoms. The argon discharge, the reaction set, and rate coefficients can be found in recent publications.32,36

For the zirconium discharge, we include zirconium atoms in the ground state and the ions Zr + and Zr 2 +. The sputtered zirconium atoms enter the IR with a velocity corresponding to the energy of 1 / 2 × E cohesive = 1 / 2 × 6.25 eV = 3.125 eV,54 (p. 50), where E cohesive is the cohesive energy of the target material. We note here that the cohesive energy of zirconium is almost as high as that of graphite.32 For a HiPIMS discharge using a graphite target, we have partially attributed the low ionized flux fraction to the high cohesive energy of graphite, resulting in a low residence time of the carbon atoms within the ionization region. Here, in the case of zirconium, the velocity with which the atoms leave the target remains moderate, as the mass of zirconium is high with 91 m p, where m p is the proton mass. Therefore, the probability of ionization of zirconium is expected to be higher than that of carbon. Consequently, we expected a substantial density of both zirconium atoms and ions in the discharge, in particular, late in the pulse.

Due to this composition of the discharge, we need to calculate and account for the collisional loss for each electron-ion pair created E c for zirconium in the electron energy balance. For this purpose, we use the electron impact ionization cross section calculated by Deutsch et al.55 with an ionization potential of 6.63 V. Our calculations of the collisional energy loss also include the seven lowest excited levels of the atom listed in Table II. As the electron impact excitation cross sections for the zirconium atom are mostly unknown, we assume that each excitation cross section follows the Thomson cross section56 (p. 71) with a peak at 1/5 of the peak of the ionization cross section. If the electron impact excitation cross sections are overestimated (underestimated), the collisional energy loss per electron-ion pair created from Zr atoms is overestimated (underestimated) slightly, and the Zr + ion density and the electron density are underestimated (overestimated). However, as we will see later that the Zr + ion is not the dominating ion in the discharge, so this assumption does not have much influence on the overall results. We assume the cross section for electron elastic scattering on Zr atoms to be the same as for tungsten.57 For electron energies above 50 eV, the total electron elastic cross section agrees well with the elastic cross section for zirconium calculated using the NIST Electron Elastic-Scattering Cross-Section Database SRD 64.58 To find an electron impact ionization cross section for Zr + to create the doubly ionized Zr 2 +, we use the cross section for the first ionization of the zirconium atom from Deutsch et al.55 and scale it down by a factor of 10 and shift the energy axis by the difference in ionization energy between Zr + and Zr 2 +. The reactions and the rate coefficients for electron impact ionization of Zr and Zr + by both primary (cold) and secondary (hot) electrons are listed in Table III. The rate coefficients for electron impact collisions are calculated assuming a Maxwellian EEDF. The fits are valid in the range 1–7 eV for the cold electrons and in the range 200–1000 eV for the hot electrons.

TABLE I.

Discharge parameters, the measured ionized flux fraction Fflux, and the measured deposition rate normalized to the deposition rate in a dcMS, operated at the same power and pressure, Fdep, at the axial position zQCM, and the internal discharge parameters ionization probability αt, the back-attraction probability βt and the peak in the degree of working gas rarefaction derived from the modeling of HiPIMS discharges with zirconium target for 0.5 and 1 Pa pressure.

tpulse (μs)Pressure (Pa)JD, peak (A/cm2)VD (V)zQCM (cm)αt (%)βt, pulse (%)βt (%)Fflux (%)Fdep (%)1 − nAr/nAr, 0 (%)
50 550 10 86 73 71 45 23 72 
100 549 10 85 68 67 48 27 78 
100 0.5 485 10 73 76 75 25 43 49 
50 0.5 485 10 75 73 71 31 39 50 
50 575 10 91 79 76 59 13 80 
50 0.5 488 10 88 70 68 54 21 85 
50 548 10 88 78 76 46 23 72 
50 538 10 85 76 74 43 22 67 
50 535 85 74 72 46 a 68 
50 534 86 70 68 53 a 74 
50 529 86 75 73 54 a 69 
50 529 85 78 75 52 21 65 
100 536 84 73 72 53 23 71 
50 0.5 467 73 80 77 34 36 45 
100 0.5 488 75 75 74 38 36 52 
50 488 86 73 71 58 23 70 
50 0.5 488 88 75 72 61 16 81 
tpulse (μs)Pressure (Pa)JD, peak (A/cm2)VD (V)zQCM (cm)αt (%)βt, pulse (%)βt (%)Fflux (%)Fdep (%)1 − nAr/nAr, 0 (%)
50 550 10 86 73 71 45 23 72 
100 549 10 85 68 67 48 27 78 
100 0.5 485 10 73 76 75 25 43 49 
50 0.5 485 10 75 73 71 31 39 50 
50 575 10 91 79 76 59 13 80 
50 0.5 488 10 88 70 68 54 21 85 
50 548 10 88 78 76 46 23 72 
50 538 10 85 76 74 43 22 67 
50 535 85 74 72 46 a 68 
50 534 86 70 68 53 a 74 
50 529 86 75 73 54 a 69 
50 529 85 78 75 52 21 65 
100 536 84 73 72 53 23 71 
50 0.5 467 73 80 77 34 36 45 
100 0.5 488 75 75 74 38 36 52 
50 488 86 73 71 58 23 70 
50 0.5 488 88 75 72 61 16 81 
a

No dcMS reference measurements were made.

TABLE II.

Lowest few excited states of the zirconium atom that are used to calculate the collisional loss per electron-ion pair created.

ConfigurationTermThreshold (eV)
4d25s2 a 30–0.15 
4d25s2 a 30.52–0.54 
4d3(4F)5s a 50.60–0.73 
4d25s2 a 10.63 
4d25s2 a 11.00 
4d3(4F)5s a 11.44–1.53 
4d3(3G)5s a 11.55–1.58 
ConfigurationTermThreshold (eV)
4d25s2 a 30–0.15 
4d25s2 a 30.52–0.54 
4d3(4F)5s a 50.60–0.73 
4d25s2 a 10.63 
4d25s2 a 11.00 
4d3(4F)5s a 11.44–1.53 
4d3(3G)5s a 11.55–1.58 
TABLE III.

Reactions and rate coefficients used in the IRM involving zirconium determined for both hot and cold electrons. The rate coefficients are calculated assuming a Maxwellian electron energy distribution function and fit in the range Te = 1 − 7 eV for cold electrons and 200–1000 eV for hot electrons.

ReactionThreshold (eV)Rate coefficient (m3/s)Electron groupReference
(R1) e + Zr → Zr+ + e 6.63  1.69 × 10 13 T e 0.171 exp ( 7.825 / T e ) Cold 55  
   3.04 × 10−13 − 2.18 × 10−16 × Te Hot  
(R2) e + Zr+ → Zr2+ + e 13.13  3.06 × 10 14 T e 0.042 exp ( 14.39 / T e ) Cold  
   3.09 × 10−14 − 2.21 × 10−17 × Te Hot  
(R3) Ar + + Zr → Ar + Zr+  2 × 10−16  62  
(R4) Ar(4s’[1/2]0) + Zr → Ar + Zr+ + e  5.3 × 10−15   
(R5) Ar(4s[3/2]2) + Zr → Ar + Zr+ + e  5.3 × 10−15   
ReactionThreshold (eV)Rate coefficient (m3/s)Electron groupReference
(R1) e + Zr → Zr+ + e 6.63  1.69 × 10 13 T e 0.171 exp ( 7.825 / T e ) Cold 55  
   3.04 × 10−13 − 2.18 × 10−16 × Te Hot  
(R2) e + Zr+ → Zr2+ + e 13.13  3.06 × 10 14 T e 0.042 exp ( 14.39 / T e ) Cold  
   3.09 × 10−14 − 2.21 × 10−17 × Te Hot  
(R3) Ar + + Zr → Ar + Zr+  2 × 10−16  62  
(R4) Ar(4s’[1/2]0) + Zr → Ar + Zr+ + e  5.3 × 10−15   
(R5) Ar(4s[3/2]2) + Zr → Ar + Zr+ + e  5.3 × 10−15   
The sputter yield for Ar + and Zr + ions bombarding a zirconium target was estimated using the TU Wien Sputter Yield Calculator,59 which is based on the empirical equations for sputter yields at normal incidence developed by Matsunami et al.60 The calculated sputter yields were fitted using a power-law equation
Y = a E i b ,
(3)
where a and b are the fitting parameters. Here, a = and b = 0.7936 for Ar + sputtering of zirconium and for self-sputtering of zirconium a = and b = 0.9316.

For the secondary electron emission yield due to bombardment of the target by argon ions, we use the fit given for clean metals by Phelps and Petrović.61 For the zirconium ions bombarding the zirconium target, the secondary electron emission yield is essentially zero. Furthermore, we neglect secondary electron emission due to the bombardment of the target by Zr 2 + ions.

Figure 1 shows the measured ionized flux fraction vs the discharge current density at a working gas pressure of 0.5 and 1 Pa. We see that at 1 Pa the ionized flux fraction is in the range 25%–61% and increases with increased discharge current density in the range 0.5–2.0 A/cm 2. The ionized flux fraction was measured at 3 cm from the target surface, facing the race track, representing the edge of the ionization region,6 and 10 cm from the target surface, representing a typical substrate distance. The ionized flux fraction was also measured at 4, 6, and 8 cm from the target surface for J D , peak = 1 A/cm 2. All the measured ionized flux fraction values are listed in Table I and shown in Fig. 1. We see that the ionized flux fraction is slightly higher when measured at 3 cm from the target than when measured at 10 cm from the target surface. This can be understood from a larger ion sputter cone compared to the neutral sputter cone.34,50 The lower pressure (0.5 Pa) delivers a slightly higher ionized flux fraction as shown by the open circles in Fig. 1. Furthermore, longer pulses (100  μs) also give higher ionized flux fraction, except at the lowest peak discharge current density (0.5 A/cm 2). This contradicts the recent findings of Shimizu et al.63 that observed, while studying a HiPIMS discharge with titanium target, that there is an increase in the ionized flux fraction for decreasing pulse length for peak discharge current density J D , peak = 1.1 A/cm 2 and that there is a small decrease in the ionized flux fraction with decreasing pulse length for low J D , peak = 0.37 A/cm 2. In their study, the ionized flux fraction was measured to be in the range 20 to 40% and increased with increased peak discharge current density.

FIG. 1.

Measured ionized flux fraction vs the peak discharge current density. The working gas pressure was 0.5 Pa (open circles) and 1 Pa (solid dots), and the pulse length was 50 and 100  μs and the ionized flux fraction was measured 3, 4, 6, 8, and 10 cm from the target surface.

FIG. 1.

Measured ionized flux fraction vs the peak discharge current density. The working gas pressure was 0.5 Pa (open circles) and 1 Pa (solid dots), and the pulse length was 50 and 100  μs and the ionized flux fraction was measured 3, 4, 6, 8, and 10 cm from the target surface.

Close modal

For comparison, measurements with a copper target find the ionized flux fraction to be in the range of 31%–62% at the substrate position (9 cm from the target) and increase with increased peak discharge current density in a discharge operated at 1 Pa for a 50  μs long pulse and J D , peak in the range 1–1.5 A/cm 2.64 For aluminum and titanium targets, Lundin et al.65 measured the ionized flux fraction to increase from about 20% to roughly 70% as the average discharge current density J D , average was varied from 0.5 to 2.0 A/cm 2, for working gas pressure of 0.5 and 2.0 Pa, and 100  μs long pulses 4 cm from the target surface. Lower working gas pressure resulted in a slightly higher ionized flux fraction, a trend that has also been observed for a discharge with a copper target,64 as well as titanium and aluminum targets.65 This latter effect is also seen for the zirconium target in Fig. 1.

The measured normalized deposition rate vs the peak discharge current density is shown in Fig. 2. The measured normalized deposition rate is the deposition rate for HiPIMS operation divided by the deposition rate determined from dc magnetron sputtering operated at the same average power. We see in Fig. 2 that the measured normalized deposition rate decreases with increased peak discharge current density. This is commonly observed in HiPIMS operations. For a given pulse length and average power, the deposition rate decreases as the peak discharge current density increases.36,63,65,66 The normalized deposition rate for a given discharge current density is higher when measured 10 cm from the target surface than when measured at 3 cm. It can also be seen in Fig. 2 that the normalized deposition rate is slightly lower for the lower working gas pressure (0.5 Pa) (open circles). The normalized deposition rate is also slightly higher for the longer pulse length (100  μs). This again contradicts the findings of Shimizu et al.63 for a HiPIMS discharge with a titanium target as they observed a decrease in the normalized deposition rate as the pulse length was increased from 50  μs at J D , peak = 1.1 A/cm 2. In general, for a fixed peak discharge current density, they found that the deposition rate increases with decreasing pulse length and reaches a maximum at around 25–50  μs, a trend that had been predicted earlier using the IRM.44 They also found that further shortening the pulse length decreases the deposition rate.63 

FIG. 2.

Measured normalized deposition rate vs the peak discharge current density. The working gas pressure was 0.5 Pa (open circles) and 1 Pa (solid dots) and the pulse length was 50 and 100  μs, measured 3 and 10 cm from the target surface.

FIG. 2.

Measured normalized deposition rate vs the peak discharge current density. The working gas pressure was 0.5 Pa (open circles) and 1 Pa (solid dots) and the pulse length was 50 and 100  μs, measured 3 and 10 cm from the target surface.

Close modal

Overall, we observe that the ionized flux fraction increases (Fig. 1) and the normalized deposition rate decreases (Fig. 2) as the peak discharge current density is increased. This is a manifestation of the HiPIMS compromise, which states that the increased ionized flux fraction comes at the cost of a lower deposition rate.67 

As discussed in Sec. II B, the IRM is a semi-empirical model and has three unknown fitting parameters: the ion back-attraction probability, the potential drop across the IR, and the electron recapture probability. The last parameter is given a fixed value as discussed above. This leaves the ( β t , pulse, f = V IR / V D) parameter space as the one to be explored through a model fitting procedure, where we find the best fit to the experimentally determined discharge current waveform. The best fit is determined using a fitting map showing the fraction of the discharge voltage that drops across the ionization region f, vs the back-attraction probability of an ion of the sputtered species β t , pulse during the pulse. The fitting procedure is shown in Fig. 3 for one particular discharge with a zirconium target for a 50  μs long pulse with peak discharge current density J D , peak = 1 A/cm 2, and working gas pressure of 1 Pa, and the ionized flux fraction used to lock the model was measured 10 cm from the target surface (the discharge parameters listed in the first line of Table I). The parameters that define the size of the IR were set as follows: r c 1 = 6 mm, r c 2 = 19 mm, z 1 = 2 mm, and z 2 = 13 mm. The figure of merit (FOM), shown in Fig. 3, is calculated as the weighted sum of square residuals normalized by the weighted total sum of squares (see Gudmundsson et al.35). The regions on the fitting map where the modeled discharge current matches the experimental discharge current the best is shown as a yellow zone. This yellow zone indicates the combination of f = V IR / V D and β t , pulse where the weighted square deviation of the discharge current is the smallest. The ionized flux fraction is shown as black contour lines. As this yellow zone is large, an additional constraint from an experimentally determined quantity is necessary. This is done by using the measured ionized flux fraction to lock the model as suggested by Butler et al.48 [see Eq. (1)]. We use the ionized flux fraction measured (45%) at 10 cm from the target surface over the racetrack to lock the model. The measured discharge current waveform and the measured discharge voltage waveform are shown by solid lines in Fig. 4. The resulting best fit determined by the IRM for the discharge current waveform and the measured ionized flux fraction is shown with a dashed line in Fig. 4. The modeled discharge current matches the experimental discharge current very well.

FIG. 3.

FOM and the ionized flux fraction F flux, displayed as a color map and contour lines, respectively, for a grid scan over β t , pulse and f = V IR / V D for a zirconium target, a 50  μs long pulse, peak discharge current density J D , peak = 1 A/cm 2, working gas pressure of 1 Pa, and the ionized flux fraction used to lock the model was measured 10 cm from the target surface. The parameter combination giving the best fit while meeting the F flux constraint is highlighted with a red × inside a circle.

FIG. 3.

FOM and the ionized flux fraction F flux, displayed as a color map and contour lines, respectively, for a grid scan over β t , pulse and f = V IR / V D for a zirconium target, a 50  μs long pulse, peak discharge current density J D , peak = 1 A/cm 2, working gas pressure of 1 Pa, and the ionized flux fraction used to lock the model was measured 10 cm from the target surface. The parameter combination giving the best fit while meeting the F flux constraint is highlighted with a red × inside a circle.

Close modal
FIG. 4.

Measured temporal evolution of the cathode voltage (solid red line and the right y-axis) and the discharge current (solid blue line and the left y-axis) as well as the model fit (purple dash dot line and the left y-axis) for the discharge current with a zirconium target, a 50  μs long pulse, a peak discharge current density J D , peak = 1 A/cm 2, working gas pressure of 1 Pa, and the ionized flux fraction used to lock the model was measured 10 cm from the target surface.

FIG. 4.

Measured temporal evolution of the cathode voltage (solid red line and the right y-axis) and the discharge current (solid blue line and the left y-axis) as well as the model fit (purple dash dot line and the left y-axis) for the discharge current with a zirconium target, a 50  μs long pulse, a peak discharge current density J D , peak = 1 A/cm 2, working gas pressure of 1 Pa, and the ionized flux fraction used to lock the model was measured 10 cm from the target surface.

Close modal

The temporal evolution of the species densities calculated by the IRM for the discharge fitted in Fig. 3 is shown in Fig. 5, the neutral species densities in Fig. 5(a) and the ions in Fig. 5(b). As to be expected, the ground state working gas argon atoms dominate the discharge. The cold argon ground state density [denoted Ar C(3p 6) in Fig. 5(a)] decreases steadily to a minimum and then rises slightly to the end of the pulse. The minimum in Ar C density appears close to the maximum in the discharge current. We see that there is an increase in the density of both the hot (Ar H) and warm (Ar W) argon atoms, during the pulse, followed by a decay in the afterglow. Furthermore, the warm argon atom density approaches the cold argon density during its minimum. We also see in Fig. 5(a) that the zirconium atom density increases rapidly early in the pulse and then decays slowly to the end of the pulse, when the sputtering by energetic ion bombardment comes to an end. In the afterglow, the density of the ground state zirconium atoms decreases sharply at first and then slower. As seen in Fig. 5(a) toward the end of the pulse the working gas is rarefied, and the zirconium atoms pass through at high speed, while after the pulse is off there is back diffusion of argon that shortens the mean free path of the zirconium atoms and slows them down which appears as a slower decay of the zirconium atom density. Recall that the zirconium atoms enter the IR with a velocity that is directed away from the target surface and this dictates the decay rate in the afterglow. We note that the hot argon atoms, which also have a directed velocity away from the target surface, have a similar decay rate, while warm argon atoms that have lower velocity decay slower in the afterglow. The temporal behavior of the densities of the metastable argon atoms show an increase in the beginning of the pulse a drop and a peak at the end of the pulse and then a much slower decay in the afterglow, but the densities are much lower. As mentioned, the temporal evolution of the neutral argon density in Fig. 5(a) shows a significant drop toward the end of the pulse. This is what is referred to as working gas rarefaction. Working gas rarefaction is known to occur in magnetron sputtering discharges68,69 and has been observed experimentally in HiPIMS operation.70–72 Note that the total neutral argon density within the IR is the sum of the cold, warm, and hot argon atoms in the ground state, and the two metastable states. Hence, working gas rarefaction is not only the drop in the cold argon atom density shown in Fig. 5(a), it is the drop in the total neutral argon density. The calculated values for the degree of working gas rarefaction, including all the neutral argon atom populations, are listed in Table I for all the cases explored.

FIG. 5.

Temporal evolution of the (a) neutral particle densities and (b) the ion densities for a zirconium target, a 50  μs long pulse, with peak discharge current density J D , peak = 1 A/cm 2, working gas pressure of 1 Pa, and the ionized flux fraction used to lock the model was measured 10 cm from the target surface.

FIG. 5.

Temporal evolution of the (a) neutral particle densities and (b) the ion densities for a zirconium target, a 50  μs long pulse, with peak discharge current density J D , peak = 1 A/cm 2, working gas pressure of 1 Pa, and the ionized flux fraction used to lock the model was measured 10 cm from the target surface.

Close modal
The degree of working gas rarefaction is defined as
degree of working gas rarefaction = 1 n Ar ( t ) n Ar , 0 ,
(4)
where n Ar , 0 is the total argon density at the start of the pulse and n Ar ( t ) is the temporal variation of the total argon density. The peak in the degree of working gas rarefaction at p g = 1 Pa and J D , peak = 1 A/cm 2 for a 50  μs long pulse is roughly 70%, and at J D , peak = 2 A/cm 2, it is roughly 80%. At 0.5 Pa, the peak in the degree of working gas rarefaction for J D , peak = 1 A/cm 2 is 81%–85%. Lower working gas pressure and high peak discharge current density leads to a higher degree of working gas rarefaction. Keep in mind that the value of the degree of working gas rarefaction depends on the volume size of the IR, so the values given are estimates.

In a separate study, we have applied the ionization region model to determine the various contributions to working gas rarefaction in HiPIMS discharges with several different cathode targets.38 This study revealed that working gas rarefaction is driven by electron impact ionization by both primary (or cold) and hot electrons as well as by kick-out by fast neutrals coming from the target. The fast neutral species coming from the target can be either the sputtered target species or hot argon atoms. Charge exchange was found to have a negligible contribution to working gas rarefaction for all the target materials. The role of kick-out increases and the role of electron impact ionization decreases with increased sputter yield of the target material. When comparing the various contributions to working gas rarefaction for different target materials, we observed that the sputter yield is the determining factor regarding which process contributes the most to working gas rarefaction in HiPIMS operation.38 

For the zirconium target, the contributions of the various processes to working gas rarefaction in a HiPIMS discharge vs the peak discharge current density are shown in Fig. 6. When comparing the relative contributions of each of the processes to working gas rarefaction, they are all determined by integrating the contribution of each term throughout the entire pulse and the afterglow. We see that ionization by cold primary electrons is the dominating process at all discharge current densities with a contribution in the range of 63%–65%, while ionization by secondary electrons has 14%–19% contribution, the contribution of kick-out by Zr atoms decreases from 16% to 12% and the contribution of hot argon atoms decreases from 7% to 4%, with increasing peak discharge current density in the range 0.5–2.0 A/cm 2. In this case, the location of the ionized flux fraction measurement used to lock the model was 10 cm from the target surface. We see that the peak discharge current density does not have much influence on the relative contribution of the various terms. Zirconium has a rather low sputter yield and, therefore, electron impact ionization is expected to be the most important process.38 This confirms our expectation that the sputter yield is the primary factor in determining the dominating mechanism for argon gas rarefaction among the kick-out mechanism and the ionization by the cold and hot electron population.

FIG. 6.

Contribution of the various processes to working gas rarefaction within the ionization region for a discharge with 2 in. zirconium target vs the peak discharge current density for argon working gas pressure of 1 Pa and pulse length of 50  μs, and the ionized flux fraction used to lock the model was measured 10 cm from the target surface. Ionization cold and hot refers to electron impact ionization of argon atoms by the cold and hot electron populations, respectively.

FIG. 6.

Contribution of the various processes to working gas rarefaction within the ionization region for a discharge with 2 in. zirconium target vs the peak discharge current density for argon working gas pressure of 1 Pa and pulse length of 50  μs, and the ionized flux fraction used to lock the model was measured 10 cm from the target surface. Ionization cold and hot refers to electron impact ionization of argon atoms by the cold and hot electron populations, respectively.

Close modal

The temporal evolution of the charged particle densities is shown in Fig. 5(b). The Ar + ion is always the dominating ion and the Zr + ion has always a smaller density. The densities of the doubly charged Zr 2 + and Ar 2 + ions are always more than an order of magnitude smaller than the density of the singly charged ions. The temporal evolution of the cold argon atoms and zirconium atoms is also shown in Fig. 5(b) to ease comparison. For most of the pulse duration, the density of Ar + and Zr + ions surpasses the density of zirconium atoms.

The temporal evolution of the discharge current composition at the target surface is shown in Fig. 7. We see that roughly 2/3 of the discharge current is carried by Ar + ions while only 1/3 is carried by Zr + ions. The contributions from Ar 2 + and Zr 2 + ions and secondary electron emission are smaller. The current composition is explored further in Fig. 8 where the current composition is shown for three peak discharge current densities. We see that the fractional contribution of Zr + and Zr 2 + ions increases, and the fractional contribution of Ar + ions decreases, with increased peak discharge current density. At J D , peak = 0.5 A/cm 2, the Ar + ion contribution is roughly 74%, at 1.0 A/cm 2 it is about 60%, and roughly 45% at J D , peak = 2 A/cm 2. The Zr + ion contribution is 20%, 27%, and 32%, and the Zr 2 + contribution increases from 2% to 6.6%, to about 15%, as the peak discharge current density is increased. The contribution of secondary electron current is always much smaller than the current carried by each of the ions. There is an upper limit on the current density that corresponds to where all the incoming argon atoms from the surrounding gas reservoir are ionized and drawn to the target. This upper limit defines the critical current density of J crit 0.2 A/cm 2 at 1 Pa and T g = 300 K.73,74 For all the cases discussed here, the discharge operates well above this limit and ion recycling has to take place to reach the high discharge current densities observed. As both argon and zirconium ions contribute significantly to the discharge current at the target surface, the discharge operates on a combination of working gas recycling and self-sputter recycling.74 

FIG. 7.

Temporal evolution of the discharge current composition at the target surface for a zirconium target, for a 50  μs long pulse, with peak discharge current density J D , peak = 1 A/cm 2, working gas pressure of 1 Pa, and the ionized flux fraction used to lock the model was measured 10 cm from the target surface.

FIG. 7.

Temporal evolution of the discharge current composition at the target surface for a zirconium target, for a 50  μs long pulse, with peak discharge current density J D , peak = 1 A/cm 2, working gas pressure of 1 Pa, and the ionized flux fraction used to lock the model was measured 10 cm from the target surface.

Close modal
FIG. 8.

Discharge current composition within the ionization region vs the peak discharge current density for a discharge with 2 in. zirconium target for argon working gas pressure of 1 Pa and pulse length of 50  μs, and the ionized flux fraction used to lock the model was measured 10 cm from the target surface.

FIG. 8.

Discharge current composition within the ionization region vs the peak discharge current density for a discharge with 2 in. zirconium target for argon working gas pressure of 1 Pa and pulse length of 50  μs, and the ionized flux fraction used to lock the model was measured 10 cm from the target surface.

Close modal

The IRM calculations provide, in addition to the temporal variation of the species densities, various other information and discharge parameters. This includes the internal discharge parameters such as the ionization probability α t, the back-attraction probability β t, and the voltage drop across the IR. Earlier, we applied the IRM to study a HiPIMS discharge with 75 mm diameter tungsten target as the discharge voltage was varied.36 There, the peak discharge current density J D , peak increases in the range 0.33–0.73 A/cm 2, with increased discharge voltage in the range 500–800 V. For the sputtered tungsten atoms, the ionization probability was found to increase with increased peak discharge current density and be in the range 54%–75%. For a titanium target, the ionization probability was found to increase from 45% to 84% as the peak discharge current density was varied from 0.15 to 1 A/cm 2.11,34

Another important internal discharge parameter is the back-attraction probability for the sputtered species after they have been ionized within the IR. The back-attraction probability β i for an ion species i relates the ion fluxes out of the IR toward the diffusion region and the flux toward the racetrack during the pulse. The ion flux out of the IR toward the diffusion region is calculated from the flux toward the racetrack during the pulse,31,75
T Γ ~ i DR ( t ) d t = ( 1 β i 1 ) S RT S DR T Γ ~ i RT ( t ) d t ,
(5)
where T Γ ~ i RT ( t ) d t is the ion flux toward the racetrack which has a surface area of S RT and T is the pulse period, T Γ ~ i DR ( t ) d t is the ion flux toward the diffusion region, and S DR is the surface area of the ionization region facing the diffusion region. Here, i denotes the ion, which can be Ar +, Zr +, Ar 2 +, or Zr 2 +. A significant fraction of the ion flux onto the racetrack is made up of ionized zirconium as can be seen in Figs. 7 and 8. These are zirconium atoms that were sputtered off the target and ionized within the IR and then return to the target. For the target material, we write t as a subscript. Figure 9(b) shows the target metal ion back-attraction probability β t vs the peak discharge current density for a HiPIMS discharge with a zirconium target. The back-attraction probability during the pulse is found to be in the range β t , pulse 68 % 80 %. The overall back-attraction probability β t is somewhat lower or in the range 67%–77%. There is clearly some uncertainty or scatter in the calculated back-attraction probability values. This uncertainty is at least partially due to the uncertainty in the values of the transport parameters, used in Eq. (1) to determine the flux of ions and neutrals, to lock the model. Recall that we used values that were determined experimentally for a discharge with titanium target over a limited range.50 The back-attraction probability β t for zirconium is higher than for copper, which was found to be in the range 44%–50%,35 but lower than for titanium target which was determined to be 83%–87%.34 For the sputtered tungsten, the back-attraction probability β t decreases from 87% to 67% with increasing discharge voltage or increasing discharge current density.36 
FIG. 9.

(a) Ionization probability α t and (b) the back-attraction probability β t vs the peak discharge current density determined by the IRM for a discharge with a 2 in. zirconium target for argon working gas pressure of 0.5 Pa (open circles) and 1 Pa (solid dots) and pulse length of 50 and 100  μs and the ionized flux fraction measured 3, 4, 6, 8, and 10 cm from the target surface was used to lock the model.

FIG. 9.

(a) Ionization probability α t and (b) the back-attraction probability β t vs the peak discharge current density determined by the IRM for a discharge with a 2 in. zirconium target for argon working gas pressure of 0.5 Pa (open circles) and 1 Pa (solid dots) and pulse length of 50 and 100  μs and the ionized flux fraction measured 3, 4, 6, 8, and 10 cm from the target surface was used to lock the model.

Close modal

Figure 10 shows the fractional potential drop over the IR f = V IR / V D vs the peak discharge current density. The fractional potential drop is in the range 10%–16% of the applied discharge voltage. The fractional potential drop is slightly lower at 0.5 Pa than at 1 Pa and appears to decrease slightly as the peak current density is increased. The fractional potential drop reported here for a discharge with zirconium target is higher than what was determined for a discharge with tungsten target which was in the range 6%–8%, decreasing with increasing peak discharge current density.36 For a copper target, the fractional potential drop was found to lie in the range 14%–17%,4 and for a graphite target it was found to be 14%,32 for a working gas pressure of p g 1 Pa and J D , peak 1 A/cm 2.

FIG. 10.

Fractional potential drop over the IR f = V IR / V D vs the peak discharge current density. The working gas pressure was 0.5 Pa (open circles) and 1 Pa (solid dots), the pulse length was 50 and 100  μs, and the ionized flux fraction measured 3, 4, 6, 8, and 10 cm from the target surface was used to lock the model.

FIG. 10.

Fractional potential drop over the IR f = V IR / V D vs the peak discharge current density. The working gas pressure was 0.5 Pa (open circles) and 1 Pa (solid dots), the pulse length was 50 and 100  μs, and the ionized flux fraction measured 3, 4, 6, 8, and 10 cm from the target surface was used to lock the model.

Close modal
Figure 2 shows how the measured normalized deposition rate decreases as the peak discharge current is increased. Earlier we have defined the sputter-rate-normalized deposition rate, which is given by34,
F sput = ( 1 α t ) + ( ξ ti ξ tn ) α t ( 1 β t ) ,
(6)
where ξ ti is the transport parameter for ions and ξ tn is the transport parameter for neutrals of the sputtered species.49,50 Equation (6) can be approximated to become
F sput = 1 α t β t = Γ DR Γ 0 ,
(7)
for the special case when ξ ti = ξ tn.76,77 This is the ratio of the flux of sputtered species (ions and neutrals) out of the IR toward the DR Γ DR and the total flux of atoms sputtered from the target Γ 0 (atoms/s). Keep in mind that Eq. (7) does therefore not take into account ion focusing (or spreading) en route toward the substrate.34,48,50 This equation states that the sputter-rate-normalized deposition rate is reduced as the ionization of the sputtered material increases.67 

The relative ion-to-neutral transport factors ξ ti / ξ tn in Eq. (6) describe the relative deposited fractions of target material ions and neutrals onto a substrate. Experimentally, these parameters have been determined for HiPIMS of a titanium target to be roughly ξ ti / ξ tn 0.8 for a substrate located 3 cm from the target surface and ξ ti / ξ tn 0.5 for a substrate located 7 cm from the target surface.50 A value of ξ ti / ξ tn < 1 indicates a larger spread of metal ions compared to metal neutrals, which is explained by larger scattering cross sections of ions compared to neutrals and by ions being subjected to electric fields.34 The sputter rate-normalized deposition rate calculated using Eq. (6), using the measured relative ion-to-neutral transport factors for titanium,50 shows roughly the same behavior as the experimentally determined normalized deposition rate but there is a slight difference in the value. This can be seen in Fig. 11 where the sputter rate-normalized deposition rate F sput vs the measured normalized deposition rate F dep is shown. We see that when the normalized deposition rate and the ionized flux fraction are measured 10 cm from the target surface are used to lock the model the values fall approximately on a line with slope 1 that goes through the origin, while when the flux parameters measured at 3 cm are used to lock the model F sput is slightly higher than the measured F dep. When the flux parameters measured at 10 cm are used to lock the model, we find the average value of the ratio F dep / F sput to be 0.93 with a standard deviation of 0.17, while the measured values at 3 cm are used to lock the model we find it to be 0.71 with a standard deviation of 0.15.

FIG. 11.

Sputter-rate-normalized deposition rate F sput calculated using Eq. (6) vs the measured normalized deposition rate F dep for a discharge with a 2 in. zirconium target for argon working gas pressure of 0.5 Pa (open circles) and 1 Pa (solid dots) and pulse lengths of 50 and 100  μs. The dashed line has a slope of 1.

FIG. 11.

Sputter-rate-normalized deposition rate F sput calculated using Eq. (6) vs the measured normalized deposition rate F dep for a discharge with a 2 in. zirconium target for argon working gas pressure of 0.5 Pa (open circles) and 1 Pa (solid dots) and pulse lengths of 50 and 100  μs. The dashed line has a slope of 1.

Close modal
The sputter rate-normalized deposition rate F sput and the experimentally determined normalized deposition rate F dep are related through the relative differences in the sputter rate Γ sput , HiPIMS / Γ sput , dcMS and the neutral transport parameter ratio between HiPIMS and the corresponding (same pressure and average power) dcMS discharge ξ tn , HiPIMS / ξ tn , dcMS needs to be taken into account as well or
F dep = Γ sput , HiPIMS Γ sput , dcMS ξ tn , HiPIMS ξ tn , dcMS F sput ,
(8)
where34,64,77
Γ sput , HiPIMS Γ sput , dcMS = V D , dcMS V D , HiPIMS × i ζ i Y i ( z i V D , HiPIMS ) Y A r + Zr ( V D , dcMS ) ,
(9)
and V D , HiPIMS and V D , dcMS are the discharge voltages for the corresponding HiPIMS and dcMS discharges, respectively. The sum is taken over all the ions Ar +, Zr +, Zr 2 +, and Ar 2 +, which have sputter yields Y i, and ζ i is the fraction of the ion current at the target surface that is carried by a particular ion i and z i is the charge state of that ion. The parameter i ζ i Y i ( z i V D , HiPIMS ) / Y A r + Zr ( V D , dcMS ) in Eq. (9) is fairly constant and does not vary much with the varying ion fractions and pulse voltage. The average value is 1.67 with a standard deviation of 0.07. Due to a higher voltage, the average sputter during the pulse higher in HiPIMS than in dcMS. As mentioned, Eq. (8) relates the measured normalized deposition rate F dep and the sputter rate-normalized deposition rate F sput. This information can be used to estimate the unknown neutral transport parameter ratio.34 The ratios of the neutral transport parameters in a HiPIMS discharge to dcMS discharge ξ tn , HiPIMS / ξ tn , dcMS, estimated from the measured F sput, and the calculated F sput, are shown vs the peak discharge current density, for argon working gas pressure of 0.5 and 1 Pa and pulse lengths of 50 and 100  μs, in Fig. 12. It can be seen that the ratio ξ tn , HiPIMS / ξ tn , dcMS decreases slightly with increased peak discharge current density for a given pulse length and distance from the target surface. We see that the ratio ξ tn , HiPIMS / ξ tn , dcMS is slightly higher if the flux parameters measured at 10 cm from the target surface are used to lock the model, compared to when they are measured 3 cm from the target surface. The ratios are smaller if we assume ξ ti = ξ tn and use Eq. (7) to calculate the sputter-rate normalized deposition rate F sput (not shown). Earlier we estimated the ratio ξ tn , HiPIMS / ξ tn , dcMS to be roughly 1.9 for discharges with titanium target and justified this value by a simple estimate involving the difference in argon gas temperature in HiPIMS and dcMS operation that influences the mean free path of the sputtered Ti neutrals.34 Note also that working gas rarefaction due to ionization losses in the HiPIMS process will add to this factor.
FIG. 12.

Ratio of the neutral transport parameters in a HiPIMS discharge to dcMS discharge ξ tn , HiPIMS / ξ tn , dcMS vs the peak discharge current density determined by the IRM for a discharge with a 2 in. zirconium target for argon working gas pressure of 0.5 Pa (open circles) and 1 Pa (solid dots) and pulse lengths of 50 and 100  μs.

FIG. 12.

Ratio of the neutral transport parameters in a HiPIMS discharge to dcMS discharge ξ tn , HiPIMS / ξ tn , dcMS vs the peak discharge current density determined by the IRM for a discharge with a 2 in. zirconium target for argon working gas pressure of 0.5 Pa (open circles) and 1 Pa (solid dots) and pulse lengths of 50 and 100  μs.

Close modal

We have explored experimentally the effect of the peak discharge current density on the ionized flux fraction and normalized deposition rate in a HiPIMS discharge with a zirconium target. The ionized flux fraction increases and the normalized deposition rate decreases as the peak discharge current density increases, in accordance with the HiPIMS compromise. The measured discharge current and voltage waveforms were fed into the IRM to determine the temporal evolution of the plasma parameters and the internal discharge properties, the ionization and back-attraction probabilities. At a working gas pressure of 1 Pa, the ionization probability was found to be in the range 73%–91% and the overall back-attraction probability to be in the range 67%–77% for a peak discharge current density in the range 0.5–2.0 A/cm 2. We explored the processes contributing to working gas rarefaction and found electron impact ionization to be the main contributor to working gas rarefaction, with over 80% contribution, while kick-out by zirconium atoms and argon atoms has a smaller contribution.

This work was partially supported by the Icelandic Research Fund under Grant Nos. 196141 and 217999, the University of Iceland Research Fund under Grant No. 93940, the University of Iceland Research Fund for Doctoral Students, and the Swedish Government Strategic Research Area in Materials Science on Functional Materials at Linköping University (Faculty Grant SFO-Mat-LiU No. 2009-00971).

The authors have no conflicts to disclose.

Swetha Suresh Babu: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Validation (equal); Visualization (equal); Writing – review & editing (equal). Joel Fischer: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Resources (equal); Writing – review & editing (equal). Kateryna Barynova: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Writing – review & editing (equal). Martin Rudolph: Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal). Daniel Lundin: Conceptualization (equal); Funding acquisition (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Validation (equal); Writing – review & editing (equal). Jon Tomas Gudmundsson: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal).

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

1.
J. T.
Gudmundsson
,
Plasma Sources Sci. Technol.
29
,
113001
(
2020
).
2.
R. K.
Waits
,
J. Vac. Sci. Technol.
15
,
179
(
1978
).
3.
P. J.
Kelly
and
R. D.
Arnell
,
Vacuum
56
,
159
(
2000
).
4.
J. T.
Gudmundsson
,
A.
Anders
, and
A.
von Keudell
,
Plasma Sources Sci. Technol.
31
,
083001
(
2022
).
5.
D.
Krüger
,
K.
Köhn
,
S.
Gallian
, and
R. P.
Brinkmann
,
Phys. Plasmas
25
,
061207
(
2018
).
6.
V. G.
Antunes
,
M.
Rudolph
,
A.
Kapran
,
H.
Hajihoseini
,
M. A.
Raadu
,
N.
Brenning
,
J. T.
Gudmundsson
,
D.
Lundin
, and
T.
Minea
,
Plasma Sources Sci. Technol.
32
,
075016
(
2023
).
7.
J. T.
Gudmundsson
,
N.
Brenning
,
D.
Lundin
, and
U.
Helmersson
,
J. Vac. Sci. Technol. A
30
,
030801
(
2012
).
8.
A.
Hecimovic
,
J.
Held
,
V.
Schulz-von der Gathen
,
W.
Breilmann
,
C.
Maszl
, and
A.
von Keudell
,
J. Phys. D: Appl. Phys.
50
,
505204
(
2017
).
9.
F.
Lockwood Estrin
,
S. K.
Karkari
, and
J. W.
Bradley
,
J. Phys. D: Appl. Phys.
50
,
295201
(
2017
).
10.
High Power Impulse Magnetron Sputtering: Fundamentals, Technologies, Challenges and Applications, edited by D. Lundin, T. Minea, and J. T. Gudmundsson (Elsevier, Amsterdam, 2020).
11.
M.
Rudolph
,
N.
Brenning
,
H.
Hajihoseini
,
M. A.
Raadu
,
T. M.
Minea
,
A.
Anders
,
D.
Lundin
, and
J. T.
Gudmundsson
,
J. Phys. D: Appl. Phys.
55
,
015202
(
2022
).
12.
M.
Rudolph
,
N.
Brenning
,
H.
Hajihoseini
,
M. A.
Raadu
,
J.
Fischer
,
J. T.
Gudmundsson
, and
D.
Lundin
,
J. Vac. Sci. Technol. A
40
,
043005
(
2022
).
13.
U.
Helmersson
,
M.
Lattemann
,
J.
Bohlmark
,
A. P.
Ehiasarian
, and
J. T.
Gudmundsson
,
Thin Solid Films
513
,
1
(
2006
).
14.
G.
Greczynski
,
I.
Petrov
,
J. E.
Greene
, and
L.
Hultman
,
J. Vac. Sci. Technol. A
37
,
060801
(
2019
).
15.
Z.
Hubička
,
J. T.
Gudmundsson
,
P.
Larsson
, and
D.
Lundin
, in High Power Impulse Magnetron Sputtering: Fundamentals, Technologies, Challenges and Applications, edited by D. Lundin, T. Minea, and J. T. Gudmundsson (Elsevier, Amsterdam, 2020), pp. 49–80.
16.
A.
Anders
,
Thin Solid Films
518
,
4087
(
2010
).
17.
B.
Wicher
,
O. V.
Pshyk
,
X.
Li
,
B.
Bakhit
,
V.
Rogoz
,
I.
Petrov
,
L.
Hultman
, and
G.
Greczynski
,
Mater. Des.
238
,
112727
(
2024
).
18.
G.
Greczynski
,
L.
Hultman
, and
I.
Petrov
,
J. Appl. Phys.
134
,
140901
(
2023
).
19.
H.
Luo
,
F.
Gao
, and
A.
Billard
,
Surf. Coat. Technol.
374
,
822
(
2019
).
20.
C.-C.
Kuo
,
C.-H.
Lin
,
J.-T.
Chang
, and
Y.-T.
Lin
,
Coatings
11
,
7
(
2021
).
21.
I.
Schnell
and
R. C.
Albers
,
J. Phys.: Condens. Matter
18
,
1483
(
2006
).
22.
D. R.
Olander
,
Fundamental Aspects of Nuclear Reactor Fuel Elements
(
Technical Information Center, Office of Public Affairs Energy Research and Development Administration
,
Springfield, VA
,
1976
).
23.
The Metallurgy of Zirconium, edited by C. E. Coleman (International Atomic Energy Agency, Vienna, 2022).
24.
M.
Niinomi
,
Sci. Technol. Adv. Mater.
4
,
445
(
2003
).
25.
C. J. R.
Lustosa
,
J.
Stryhalski
,
R. L. P.
Gonçalves
,
E.
Bonturim
,
O.
Florêncio
, and
M.
Massi
,
Mater. Res.
26
,
e20220566
(
2023
).
26.
J.
Chakraborty
,
K. K.
Kumar
,
S.
Mukherjee
, and
S. K.
Ray
,
Thin Solid Films
516
,
8479
(
2008
).
27.
D.
Pilloud
,
J. F.
Pierson
,
C.
Rousselot
, and
F.
Palmino
,
Scr. Mater.
53
,
1031
(
2005
).
28.
J.
Fankhauser
,
M.
Sato
,
D.
Yu
,
A.
Ebnonnasir
,
M.
Kobashi
,
M. S.
Goorsky
, and
S.
Kodambaka
,
J. Vac. Sci. Technol. A
34
,
050616
(
2016
).
29.
A.
Singh
,
P.
Kuppusami
,
R.
Thirumurugesan
,
R.
Ramaseshan
,
M.
Kamruddin
,
S.
Dash
,
V.
Ganesan
, and
E.
Mohandas
,
Appl. Surf. Sci.
257
,
9909
(
2011
).
30.
A.
Singh
,
P.
Kuppusami
,
R.
Thirumurugesan
,
V.
Ganesan
, and
E.
Mohandas
,
Int. J. Des. Manuf. Technol.
8
,
5
(
2014
).
31.
C.
Huo
,
D.
Lundin
,
J. T.
Gudmundsson
,
M. A.
Raadu
,
J. W.
Bradley
, and
N.
Brenning
,
J. Phys. D: Appl. Phys.
50
,
354003
(
2017
).
32.
H.
Eliasson
et al.,
Plasma Sources Sci. Technol.
30
,
115017
(
2021
).
33.
C.
Huo
,
M. A.
Raadu
,
D.
Lundin
,
J. T.
Gudmundsson
,
A.
Anders
, and
N.
Brenning
,
Plasma Sources Sci. Technol.
21
,
045004
(
2012
).
34.
M.
Rudolph
,
H.
Hajihoseini
,
M. A.
Raadu
,
J. T.
Gudmundsson
,
N.
Brenning
,
T. M.
Minea
,
A.
Anders
, and
D.
Lundin
,
J. Appl. Phys.
129
,
033303
(
2021
).
35.
J. T.
Gudmundsson
,
J.
Fischer
,
B. P.
Hinriksson
,
M.
Rudolph
, and
D.
Lundin
,
Surf. Coat. Technol.
442
,
128189
(
2022
).
36.
S.
Suresh Babu
,
M.
Rudolph
,
D.
Lundin
,
T.
Shimizu
,
J.
Fischer
,
M. A.
Raadu
,
N.
Brenning
, and
J. T.
Gudmundsson
,
Plasma Sources Sci. Technol.
31
,
065009
(
2022
).
37.
S.
Suresh Babu
,
M.
Rudolph
,
P. J.
Ryan
,
J.
Fischer
,
D.
Lundin
,
J. W.
Bradley
, and
J. T.
Gudmundsson
,
Plasma Sources Sci. Technol.
32
,
034003
(
2023
).
38.
K.
Barynova
,
S.
Suresh Babu
,
M.
Rudolph
,
J.
Fischer
,
D.
Lundin
,
M. A.
Raadu
,
N.
Brenning
, and
J. T.
Gudmundsson
, “On working gas rarefaction in high power impulse magnetron sputtering,”
Plasma Sources Sci. Technol.
(to be published) (2024).
39.
G.
Greczynski
,
I.
Zhirkov
,
I.
Petrov
,
J. E.
Greene
, and
J.
Rosen
,
J. Vac. Sci. Technol. A
35
,
060601
(
2017
).
40.
X.
Li
,
B.
Bakhit
,
M. P.
Johansson Jõesaar
,
L.
Hultman
,
I.
Petrov
, and
G.
Greczynski
,
Surf. Coat. Technol.
415
,
127120
(
2021
).
41.
Z.
Hubička
,
Š.
Kment
,
J.
Olejníček
,
M.
Čada
,
T.
Kubart
,
M.
Brunclíková
,
P.
Kšírová
,
P.
Adámek
, and
Z.
Remeš
,
Thin Solid Films
549
,
184
(
2013
).
42.
T.
Kubart
,
M.
Čada
,
D.
Lundin
, and
Z.
Hubička
,
Surf. Coat. Technol.
238
,
152
(
2014
).
43.
M. A.
Raadu
,
I.
Axnäs
,
J. T.
Gudmundsson
,
C.
Huo
, and
N.
Brenning
,
Plasma Sources Sci. Technol.
20
,
065007
(
2011
).
44.
M.
Rudolph
,
N.
Brenning
,
M. A.
Raadu
,
H.
Hajihoseini
,
J. T.
Gudmundsson
,
A.
Anders
, and
D.
Lundin
,
Plasma Sources Sci. Technol.
29
,
05LT01
(
2020
).
45.
M.
Rudolph
,
A.
Revel
,
D.
Lundin
,
H.
Hajihoseini
,
N.
Brenning
,
M. A.
Raadu
,
A.
Anders
,
T. M.
Minea
, and
J. T.
Gudmundsson
,
Plasma Sources Sci. Technol.
30
,
045011
(
2021
).
46.
G.
Buyle
,
D.
Depla
,
K.
Eufinger
, and
R.
De Gryse
,
J. Phys. D: Appl. Phys.
37
,
1639
(
2004
).
47.
T.
Kozák
,
Plasma Sources Sci. Technol.
32
,
035007
(
2023
).
48.
A.
Butler
,
N.
Brenning
,
M. A.
Raadu
,
J. T.
Gudmundsson
,
T.
Minea
, and
D.
Lundin
,
Plasma Sources Sci. Technol.
27
,
105005
(
2018
).
49.
D. J.
Christie
,
J. Vac. Sci. Technol. A
23
,
330
(
2005
).
50.
H.
Hajihoseini
,
N.
Brenning
,
M.
Rudolph
,
M. A.
Raadu
,
D.
Lundin
,
J.
Fischer
,
T. M.
Minea
, and
J. T.
Gudmundsson
,
J. Vac. Sci. Technol. A
41
,
013002
(
2022
).
51.
Y.
Yamamura
and
M.
Ishida
,
J. Vac. Sci. Technol. A
13
,
101
(
1995
).
52.
M.
Rudolph
,
D.
Lundin
,
E.
Foy
,
M.
Debongnie
,
M.-C.
Hugon
, and
T.
Minea
,
Thin Solid Films
658
,
46
(
2018
).
53.
A.
Anders
,
J.
Čapek
,
M.
Hála
, and
L.
Martinu
,
J. Phys. D: Appl. Phys.
45
,
012003
(
2012
).
54.
C.
Kittel
,
Introduction to Solid State Physics
, 8th ed. (
John Wiley & Sons
,
Hoboken, NJ
,
2005
).
55.
H.
Deutsch
,
K.
Becker
, and
T.
Märk
,
Int. J. Mass Spectrom.
271
,
58
(
2008
).
56.
M. A.
Lieberman
and
A. J.
Lichtenberg
,
Principles of Plasma Discharges and Materials Processing
, 2nd ed. (
John Wiley & Sons
,
New York
,
2005
).
57.
F.
Blanco
,
F.
Ferreira da Silva
,
P.
Limão-Vieira
, and
G.
García
,
Plasma Sources Sci. Technol.
26
,
085004
(
2017
).
58.
NIST electron elastic-scattering cross-section database, SRD 64, version 5.0.
59.
M.
Schmid
, “A simple sputter yield calculator,” Surface Physics, Institute of Applied Physics, Technischen Universität Wien, https://www2.iap.tuwien.ac.at/www/surface/sputteryield.
60.
N.
Matsunami
,
Y.
Yamamura
,
Y.
Itikawa
,
N.
Itoh
,
Y.
Kazumata
,
S.
Miyagawa
,
K.
Morita
,
R.
Shimizu
, and
H.
Tawara
, “Energy dependence of the yields of ion-induced sputtering of monatomic solids,” Technical Report IPPJ-AM-32, Institute of Plasma Physics, Nagoya University, 1983.
61.
A. V.
Phelps
and
Z. L.
Petrović
,
Plasma Sources Sci. Technol.
8
,
R21
(
1999
).
62.
S. C.
Rae
and
R. C.
Tobin
,
J. Appl. Phys.
64
,
1418
(
1988
).
63.
T.
Shimizu
,
M.
Zanáška
,
R. P.
Villoan
,
N.
Brenning
,
U.
Helmersson
, and
D.
Lundin
,
Plasma Sources Sci. Technol.
30
,
045006
(
2021
).
64.
J.
Fischer
,
M.
Renner
,
J. T.
Gudmundsson
,
M.
Rudolph
,
H.
Hajihoseini
,
N.
Brenning
, and
D.
Lundin
,
Plasma Sources Sci. Technol.
32
,
125006
(
2023
).
65.
D.
Lundin
,
M.
Čada
, and
Z.
Hubička
,
Plasma Sources Sci. Technol.
24
,
035018
(
2015
).
66.
V.
Tiron
,
I.-L.
Velicu
,
O.
Vasilovici
, and
G.
Popa
,
J. Phys. D: Appl. Phys.
48
,
495204
(
2015
).
67.
N.
Brenning
,
A.
Butler
,
H.
Hajihoseini
,
M.
Rudolph
,
M. A.
Raadu
,
J. T.
Gudmundsson
,
T.
Minea
, and
D.
Lundin
,
J. Vac. Sci. Technol. A
38
,
033008
(
2020
).
68.
S. M.
Rossnagel
,
J. Vac. Sci. Technol. A
6
,
19
(
1988
).
69.
S. M.
Rossnagel
,
J. Vac. Sci. Technol. A
6
,
1821
(
1988
).
70.
J.
Alami
,
K.
Sarakinos
,
G.
Mark
, and
M.
Wuttig
,
Appl. Phys. Lett.
89
,
154104
(
2006
).
71.
J.
Vlček
,
A. D.
Pajdarová
, and
J.
Musil
,
Contrib. Plasma Phys.
44
,
426
(
2004
).
72.
M.
Palmucci
,
N.
Britun
,
S.
Konstantinidis
, and
R.
Snyders
,
J. Appl. Phys.
114
,
113302
(
2013
).
73.
C.
Huo
,
D.
Lundin
,
M. A.
Raadu
,
A.
Anders
,
J. T.
Gudmundsson
, and
N.
Brenning
,
Plasma Sources Sci. Technol.
23
,
025017
(
2014
).
74.
N.
Brenning
,
J. T.
Gudmundsson
,
M. A.
Raadu
,
T. J.
Petty
,
T.
Minea
, and
D.
Lundin
,
Plasma Sources Sci. Technol.
26
,
125003
(
2017
).
75.
N.
Brenning
,
D.
Lundin
,
M. A.
Raadu
,
C.
Huo
,
C.
Vitelaru
,
G. D.
Stancu
,
T.
Minea
, and
U.
Helmersson
,
Plasma Sources Sci. Technol.
21
,
025005
(
2012
).
76.
J. W.
Bradley
,
A.
Mishra
, and
P. J.
Kelly
,
J. Phys. D: Appl. Phys.
48
,
215202
(
2015
).
77.
H.
Hajihoseini
,
M.
Čada
,
Z.
Hubička
,
S.
Ünaldi
,
M. A.
Raadu
,
N.
Brenning
,
J. T.
Gudmundsson
, and
D.
Lundin
,
Plasma
2
,
201
(
2019
).