On working gas rarefaction in high power impulse magnetron sputtering

The ionization region model (IRM) is applied to explore working gas rarefaction in high power impulse magnetron sputtering discharges operated with graphite, aluminum, copper, titanium, zirconium, and tungsten targets. For all cases the working gas rarefaction is found to be significant, the degree of working gas rarefaction reaches values of up to 83%. The various contributions to working gas rarefaction, including electron impact ionization, kick-out by the sputtered species or hot argon atoms, and diffusion, are evaluated and compared for the different target materials, and over a range of discharge current densities. The relative importance of the various processes varies between different target materials. In the case of a graphite target with argon as the working gas at 1 Pa, electron impact ionization (by both primary and secondary electrons) is the dominating contributor to working gas rarefaction, with over 90% contribution, while the contribution of sputter wind kick-out is small < 10%. In the case of copper and tungsten targets, the kick-out dominates, with up to ∼ 60% contribution at 1 Pa. For metallic targets the kick-out is mainly due to metal atoms sputtered from the target, while for the graphite target the small kick-out contribution is mainly due to kick-out by hot argon atoms and to a smaller extent by carbon atoms. The main factors determining the relative contribution of the kick-out by the sputtered species to working gas rarefaction appear to be the sputter yield and the working gas pressure.


Introduction
Magnetron sputtering [1][2][3] is a versatile and widely applied physical vapor deposition technique [4], in which the film-forming material is sputtered from a cathode target by ion bombardment.A discharge is formed in a working gas, preferentially constituting heavy noble atoms, most often argon.The ions for the sputter process are accelerated from a dense plasma region created near the target and confined there by a static magnetic field, that traps the electrons.Often, the discharge is driven by a dc voltage or current, in particular when depositing metallic films.In that case the sputtered species are mainly neutral atoms, and the ions available in the discharge are the ions of the working gas [3].
A variation of the magnetron sputtering technique is high power impulse magnetron sputtering (HiPIMS), where the discharge is driven by high power pulses delivered at a low repetition frequency, and with low duty cycle [5][6][7].As a result of the HiPIMS process, the discharge is composed of atoms and ions of both the working gas and target material.Pulsing the discharge at high peak power results in a high peak discharge current density, increased electron density [3,8], increased ionization of the sputtered species [9], and higher ionization fraction in the flux of film-forming species to the substrate [6,10,11], which ultimately leads to denser deposited films [12], that exhibit better crystallinity [13], and overall improved film properties [14,15].
The sputter process releases atoms of the film-forming species from the target, and the sputtered species enter the discharge volume with considerable energy, which, as a first approximation, can be described by the Thompson distribution [16][17][18].The most probable energy of the Thompson distribution corresponds to roughly half the cohesive energy of the solid target [17,18].The interaction between the energetic sputtered particles and the working gas atoms not only influences the momentum of the sputtered species, but also the discharge properties as it leads to a reduction in the working gas density, and increase in the working gas temperature, in front of the cathode target.The pressure drop was first identified in a dc magnetron sputtering (dcMS) discharge, in the cylindrical configuration, by Hoffman [19], who referred to the observed phenomena as 'sputtering wind', as he argued this to be a pressure variation resulting from collisions between the sputtered particles and the working gas atoms.This phenomena was further explored experimentally in a planar dcMS discharge by Rossnagel [20][21][22] and Drüsedau [23], who observed a pressure drop just in front of the cathode target and referred to it as working gas rarefaction or gas heating.Rossnagel [20,21] found the working gas rarefaction to depend on the discharge current, sputter yield, sputtered species type (velocity and collision cross section) and the mass of the sputtered species and the working gas atoms.They further argued that the reduction in working gas density drives up the plasma impedance.Therefore, the discharge requires a higher discharge voltage to operate at the same discharge current, as the resulting current density is determined by the reduced concentration of the working gas species in the target vicinity.These studies were followed by a development of analytical models to describe the working gas rarefaction process [20,[23][24][25][26].The occurrence of rarefaction has also been observed using the direct simulation Monte Carlo (DSMC) method [27] and particle-in-cell Monte Carlo simulations [28,29] of dc magnetron sputtering discharges.In fact, it has been suggested that working gas rarefaction improves both the deposition rate and the coverage in sub-micron sized holes [27].
The HiPIMS discharge is operated at much higher peak discharge current densities than the dcMS discharge, and therefore, working gas rarefaction could be expected to be even more significant.However, as the duty cycle in HiPIMS operation is short, the gas refill during the off-times could result in lower working gas rarefaction on average.A brief discussion on how the rarefaction influences the discharge current waveform in HiPIMS operation was given by Lundin [30], where it was observed that several mechanisms lead to working gas rarefaction-not only sputter wind.Experimentally, using optical emission spectroscopy (OES) [31][32][33][34][35][36], measuring time-resolved ion saturation currents by a probe array [37], and mass spectrometry [38,39], it has been demonstrated that working gas rarefaction occurs and can indeed be rather significant in HiPIMS discharges, and be even more pronounced for longer pulses [38].Alami et al [31] observed almost an order of magnitude drop in the Ar 0 emission intensity when operating with a chromium target, 50 µs long pulses, an average current density of 2.8 A cm −2 and a working gas pressure of 0.8 Pa.Palmucci et al [33] also observed a strong gas rarefaction, which significantly reduces the sputtered species energy dissipation during a certain time interval at the end of a 20 µs long pulse, when operating with a titanium target.They referred to this phenomena as 'rarefaction window'.Incidentally, recent studies seem to indicate that working gas rarefaction may be a desired property of the discharge process in the case of HiPIMS operation and have some benefits for the deposition process [40,41].Using mass spectrometry, Greczynski et al [39] observed that the time-and energy integrated metal-ion-to-gas-ion ratio increases when the peak discharge current density is increased during HiPIMS operation.This, they claim to be due to working gas rarefaction.Also, they find this effect to become even stronger with increasing atom mass of the sputtered species.Vitelaru et al [42] applied time-resolved tunable diode-laser absorption spectroscopy measurements on the argon metastable (Ar m ) level 3s 2 3p 5 ( 2 P • 3/2 )4s excited by 801.478 nm photons, in the dense plasma region in front of the titanium cathode target in a HiPIMS discharge.From the Doppler profile they determined the temporal evolution of the working gas temperature and the metastable argon Ar m density during the pulse as well as during the plasma afterglow.They showed that the metastable argon Ar m density sharply increases at the beginning of the discharge pulse, followed by a severe Ar m density depletion, along with increasing working gas temperature around the peak in the discharge current.The working gas temperature was found to increase during the pulse and more so with increased discharge current.This is in agreement with the increased sputtering of metal particles resulting in more metal-argon collisions, and thus increased momentum transfer to the neutral working gas atoms, and increased density of hot working gas neutrals, due to recombination of Ar + ions.
Working gas rarefaction in HiPIMS operation has also been explored through modeling.Kadlec [43] studied the behavior of the neutral argon working gas atoms during a HiPIMS pulse by the three-dimensional DSMC method, assuming a titanium target.When the discharge current density reached the 2.2 A cm −2 range very strong gas rarefaction was observed.The volume density of sputtered metal exceeded the working gas density several times and the working gas atoms moved rapidly away from the target as a shock wave a few microseconds into the pulse.Note that in the DSMC simulations the ionization of the working gas is neglected.In a more recent study Kozák and Lazar [44] investigated working gas rarefaction in HiPIMS operation using a three-dimensional DSMC simulation and compared the findings to results from volume-averaged models.The DSMC results indicate that the working gas rarefaction is only slightly more pronounced for target atoms with higher mass and that the rarefied region extends much further from the target than the extent of the ionization region (IR), that is typically defined for volumeaveraged modeling.They found that volume-averaged models provide good approximation for the temporal evolution of the target material density in front of the target compared to the DSMC simulation.However, they found the volume-averaged models underestimate the magnitude of the rarefaction during the pulse-on time, and predict faster return to equilibrium during the pulse-off time compared to the DSMC simulation.This is because the size of the IR assumed in volume-averaged modeling of the HiPIMS discharge is small and in reality the region where the working gas density is significantly reduced extends somewhat farther from the target surface than the extent of the high plasma density region that is maintained by the magnetic confinement.More recently the DSMC model has been updated to simulate the dynamics of both atoms and ions in an HiPIMS discharge [45].
The ionization region model (IRM) is a semi-empirical time-dependent volume-averaged plasma chemical model of the IR of the HiPIMS discharge.It provides the temporal evolution of the densities of ions, neutrals and electrons with known discharge current and voltage waveforms [46].The IRM has been applied to model HiPIMS discharges in argon with aluminum [46][47][48], titanium [46,[49][50][51], copper [52], tungsten [53,54], graphite [55], and zirconium [56] targets.From the IRM studies, using various target materials, it has been observed that there is indeed a significant working gas rarefaction.The IRM results have furthermore verified that several rarefaction mechanisms are involved [47].When operating a HiPIMS discharge with an aluminum target it has been shown that electron impact ionization has the largest contribution to working gas rarefaction [47], while when operating with a tungsten target the sputter wind appears to have the largest contribution [53].
Here, using the IRM, we explore the relative contributions of the various mechanisms that contribute to the working gas rarefaction in HiPIMS discharges with a few different target materials, in the order of increasing atomic mass, graphite, aluminum, copper, titanium, zirconium, and tungsten.This we do by reevaluating the IRM results for discharges studied in the past, while focusing on the rarefaction processes.In section 2 we give an introduction to the IRM and the various terms that contribute to working gas rarefaction.There we also introduce an updated kick-out term into the IRM.The temporal evolution of the gain and loss processes of argon atoms within the IR, as well as diffusion of argon atoms in and out of the IR, for the six target materials, spanning a wide range in atomic mass and sputter yield, is evaluated in section 3. The results are discussed in section 4, where we determine the main contributor for working gas rarefaction and how they depend on the target material and which parameter determines which contributor is the most important.The main findings are summarized in section 5.

The IRM
The IRM is a global plasma chemistry model of the IR of a pulsed magnetron sputtering discharge.The IR is taken to be an annular cylinder with outer radius r 2 , and inner radius r 1 sitting above the race track of width w RT = r 2 − r 1 , and height L = z 2 − z 1 , extending from z 1 to z 2 axially away from the target surface [46,57].The loss and gain rates across the boundaries of this annular cylinder to the target on one side, and the bulk plasma on the other side, account for the geometry of the IR [57].To determine the electron density the quasi-neutrality condition is applied.The model gives the temporal variation of the various species, electrons, ions, and neutrals, that constitute the discharge for a given discharge setup and experimentally determined discharge voltage and current waveforms.The IRM is therefore a tool that allows us to explore, among other processes, the mechanisms responsible for working gas rarefaction.
The plasma chemistry is introduced through two sets of rate coefficients that are calculated using an assumed electron energy distribution function (EEDF), one set for cold, or primary electrons, and another set for the secondary electrons, emitted from the target due to ion bombardment.This assumption has been tested against a kinetic Boltzmann solver and a good agreement has been achieved [58].The cold electrons are created through the ionization processes within the IR volume and are referred to as primary electrons in the discussion below.The majority of the electrons are primary electrons and belong to the cold Maxwellian electron population which therefore dictates the electron density and the effective electron temperature.The rate coefficients are calculated assuming Maxwellian EEDFs and fit in the range T e = 1 − 7 eV for the primary electrons, and in the range 200 -1000 eV for secondary electrons.The reaction set and the rate coefficients involving argon in the IRM are described in our earlier works on HiPIMS discharges with titanium target [49,59], with a few modifications of the rate coefficients involving the metastable argon atom [58] and addition of Ar 2+ to the reaction set [55].The reaction set and the parameters that describe the plasma surface interactions, such as sputter yields, and secondary electron emission, involving the various target materials are given in respective publications, for graphite [55], aluminum [46], copper [52], titanium [59], zirconium [56], and tungsten [53] targets.

The model implementation
To further explore working gas rarefaction we look at the processes that are involved in the gain and loss of argon atoms within the IR.There are a number of processes that contribute to working gas rarefaction in the magnetron sputtering discharge.Below we discuss these processes and how they are implemented in the IRM, following the discussion given by Huo et al [46], which also provides a more detailed discussion of the IRM in general.We also discuss a number of modifications to the IRM made for this current study.
The film-forming species are sputtered out of the cathode target by ion bombardment.The rate at which the sputtered species enter the discharge is given by where n stands for neutral atom sputtered off the target and i stands for the ion species involved in the process, Γ RT i is the flux of ion species i towards the target in [ions/m 2 s], S RT is the area of the sputtered region (racetrack area), Y i (E i ) is the energy-dependent sputter yield for ion species i bombarding the target, and V IR is the total volume of the IR.The sum is taken over all the positive ion species in the discharge, and each ion species i has its energy-dependent sputter yield.The sputter yields for most of the various targets are taken from fits suggested by Anders [60], but for titanium the sputter yields are taken from fits provided by Tomas Kubart at Uppsala University [59].For a zirconium target the sputter yield was estimated using the TU Wien Sputter Yield Calculator [61], which is based on the empirical equations for sputter yields at normal incidence developed by Matsunami et al [62].The sputter yields depend on the ion energy E i (t) which we take to be the energy equivalent of the discharge voltage V D (t).
In addition to cold argon neutrals in ground state Ar C with density n C Ar , and metastable argon (the densities of both Ar(4s[3/2] 2 ) and Ar(4s'[1/2] 0 )), the model considers two additional populations of argon atoms originating from argon ions that bombard the target and then return to the discharge volume as neutrals.These are warm argon atoms with density n W Ar and hot argon atoms with density n H Ar .The hot argon population originates from argon species that are reflected from the target [63,64].They are assumed to have an average energy of 2 eV [47].The warm population Ar W is due to argon ions that penetrate the target surface, and then slowly diffuse back as atoms.Their energy is taken to be the thermal energy of the surface, with about 0.1 eV (∼1000 K) as an upper bound [65].We assume that a fraction ξ H of the recombined Ar + ions return as hot neutrals Ar H during the pulse, and a fraction (1 − ξ H ) return as warm neutrals Ar W during the pulse.We further assume that all target-implanted argon atoms leave the target during the pulse [47,66].Of importance for the working gas rarefaction are the hot argon atoms, as they have a considerable momentum.They are incorporated in the IRM as a generation term for hot argon neutrals Ar H where Γ RT Ar + is the flux of Ar + ions and Γ RT Ar 2+ is the flux of Ar 2+ ions towards the target racetrack.For the generation of warm neutrals ξ H in equation ( 2) is replaced by (1 − ξ H ). Coming from the target, the hot argon neutrals Ar H and the warm argon neutrals Ar W have a directed flux away from the target, giving a loss out of the IR at random velocity defined by where T n is the temperature and m n is the mass of the neutral species and thus the loss rate is where the superscript Z stands for hot (H) and warm (W) argon atoms.For this current study we assume ξ H = 0.5 i.e. 50% are Ar W , with T W Ar = 0.1 eV, and 50% are Ar H with T H Ar = 2 eV for all the target materials studied.This choice is arbitrary and has been motivated in earlier studies [47,66].However, ξ H will possibly vary with the mass of the target element, and for heavier target elements the fraction of Ar W is expected to be higher (see Rudolph et al [64]), which we neglect in this current study.
Neutral atoms created through volume reactions within the IR along with atoms sputtered or released from the target are lost as they diffuse out of the IR, described by a loss term where Γ n,diff is the flux of neutral atoms or molecules through the border of the IR with the diffusion region (DR), S DR is the surface area of the IR facing the DR, and S DR /V IR is the distance through the IR, which represents the typical length that species with a directed flow from the target travel when diffusing out of the IR.The atom flux is where λ n,Ar = 1/(σ m n Ar ) is the mean free path for target atoms colliding with argon atoms and σ m is the momentum transfer cross section for collisions between atoms.For the cold working gas atoms Γ n,0 is the random atom flux governed by the thermal energy.For the species coming off the target, the sputtered species and warm and hot argon atoms, the flux Γ n,0 is governed by the velocity of the particle coming off the target, directed away from the target surface.For the sputtered species the flux is dictated by the cohesive energy of the target.The cross section σ m for collisions of sputtered metal atoms and argon atoms is based on the momentum-exchange Table 1.Selected atomic data for the various target atoms.The values for the cohesive energy E cohesive are taken from Kittel [69] and the atomic radius is from Clementi et al [68].cross section calculated for the Ar-Ar interaction by Phelps et al [67].As pointed out by Rossnagel [22], it has to be noted that the momentum transfer cross section for the sputtered atoms, with energy of few eVs, is up to a factor 10 larger than the momentum transfer cross section for the energetic reflected neutrals with energy of few hundred eVs (see also Phelps et al [67]).To get a more reasonable value for the momentum-exchange between the sputtered species and the argon atoms we approximate this to be a billiard-ball collision, and assume that the momentum-exchange cross section scales as π(a 1 + a 2 ) 2 , where a 1 is the atomic radius of the sputtered species and a 2 is the atomic radius of the argon atom.The velocity of the particle coming off the target is assumed to be the most probable velocity from the Thompson distribution [16,17] or 1 2 E cohesive .The Ar-Ar cross section is determined at the most probable energy for each metal atom using the fit given in Phelps et al [67].This value is then multiplied by the ratio ((a 1 + a 2 )/(a 2 + a 2 )) 2 to get the momentum exchange cross section for each argon-metal atom pair.The values used to calculate the cross sections and the calculated momentum transfer cross sections are given in table 1.The values for the atomic radius are taken from the work of Clementi et al [68] and the values for the cohesive energy are from the textbook by Kittel [69].This is a revision from our earlier works where we assumed the metal-Ar momentum transfer cross section to be 2 × 10 −19 m 2 as a typical cross section for all neutral-neutral collisions [46,47,57].
For this study the working gas temperature (cold argon atoms) is assumed to be 500 K.At a gas temperature of 500 K and using the cross sections in table 1 the mean free path for the sputtered atoms is roughly 8-30 mm at 1 Pa and 2-8 mm at 4 Pa.Due to the energy transfer from the sputter process and heat conduction from the cathode target the effective gas temperature is high.We will see later (section 3) that late in the pulse a significant fraction of the argon atoms within the IR are warm and hot atoms.Therefore, the effective working gas temperature can be significantly higher, and argon gas a temperature above 1200 K has been measured for a 200 µs long pulse [42].
In the IRM, gas rarefaction by the effect of the sputter wind [19] is implemented as an argon kick-out term due to collisions with fast sputtered particles [46,57].Here, we slightly modify the model from our previous studies to also include the hot argon atoms Ar H species that originate from the target with a considerable energy.The warm argon species Ar W on the other hand, also originating from the target, are still neglected in the model, as their energy of 0.1 eV is too low to have a significant impact on gas rarefaction by kicking out argon species.Also, we neglect kick-out by the metal ions.
For this current study we significantly revise the kick-out term in the IRM code from our earlier studies [46,47,57].For the derivation of a kick-out term, we denote the kicking-out species by an X, and those that are kicked-out by a Y. Here, X = {M, Ar H }, where M stands for the target atoms, and Y = {Ar C , Ar(4s[3/2] 2 ), Ar(4s'[1/2] 0 )}.In the model, we assume that a collision of a species X with a species Y leads to the instantaneous loss of species Y from the IR.This is acceptable if two conditions are met: (i) The momentum of species X is always higher than the average momentum of the cold Ar species (species Y) at an assumed working gas temperature of 500 K.The lightest target atom studied here, carbon, has the mass M = 12M p , where M p is the proton mass, and an ejection energy E ejection = 1  2 E cohesive = 3.7 eV [55].This yields a momentum of 10 −22 kg m s −1 which is higher than the momentum of an average argon species at T g = 500 K which is ∼ 10 −23 kg m s −1 .We therefore consider the first condition to be fulfilled.(ii) The length of a HiPIMS pulse is longer than the typical loss time of species Y out of the IR after the collision.For example, a collision in the middle of the IR with a typical height h = 2 cm and a post-collision velocity of v = 1000 m s −1 , results in a loss of species Y within t = h/2v = 10 µs.The pulse lengths of the HiPIMS discharges investigated in this study are longer by a factor of 4 to 20, which is why the assumed instantaneous loss is an acceptable assumption.We neglect that this assumption underestimates the momentary argon density.This approximation of instant loss of species from the IR is therefore acceptable for the discharges studied in this work.Furthermore, for collisions between Ar H and Ar C , we neglect the effect that headon collisions would simply result in the exhange of velocity vectors with no net change in the argon density in the IR.Collisions under an angle result in both particles to be lost out of the IR.As collisions under an angle are much more probable compared to head-on collisions, also this is an acceptable assumption.
For each species X, we assume that there is a certain probability for these particles to collide with particles of the species Y.This is given by where L is the height of the IR and the mean free path λ X→Y of a species X in a background gas composed of species Y is given by where the cross sections σ X→Y are the momentum transfer cross sections, as discussed above for each pair of X and Y, and n Y is the density of species Y.Note that F coll,X→Y is the fraction of the momentum carried by the sputtered species that is transferred to the kicked-out species Y.We can therefore link the sputter flux Γ sputter (in m −2 s −1 ) to the kick-out flux Γ kickout out of the IR by where S RT is the surface area of the IR facing the racetrack, and S DR is the surface area of the IR facing the DR [57].The sputtered flux is where Y i (E i ) is the sputter yield for an ion species i bombarding the target.Note that equation ( 9) represents 6 equations, representing each pair (X,Y) of kicking-out species X and species Y that are kicked-out.Note that this model assumes that there is at most one collision between a sputtered species and a gas species.Based on the long mean free path of sputtered species in the IR compared to the typical height of the IR (see above), this is acceptable assumption.
A second loss mechanism is the ionization of the argon atoms followed by attraction to the target.The argon atoms within the IR are lost through electron impact ionization e + Ar −→ Ar + + 2e where the argon atom can be in the ground state or in an excited state.This includes cold, warm and hot argon atoms.The electrons that drive the reaction can be from either the cold (primary) or hot (secondary) population.In addition charge exchange contributes to adding argon atoms to the IR, however the contribution is expected to be very small.Due to the electric fields within the IR, most of these gas ions are drawn toward the target and are lost from the IR.
As discussed above, gas rarefaction lowers the density of the working gas (the neutral argon atoms) within the IR below the density value in the surrounding gas reservoir, n g,0 [19,20,29,30].This leads to back-diffusion (gain) that is modeled by the term where the subscript g stands for the atoms of the working gas and v g,ran is their random thermal velocity as defined by equation ( 3).The argon gas diffusional refill term is determined by the gas temperature and the gas density difference (n Ar,0 − n Ar ) between the IR and the surrounding volume.By definition, only atoms moving towards the boundary are involved so that the densities are taken to be one half of the volume densities.

The degree of working gas rarefaction
The working gas rarefaction is either presented as a percentage of the total neutral argon density at the start of the pulse n Ar (t)/n Ar,0 or as a degree of working gas rarefaction degree of working gas rarefaction 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.As discussed in section 2.1 there are several factors that contribute to working gas rarefaction, including electron impact ionization of argon atoms and kick-out of argon atoms by the sputter wind, which is then balanced by diffusion (refill) of cold argon atoms from the bulk plasma, returning hot and warm argon atoms from the target, and charge-exchange collisions [47].When we compare the relative contribution 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.

Overview
As mentioned in section 1 the IRM has been applied to study HiPIMS discharges using a number of different target materials including graphite [55], aluminum [46,47], copper [52], titanium [51], and tungsten [53].For all the target materials the IRM calculations have shown that the cold (or primary) argon ground state density (denoted Ar C (3p 6 )) decreases steadily to a minimum close to the peak in the discharge current and then it increases again.The question that we will answer with this work is: What processes contribute to working gas rarefaction in the HiPIMS discharge?Is the sputter wind important?In the following, we will re-analyze some of these discharges in terms of working gas rarefaction.
In the following we explore how much each of the four terms described in section 2.1 contributes to working gas rarefaction for a few target materials, from low atom mass (graphite) to high atom mass (tungsten).For this we model discharges with targets of various materials and of varying sizes.For the various target sizes the dimensions of the IR for the IRM calculations are listed in table 2. Note that in some cases we use different dimensions for the size of the IR in this current study than in the original study of that particular target material.However, all the dimensions are within ±1 mm from the earlier assumed dimensions.The size of the IR is chosen rather arbitrary.Also, it has been observed experimentally that the size of the IR varies with the magnetic field strength among other operating parameters [70].In fact the absolute value of the degree of rarefaction scales with the size of the IR.Electron impact ionization scales with 1/V IR , while kick-out scales as 1/L, and therefore the absolute values mentioned in the text for the degree of working gas rarefaction are just rough estimates.Also keep in mind that as mentioned in section 1 that the size of the IR is small compared to the actual extent of the working gas rarefaction in the discharge [44], which also influences the absolute value of the degree of working gas rarefaction.Working gas rarefaction is therefore expected to be less pronounced when modeling with volume average models compared to DSMC simulations.Furthermore, Kozák and Lazar [44] point out that volume-averaged models do not take into account the spatial distribution of the neutral Ar and M densities, and therefore the velocity and angular distribution of the sputtered atoms [71,72], and secondary M-Ar and Ar-Ar collisions are neglected.The latter is justified by a mean free path of a few tens of mm as discussed in section 2.1 and given the extension of the IR it means that only a single collision occurs.

Graphite target
In a recent study we applied the IRM to analyze HiPIMS discharges with a 50 mm diameter graphite target and argon working gas at a pressure of 1 Pa [55].It was observed that the discharge operates on working gas recycling and most of the discharge current at the cathode target surface is composed of Ar + ions, which constitute over 90% of the discharge current, while the contribution of the C + ions is always small (<5%).The ion back-attraction probability during the pulse β t is high (>83%), and the ionized flux fraction is low, or in the range 2%-4%.The maximum in the degree of working gas rarefaction derived from the IRM is 45%, 51%, and 55%, for peak discharge current densities of 1, 2, and 3 A cm −2 , respectively.These values are determined from the maximum drop in the total argon atom density within the IR, calculated using equation (12), by adding the densities of all the neutral argon atom species densities within the IR.Earlier we reported a maximum in the degree of cold argon atom rarefaction of 66%, 74%, and 81% for discharge current densities of 1, 2, and 3 A cm −2 , respectively [55].The difference in the degree of working gas rarefaction values, reported here, compared to the earlier published values, is mainly due to warm and hot argon atoms that enter the IR during the pulse, which have influence on the rarefaction, and were not taken into account when the degree of working gas rarefaction was evaluated in the earlier study.Note, that the various values we report here for the discharge with graphite target have changed slightly as we discovered a few minor errors in the calculations published earlier [55], that have now been corrected, in addition to the modifications of the kick-out term discussed in section 2.1.Also, note that this does not affect the key results of that study concerning the reasons for low carbon ionization in HiPIMS.Furthermore, we have adjusted the size of the IR.
Here, we analyze the contributions of the various processes to rarefaction for a HiPIMS discharge with a graphite target in more detail.Figure 1 shows the temporal evolution of the reaction rates for the loss and gain of argon atoms within the IR for the J D,peak = 1 A cm −2 and 50 µs long pulse case explored earlier by Eliasson et al [55].The main contributor to the loss of argon atoms is electron impact ionization of the argon atoms by primary electrons (referred to as ionization cold), and the second most important loss process is electron impact ionization by secondary electrons (referred to as ionization hot) has much smaller contribution.This is the case even though both argon ions and carbon ions contribute to the creation of secondary electrons as they bombard the cathode target.Warm and hot argon atoms released from the target enter the IR and constitute the main contribution to the gain of argon atoms within the IR.The reaction gain rates for the warm and hot argon atoms in figure 1 are assumed to be the same and overlap, due to the assumption that equal number of argon atoms leaves the target during one pulse [47].We see in figure 1 that when operating with a graphite target the contributions of kick-out is small and charge-exchange is negligible (not shown).We note that diffusion contributes to a net loss of argon atoms during the pulse, but to a flow into the IR after the pulse is off.
We explore the diffusion terms more closely in figure 2. The main contribution to the diffusion is the refill of cold argon atoms into IR, while the warm and hot argon atoms escape out of the IR, and the hot atoms are lost faster than the atoms.The total diffusion (the dashed pink line in figure 1), i.e. the sum of the diffusion terms for Ar C , Ar m , Ar W , and Ar H , is also shown in figure 2. During the pulse-on time the escape of warm and hot argon atoms out of the IR is larger than the refill by cold argon atoms, this is the reason why the total diffusion term appears negative during the pulse.This reverses after the pulse is off.Almost a fifth of the warm and hot argon atoms that are released from the target escape out of the IR without being ionized.For J D,peak = 1 A cm −2 , at the peak in the degree of working gas rarefaction cold argon atoms in ground state account for 42%, metastable argon atoms 0.5%, warm argon atoms 37%, and hot argon atoms 21% of the argon atoms within the IR.So a substantial portion of the argon atoms within the IR, during the pulse, consists of warm and hot atoms.
Figure 3 shows the contribution of each of the terms to the working gas rarefaction versus the peak discharge current density for discharges with graphite target.We see that electron impact ionization by primary and secondary electrons has over 90% contribution and its role increases with increased peak discharge current density, and is the dominating process.Electron impact ionization by hot secondary electrons has about ∼10% overall contribution.Kick-out by the sputtered species, the sputter wind, has small (<10%) contribution on working gas rarefaction when operating with graphite target at a working gas pressure of 1 Pa, and 87% is due to kick-out by hot argon atoms and 13% is due to sputtered carbon atoms.The discharge current density does not have much influence on the relative contribution of the various terms.From the above discussion we see that the composition of the argon atoms within the IR changes during the pulse.

Aluminum target
The early development of the IRM [57] was based around HiPIMS discharges with an aluminum target, that were studied experimentally by Anders et al [73], and included studies of the discharge composition at the target surface [46], working gas rarefaction [47], and electron heating mechanisms [46,66].When the discharge enters the HiPIMS operating regime the Al + ions dominate the discharge current at the target surface, while the contribution of Ar + ions is low [46] and the discharge operates in the self-sputter regime to reach the high discharge currents [74].When operating with aluminum target, electron impact ionization of argon atoms was determined to be the biggest contributor to working gas rarefaction, when the degree of working gas rarefaction was determined to be about 50%, for J D,peak ≈ 0.6 A cm −2 and t pulse = 400 µs at p g = 1.8 Pa [47].
Here, we analyze a few discharges that were explored experimentally by Lundin et al [10], who measured the electron density and the ionized flux fraction as the working gas pressure, pulse length, and discharge current density was varied.The aluminum target was 50 mm in diameter and the working gas pressure was 0.5 and 2.0 Pa.At average current density J D,average ≈ 1.4 A cm −2 the measured ionized flux fraction was 50% at 0.5 Pa and at J D,average ≈ 1.2 A cm −2 the ionized flux fraction was 38% at 2 Pa for a 100 µs long pulse.Here, we further explore these discharges with the help of the IRM.For the IRM calculations the rate coefficients for reactions involving aluminum atoms and ions are the same as given by Huo et al [46].When applying the IRM we use the measured ionized flux fraction to lock the model as proposed by Butler et al [75].The maximum degree of working gas rarefaction derived from the IRM calculations is 83% at 0.5 Pa and 57% at 2 Pa close to the end of the pulse.The working gas rarefaction is much more significant for the lower pressure.The back-attraction probability of the ionized aluminum is 70% at 0.5 Pa and 75% at 2.0 Pa.
The reaction rates for the argon atom loss and argon atom gain within the IR for a discharge with a 50 mm aluminum target operated at a working gas pressure of 0.5 Pa are shown in figure 4. We see that the loss of argon atoms is mainly due to electron impact ionization of the argon atom, while kickout also has 14% contribution.Electron impact ionization by the primary electrons has 46% contribution, and the secondary electrons 40% contribution, to the loss of argon atoms from the IR.The diffusion processes (figure 5) are dominated by refill of cold argon atoms, while the warm and hot argon atoms escape out of the IR.At 2 Pa (figure 6) kick-out has similar contribution to the loss of argon atoms from the IR as does electron impact ionization.Electron impact ionization by the primary electrons and secondary electrons have each similar contributions.
The contribution of kick-out increases significantly (from 14% to 53%) with increasing working gas pressure from 0.5 to 2 Pa.At 0.5 Pa the kick-out is 83% due to aluminum atoms and 17% due to hot argon atoms, while at 2 Pa 86% is due to aluminum atoms and 14% due to hot argon atoms.As before, argon atoms enter the IR as returning warm and hot atoms from the target and by diffusion of cold argon atoms.Huo et al [47] pointed out that the long mean free path is the reason why rarefaction by electron impact ionization losses dominate over the sputter wind in the discharge.Therefore, for higher working gas pressures the sputter wind contribution would become  more significant, which is indeed what is observed here.At the peak in the degree of working gas rarefaction (for 0.5 Pa) cold argon atoms in the ground state are 44%, metastable argon atoms 0.5%, warm argon atoms 31%, and hot argon atoms 25% of the argon atoms within the IR.Again, more than half the argon atoms within the IR are warm and hot atoms.

Copper target
In a recent study the IRM was applied to study a few historical HiPIMS discharges operated with a copper target [52].It was observed that Cu + ions dominate the total ion current at the target surface.This indicates that the discharge is dominated by self-sputter recycling in order to reach the high discharge currents [74].For peak discharge current densities in the range 0.9-1.3A cm −2 the back-attraction probability was found to be in the range 44%-50%, while the ionization probability was in the range 61%-69%, and the ionized flux fraction was in the range 32%-40% [52].The model results showed that copper ions dominate the ion flux out of the IR, with about ∼77%-88% contribution, in agreement with experimental observations [32].Recall that for a HiPIMS discharge with copper target, the ionized flux fraction was early on determined experimentally to be as high 70% [76] and more recently an ionized flux fraction up to 80% has been measured experimentally [77].Gas compression and rarefaction have been observed in a HiPIMS discharge with a copper target by measuring time-resolved ion saturation currents from probe array [37].It was observed as an onset of the sputter flux that causes a transient densification of the working gas, followed by rarefaction.
Here, we explore reaction rates for the gain and loss of argon atoms within the IR for a discharge created with a 50 mm diameter copper target operated at a working gas pressure of 0.5 Pa, with a peak discharge current density of J D,peak = 1.0A cm −2 and 40 µs long pulse.The discharge current and voltage waveforms were recorded by Cemin et al [78] and explored in an earlier work as Case I [52].The degree of working gas rarefaction was determined to reach 60% toward the end of the pulse.
The reaction rates for the loss and gain of argon atoms within the IR are shown in figure 7. The main contributor to the loss of argon atoms is kick-out by the sputtered copper atoms while kick-out by the hot argon atoms has rather small contribution.Electron impact ionization of the argon atoms by primary and secondary electrons have smaller contributions.Warm and hot argon atoms released from the target and diffusion adds argon atoms to the IR.The diffusion terms are explored more closely in figure 8.The main contribution to the diffusion is the refill of cold argon atoms into the IR, while the warm and hot argon atoms escape out of the IR.The hot argon atoms are lost faster than the warm atoms as to be expected.At the peak in the degree of working gas rarefaction, the cold argon atoms in ground state constitute 75%, metastable argon atoms 0.5%, warm argon atoms 16%, and hot argon atoms 8%, of the argon atoms within the IR.

Titanium target
For a HiPIMS discharge with a titanium target the IRM results have shown that the ion composition at the target surface is composed of both argon and titanium ions in roughly equal numbers, and roughly a third of the titanium ions are the doubly ionized Ti 2+ , depending on the peak discharge current [46].In this case, as the self-sputter yield is somewhat below unity, a combination of self-sputter recycling and working gasrecycling is necessary to maintain the high discharge currents.
Here, we model discharges that were explored experimentally by Hajihoseini et al [11].As the magnet configuration was varied, the deposition rate and the ionized flux fraction was determined, while maintaining fixed averaged power by varying the repetition frequency as either the discharge current or discharge voltage was kept fixed.The titanium target was 100 mm in diameter, the working gas pressure 1 Pa, and the average power 300 W. These discharges have been analyzed extensively in order to gain understanding on how the magnetic field strength and topology influence the discharge parameters and operation, including the ionization probability [9], the deposition rate and ionized flux fraction [11,79,80], the size of the IR [70], and transport parameters for both ions and neutrals [72], as well as modeling by the IRM [51] and DSMC simulations [45] to determine the ionization and the target ion back-attraction probabilities.The IRM studies showed that the back-attraction probability is high > 0.8 [51].Here, we explore the various contributions to rarefaction in the discharge operated with the strongest magnetic field, referred to as C0E0 by Hajihoseini et al [11].The peak discharge current density was J D,peak = 1.0A cm −2 and the argon working gas pressure p g = 1 Pa.The IRM calculations give a peak in the degree of working gas rarefaction of 77%.For comparison for this particular discharge the DSMC simulations give the maximum in the degree of working gas rarefaction of 53% shortly after the end of the pulse [45].The various contributions to rarefaction are shown in figure 9.The loss of argon atoms is due to a combination of electron impact ionization by primary electrons and ionization by hot electrons, as well as kick-out, all with similar contributions.Charge-exchange has negligible contribution as before (not shown).The kick-out is split up in 74% contribution due to titanium atoms and 26% due to hot argon atoms.The large fraction of Ar + and Ti 2+ ions at the target surface lead to a high contribution of secondary electrons in the ionization process.Hot and cold argon atoms as well as diffusion of argon atoms into the IR add to the argon atom density within the IR.The contribution of diffusion is explored further in figure 10, and it is seen that diffusion of cold argon atoms into the IR is the most important factor.At maximum degree of working gas rarefaction the cold ground state argon atoms constitute 42%, metastable argon atoms 0.3%, warm argon atoms 36%, and hot argon atoms 22% of the argon atoms within the IR.

Zirconium target
We apply the IRM to a discharge operated with a 50 mm diameter zirconium disk.The discharge voltage V D was kept at 550 V, the pulse was kept at constant length of 50 µs and the argon working gas pressure was kept at 1 Pa [56].The ionized flux fraction and the normalized deposition rate was measured as the peak discharge current density was varied in the range 0.5 -2.0A cm −2 .We use the ionized flux fraction measured at 30 mm (45%) to lock the model.We apply the IRM to study a discharge operated with peak current density of J D,peak = 1 A cm −2 .The back-attraction probability is determined by the IRM to be 73% and the peak in the degree of working gas rarefaction was determined to be 70%.We also note that aproximately 2/3 of the discharge current at the target surface is carried by Ar + ions [56].This discharge therefore operates on combination of working gas recycling and selfsputter recycling to reach the high discharge currents [74].
The reaction rates for loss and gain of argon atoms within the IR are shown in figure 11.Electron impact ionization by primary electrons contributes 67% to the total rarefaction, while secondary electron ionization contributes 18% to the loss of argon atoms and kick-out contributes 15%.The kickout is 74% due to zirconium atoms sputtered from the targets and 26% due to hot argon atoms.The diffusion term is analyzed further in figure 12 and shows a refill by cold argon atoms and loss due to diffusion of warm and hot argon atoms out of the IR.At the peak in the degree of working gas rarefaction cold argon atoms in the ground state constitute 50%, metastable argon atoms 0.4%, warm argon atoms 32%, and hot argon atoms 18% of the argon atoms within the IR.

Tungsten target
Earlier, we applied the IRM to study a HiPIMS discharge with 75 mm diameter tungsten target as the discharge voltage was varied [53].The peak discharge current and the peak discharge current density J D,peak increases in the range 0.33 -0.73A cm −2 , with increased discharge voltage in the range 500 -800 V.The details of the experiment, experimental setup, and method can be found elsewhere [36].The model results show that when operating with a tungsten target an initial peak appears in the discharge current, which is due to argon ions  bombarding the cathode target [53].After this initial peak W + ions become the dominating ions and remain as such to the end of the pulse, and the role of W + ions increases with increased discharge voltage [53].However, there is always a rather significant contribution from the Ar + ions, which contribute to the creation of secondary electrons.For the sputtered tungsten the back-attraction probability β t decreases from 91% to 68% with increasing discharge voltage.With increased discharge voltage, the degree of working gas rarefaction increases from 34% at 500 V (J D,peak = 0.33 A cm −2 ) to 64% at 800 V (J D,peak = 0.73 A cm −2 ), when all the neutral argon species are included in the calculation.These are somewhat lower values than we reported in the earlier work [53] as there the degree of rarefaction was calculated assuming only cold argon atoms in the ground state when reporting the degree of working gas rarefaction.
Figure 13 shows the reaction rates for the loss and gain of argon atoms within the IR for the 600 V (J D,peak = 0.54 A cm −2 ) case explored earlier by Suresh Babu et al [53].The degree of working gas rarefaction peaked at 46% when all the argon atoms are taken into account.We see that the main contributor to the loss of argon atoms from the IR is kick-out of the argon atoms by tungsten atoms sputtered from the target.The second most important loss process is electron impact ionization by secondary electrons followed by electron impact ionization by the primary electrons.Charge exchange has negligible contribution (not shown).Diffusional refill of argon atoms is the main contributor to adding argon to the IR, while warm and hot argon atoms released from the target also have a contribution to add argon atoms to the IR.The reaction rates for the warm and hot argon atoms are the same and overlap, due to the assumption that an equal number of argon atoms leaves the target during one pulse [47].The diffusion of argon atoms is explored further in figure 14, where it is seen that the main contribution to the diffusion is the refill of cold argon atoms into the IR, while the warm and hot argon atoms escape out of the IR, and as expected that the hot argon atoms are lost faster than the warm atoms.The total diffusion is also shown in figure 14.At the peak in the degree of working gas rarefaction cold argon atoms in the ground state constitute 78%, warm argon atoms 17%, and hot argon atoms 5% of the argon atoms within the IR.
Figure 15 shows the contribution of each of the terms to the working gas rarefaction versus the peak current density.We see that kick-out has 49%-56% contribution to working gas rarefaction and is the dominating process, and its relative contribution increases with increased discharge current density.The kick-out is mostly due to tungsten atoms sputtered out of the target.The second most important process is electron impact ionization by secondary electrons, which has about 30% contribution, and its role also increases with increased discharge current density.The contributions of electron impact ionization by primary electrons is always smaller.

Discussion
We have applied the IRM to determine the various contributions to working gas rarefaction in HiPIMS discharges with a number of different cathode targets, spanning a wide range in atomic mass and sputter yield.We have observed that the working gas rarefaction is driven by electron impact ionization by both primary and hot electrons as well as by kick-out by fast neutrals coming from the target.We observed chargeexchange to have a negligible contribution to working gas rarefaction for all the target materials.
Figure 16 shows the different pathways for argon atoms within the IR and how they enter and are lost from the IR.The green arrows denote the neutrals, orange the hot and warm argon atoms (Ar H and Ar W ), and blue arrows denote the ions.The argon ions that bombard the target return to the IR as hot (Ar H ) and warm (Ar W ) argon atoms.The argon atoms can be kicked out into the DR by hot argon atoms Ar H and by sputtered metal neutrals M (not shown in figure 16) and cold argon neutrals can be re-filled from the DR.We see that diffused Ar W and Ar H can be ionized and back-attracted again.This loop can proceed several times and appears as a working gas recycling loop [74].Eventually, these particles escape from the IR.To not overestimate the contribution of ionization to the overall rarefaction, in the following we count only the first ionization of the argon species (hatched horizontal arrow).This can then be compared to the kick-out of argon neutrals by sputtered species and hot argon atoms (vertical hatched arrow).These are the two principal processes that lead to working gas rarefaction.
Figure 17 shows the various contributions to rarefaction, versus the atomic mass of the target material for discharges operated at discharge current densities close to 1 A cm −2 and working gas pressures close to 1 Pa.The results show that the processes that are responsible for working gas rarefaction and their relative contributions vary greatly depending on the target material.The relative contribution is determined by integrating the reaction rate for each process throughout the entire pulse and the afterglow.Table 1 summarizes the atomic properties, for the six target atoms explored.The role of electron impact ionization by primary electrons is significant for most of the target materials explored, while its contribution is however smaller for a discharge with copper and tungsten targets.Electron impact ionization by hot (secondary) electrons has ∼10% contribution when operating with a graphite target while for titanium and tungsten targets the contribution is ∼30%.We also note, for the zirconium case that the role of electron impact ionization is large, or well over 80%, when both primary and secondary electrons are taken into account, while kick-out has only a small contribution.For titanium the overall contribution of electron impact ionization is high or almost 60%.The role of kick-out, or sputter wind, plays a significant role in a discharge with target made of the heaviest target atom, tungsten (183.8 amu), and a larger and indeed rather significant role for a discharge with a copper (63.5 amu) target, while for a discharge with a zirconium (91.2 amu) target the contribution is small.There is therefore no apparent dependence of the various contributions on the target atom mass as can be seen in figure 17.
The missing correlation between target material mass and the contribution to the overall gas rarefaction by the kickout mechanism is to be expected, as our kick-out model does not explicitly depend on the mass ratios.The justification is based on the fact that argon species are quickly lost on time scales that are short compared to typical pulse lengths (see section 2.1).This short residence time of an argon species in the IR after a collision is in our model therefore approximated by zero.In addition there is at most one collision between a sputtered species from the target and an argon species, due to the long mean free path compared to typical heights of the IR (see section 2.1).The momentum of a sputtered species is therefore unlikely to be shared between more than one argon species.This leads us to the conclusion that the mass ratio is only of secondary importance for determining the contribution of kick-out to the overall gas rarefaction.
Figure 18 shows the fractional contributions of the various processes to working gas rarefaction versus the self-sputter yield of the various target ions.Note that we have chosen to plot the data versus the self-sputter yield, although for argondominated discharges, the sputter yield would be the more relevant parameter.For the materials under investigation here, the numerical value of both is very similar, which is why the plot and the conclusions drawn from it would not change if we had used the sputter yield instead of the self-sputter yield.We see that the fractional contribution of kick-out increases with increased self-sputter yield.The total contribution of electron impact ionization decreases with increased self-sputter yield.The sputter yield or the self-sputter yield appears to be the primary factor for which process is the dominating contributor to working gas rarefaction.This is the reason why kick-out is so significant for copper, which has high sputter yield, even though the mass ratio and cohesive energy are smaller than for Zr.In general we see that for the metal targets the kickout is mainly due to metal atoms sputtered from the target and that kick-out by hot argon atoms has smaller contribution.This is different for the graphite target where hot argon atoms are the dominant contributor by far and carbon atoms only have a small contribution due to its low sputter yield.
A secondary trend is visible in the data in figure 18.From copper with a high sputter yield, to titanium with a moderate sputter yield, the contribution of electron impact ionization increases as discussed in the preceding paragraph.At the same time the share of electron impact from the hot electron population increases.This is due to the IR becoming more argon-dominated as opposed to metal-dominated.As the bombardment of a metal target with argon ions produces secondary electrons, while the bombardment of singly ionized metal ions does not, there is a higher density of hot electrons in these discharges, explaining the stronger contribution of ionization from this electron population for titanium compared to copper.The continuation of this trend cannot be seen for zirconium, nor for graphite.
The above observations, and the discussion above on the working gas rarefaction, highlights its importance for the deposition processes based on magnetron sputtering.In some of the earlier studies of working gas rarefaction [27,33,81] the deposition flux is suggested to be influenced in both its magnitude and kinetic energy by the working gas rarefaction.On the one hand, the reduced density of heavy species in a pronounced rarefaction window decreases the energy dissipation of sputtered species on their path through the IR and to the substrate [33], while on the other hand, fewer particles are scattered, possibly increasing the deposition rate in the axial direction [27,81].Finally, the reduction of heavy species in front of the target also reduces electron-neutral collision frequency and, therefore, reduces classical (collisional) diffusion of electrons across the magnetic field lines, which is suggested to promote the appearance of plasma instabilities, termed spokes, to provide an alternative path for electron transport across the magnetic field lines [82][83][84][85].These spokes have been suggested to positively influence the release of target ions toward the substrate [86].Studying the effect of the degree of gas rarefaction on the thin film deposition process is left for the future.

Conclusion
The IRM has been applied to determine the degree of working gas rarefaction and the relative contribution of various processes to working gas rarefaction in HiPIMS discharges with different target materials.The dominating contribution of the various processes to working gas rarefaction varies between the different target materials.For targets with low sputter yield electron impact ionization is the dominating process, while for high sputter yield target materials, tungsten as well as copper targets, kick-out of argon atoms by the metal atoms is the dominating process, with over 60% contribution.For the metal targets the magnitude of the kick-out is mainly due to metal atoms sputtered from the target and kick-out by hot argon atoms has a smaller contribution.For the graphite target, the small kickout contribution is dominated by a kick-out by the hot argon atoms, while carbon atoms only have a small contribution.The sputter yield is the primary factor that dictates which process is the most important when it comes to working gas rarefaction.We also see that the degree of working gas rarefaction depends on the working gas pressure as demonstrated for a discharge with an aluminum target.Working gas rarefaction is much more significant for the lower pressures and the kickout mechanism is a much more important at higher working gas pressure.Furthermore, we note that in most cases there is a significant fraction of hot and warm argon atoms within the IR.This value is highest 67% when operating with the graphite target.However, this fraction is smaller for the copper target (16%) and the tungsten target (26%), as much of the sputtering is self-sputtering.This may explain the high neutral gas temperature that has been observed experimentally [42].

Figure 1 .
Figure 1.The reaction rates for the argon atom loss and argon atom gain within the ionization region for a discharge with 50 mm diameter graphite target operated at working gas pressure of 1 Pa, with a peak discharge current I D,peak of 20 A (J D,peak = 1 A cm −2 ) and 50 µs long pulse.

Figure 2 .
Figure 2.The reaction rates for the cold argon atom diffusion and warm and hot argon atom escaping from the ionization region for a discharge with 50 mm diameter graphite target operated at working gas pressure of 1 Pa, with a peak discharge current I D,peak of 20 A (J D,peak = 1 A cm −2 ) and 50 µs long pulse.

Figure 3 .
Figure 3.The contribution of the various processes to working gas rarefaction within the ionization region for a discharge with 50 mm diameter graphite target versus the peak discharge current density for argon at 1 Pa, pulse length of 50 µs and average discharge power ⟨P D ⟩ of 80 W.

Figure 4 .
Figure 4.The reaction rates for the argon atom loss and argon atom gain within the ionization region for a discharge with 50 mm aluminum target operated at working gas pressure of 0.5 Pa, with a discharge voltage of V D = 730 V giving average discharge current I D,average of 27 A (J D,average = 1.4A cm −2 ) for 100 µs long pulse.

Figure 5 .
Figure 5.The reaction rates for the cold argon atom diffusion and warm and hot argon atom escaping the ionization region for a discharge with 50 mm aluminum target operated at working gas pressure of 0.5 Pa, with a discharge voltage of V D = 730 V giving average discharge current I D,average of 27 A (J D,average = 1.4A cm −2 ) for 100 µs long pulse.

Figure 6 .
Figure 6.The reaction rates for the argon atom loss and argon atom gain within the ionization region for a discharge with 50 mm aluminum target operated at working gas pressure of 2.0 Pa, with a discharge voltage of V D = 540 V giving average discharge current I D,average of 23 A (J D,average = 1.2A cm −2 ) for 100 µs long pulse.

Figure 7 .
Figure7.reaction rates for the argon atom loss and argon atom gain within the ionization region for a discharge with 50 mm diameter copper target operated at working gas pressure of 0.5 Pa, with a peak discharge current density of J D,peak = 1.0A cm −2 for 40 µs long pulse.

Figure 8 .
Figure 8.The reaction rates for the cold argon atom diffusion and warm and hot argon atom escaping the ionization region for a discharge with 50 mm diameter copper target operated at working gas pressure of 0.5 Pa, with a peak discharge current density of J D,peak = 1.0A cm −2 for 40 µs long pulse.

Figure 9 .
Figure 9.The reaction rates for the argon atom loss and argon atom gain within the ionization region for a discharge with 100 mm diameter Ti target operated at working gas pressure of 1 Pa, with a discharge voltage V D = 625 V giving peak discharge current I D,peak of 80 A (J D,peak = 1.0A cm −2 ) and 100 µs long pulse.

Figure 10 .
Figure 10.The reaction rates for the cold argon atom diffusion and warm and hot argon atom escaping the ionization region for a discharge with 100 mm diameter Ti target operated at working gas pressure of 1 Pa, with a discharge voltage V D = 625 V giving peak discharge current I D,peak of 80 A (J D,peak = 1.0A cm −2 ) and 100 µs long pulse.

Figure 11 .
Figure 11.The reaction rates for the argon atom loss and argon atom gain within the ionization region for a discharge with 50 mm diameter Zr target operated at working gas pressure of 1 Pa, with a discharge voltage V D = 550 V giving peak discharge current density of J D,peak = 1.0A cm −2 and 50 µs long pulse.

Figure 12 .
Figure 12.The reaction rates for the cold argon atom diffusion and warm and hot argon atom escaping the ionization region for a discharge with 50 mm diameter Zr target operated at working gas pressure of 1 Pa, with a discharge voltage V D = 550 V giving peak discharge current density of J D,peak = 1.0A cm −2 and 50 µs long pulse.

Figure 13 .
Figure 13.The reaction rates for the argon atom loss and argon atom gain within the ionization region for a discharge with 75 mm tungsten target operated at working gas pressure of 1 Pa, with a discharge voltage of V D = 600 V giving peak discharge current I D,peak of 24 A (J D,peak = 0.54 A cm −2 ) for 100 µs long pulse.

Figure 14 .
Figure 14.The reaction rates for the argon atom diffusion and hot and warm argon atoms escaping out of the ionization region for a discharge with 75 mm tungsten target operated at working gas pressure of 1 Pa, with a discharge voltage of V D = 600 V giving peak discharge current I D,peak of 24 A (J D,peak = 0.54 A cm −2 ) for 100 µs long pulse.

Figure 15 .
Figure 15.The contribution of the various processes to working gas rarefaction within the ionization region for a discharge with 75 mm tungsten target versus the discharge current density for argon working gas pressure of 1 Pa and pulse length of 100 µs.

Figure 16 .
Figure 16.A schematic showing the processes involved in working gas rarefaction.The green arrows denote the neutrals, orange the hot (Ar H ) and warm (Ar W ) argon atoms, and blue arrows denote the ions.Metal sputtering and its influence on working gas rarefaction is omitted in this sketch for clarity.

Table 2 .
The dimensions of the ionization region used in the model calculations for the different targets and target sizes.