I-V characteristics of magnetron discharge are commonly presented on a log-log plot as the I-V characteristic can be empirically described as I = kVⁿ. In the case of HPPMS its quite common to plot the peak current as a function of the discharge voltage. A linear fit through the data points permits in this way to determine the value of n which expresses the I-V characteristic steepness and reflects the ionization efficiency in the considered working conditions. To illustrate the impact of the steepness on the overall waveform measured during HPPMS, magnesium targets were sputter eroded. The influence of the target erosion groove depth can be understood from the increase of the magnetic field strength when the target becomes more eroded. At sufficient high pressure, the increased magnetic field strength generally results in an increase of the steepness [28]. This behavior was shown for HPPMS by Čapek et al. by increasing the target-to-magnet distance with paramagnetic Cu spacers [29, 30]. Magnesium has one of the highest sputtering yield as compared to other metals in this study. This permits to erode the target in a relative short time, and study the effect of target erosion on the HPPMS waveform and the I-V characteristic of the discharge. Figure 2 shows the change of the current waveform as a function of the target erosion depth. A clear peak is followed by stable plateau irrespective of the erosion groove depth. The figure shows also an analysis of the peak current and the plateau current. Both strongly increase in a similar fashion with the erosion groove depth. The ratio between both (not shown) remains more or less constant. The I-V characteristics for the same erosion depths were measured by increasing the applied voltage between 300 V and 650 V.

The steepness of the slope n is shown as function of the erosion depth in the top left panel of Figure 2. An increase of the steepness is observed. It is clear that with increasing erosion groove depth both the peak current, the plateau current, and the steepness of the I-V characteristic increase. The right top panel shows the deposition rate as a function of the erosion groove depth. A linear correlation (correlation coefficient 0.9725 for 8 data points) is observed.

Figure 3 shows the measured current (I-t) (red traces), and the voltage-time (V-t) pulse (blue traces) for the 17 different target materials. The effective discharge voltage for all materials lies between 482 and 504 V, but no systematic trends between the used target material and the average discharge voltage within the pulse were noticed. A well-defined rectangular voltage is observed, except for Ag, Cu, Pb, W, and Zn. For these latter elements, a transient regime toward 0 V is noticed when the discharge voltage is switched off. This behavior is probably related to the higher plasma impedance for these target materials which hinders the charge removal in the pulse-off time. This point is inspired by the fact that exactly for these five materials the effect of gas rarefaction is the strongest (see further, Figure 4).

A clear difference can be noticed in both peak current and the overall behavior of the discharge current as a function of time between the different materials. Nevertheless, all current waveforms have a similar shape fitting to mode V as presented in the paper of Wu et al. [21], i.e. a clear peak followed by a stable plateau current. For Nd and Sm, the peak is less defined, and one could also argue that the shape fits to mode III. Important for the following discussion is that for some materials (Ag, Cu, and Zn) the selected settings do not result in a HPPMS discharge according to the classification by Gudmundson et al. [31]. For all other materials the peak power density is well above the defined threshold of 0.05 kW.cm⁻² for direct current magnetron sputtering (DCMS) and ranges between 0.1 kW.cm⁻² (W) and 0.6 kW.cm⁻² (Nb). Statistically significant correlations between on the one hand some characteristics such as peak current and plateau current, and on the other hand material properties were systematically investigated. The results are discussed in the following subsections.

The presence of a peak in the I-t diagram has been discussed in the literature. The main reason is the rarefaction of the working gas due to momentum transfer between the sputtered atoms, and working gas atoms. This reasoning is substantiated by experimental evidences based on different plasma diagnostic techniques [32]. However, modeling also indicates there is an alternative mechanism for gas rarefaction, i.e. ionization losses [33]. Although the authors of the latter paper conclude that the sputter wind contribution would become more important at higher pressure. From a more conceptual viewpoint, the above reasoning regarding gas rarefaction can easily be tested. On the one hand, the applied voltage will, similarly to DCMS, result in a current increase defined by the discharge impedance. Indeed, as illustrated with the magnesium experiments, the peak current increases if the discharge is run in a condition for which ionization is more efficient. The latter can be explained from an increased effective secondary electron emission. The electrons are trapped closer to the target for a stronger magnetic field. This results in more ionization within the sheath. The electrons formed during the ionization can also gain energy within the sheath which can be seen as a multiplication of the initial secondary electron [34]. The electron yield is also strongly material dependent, and therefore, as shown by Depla et al. [28], the steepness of the I-V characteristic depends on the ion induced electron yield of the target material. As the steepness of the I-V characteristic increases with increasing electron yield, one can therefore expect a higher peak current. On the other hand, the discharge current will decrease due to the momentum transfer as the local density of potential charge carriers will decrease. The momentum transfer can be estimated on the average energy of the sputtered atoms, and the target sputter yield. Based on the energy transfer function Λ (see Equation 2), the average momentum transferred to the argon atoms can be calculated. For materials with a higher sputter yield, this transfer will occur more frequently. The above reasoning leads to the following test parameter,

where Y is the sputter yield of the target material, E_avg the average energy of the sputtered atoms, m_M the atomic mass of the target material, and γ_ISEE the ion induced electron yield. The energy transfer function Λ equals

where m_Ar the atomic mass of argon. The sputter yield of the target material can be calculated based on the approach published before by our research group [35], i.e. the ion energy is set equal to 0.75 times the average discharge voltage in the pulse, and the sputter yield is corrected for the contribution of high energetic neutrals. The average energy of the sputtered atoms was calculated based on the simplified equation proposed by Eckstein [36],

where U_s is the surface binding energy, and E_max the maximum energy of the sputtered atoms. The latter is approached in the paper by Eckstein as ΛE_ion, with E_ion the ion energy. As shown by Eisenmenger-Sittner et al. [37] a better approach for normal incidence impact of the ion is fΛE_ion with f equal to 0.4. The ion induced electron yield is calculated based on the equation presented in Depla et al. [28]. The above reasoning is not completely correct as one needs to account for the number of collisions that occurs close to the target. Collisions between the sputtered atoms and the argon atoms that take place far from the target will not influence the discharge properties. As discussed in section 2 the energy transferred per sputtered atom in a small volume above the target can be simulated. This leads to a better description of the test parameter as

As the experimental pressure is relatively high, the number of collisions that occur in the volume above the target is rather high, i.e. on average approximately 15 collisions. Therefore, the first approach overestimates the transferred momentum only by a factor of 2. Moreover, there is a linear correlation between the momentum transfer calculated with the two methods. Figure 4 shows the correlation between the calculated value for p_test,1 (see Equation 4), and the (natural) logarithm of the measured peak current. A strong significant correlation is found (correlation coefficient r² = 0.7416 for 17 data points, degree of confidence 99.9995%). One element, i.e. Pb, deviates from the fitted line (based on studentized residual analysis with a significance level of 0.05).

The much larger cross section for electron impact ionization (see further) can probably explain this behavior. The return probability toward the cathode will be higher for materials with a higher cross section for electron impact ionization. As the self-sputtering yield of Pb is lower than the argon based sputter yield, the effective sputter yield of Pb will be lower, or stated differently a lower value of p_test,1 can be expected. If the Pb data point is considered as an outlier, the correlation coefficient even increases to r² = 0.8765 (16 data points, degree of confidence is practically 100%). One could argue that the three materials with a low peak current (Ag, Cu, and Zn) have a strong impact on the linear correlation. However, even when these three elements are dropped from the analysis, the correlation is still statistically significant (r² = 0.4425 for 13 data points, degree of confidence 99.345%), and the fitted line (indicated in gray in Figure 4) hardly changes. For these three elements the resulting peak current is low, and a DC like discharge current density is observed. Rossnagel [38] has studied gas rarefaction during DCMS, and used a similar argumentation that leads to Equation (1). Further, in a study on I-PVD by the same author [39], the effect of gas density reduction on the ionization probability was already discussed. It is interesting to notice that the correlation between the peak current and the test parameter holds for both the HPPMS and the DCMS like conditions. Hence, the result shown in Figure 5 allows to significantly conclude that the sputter wind contribution to gas rarefaction is an important mechanism. This seems to be in contrast to the conclusion made by Huo et al. [33] that ionization losses is the dominant mechanism for gas rarefaction. This latter conclusion is based on modeling of the HiPIMS current waveform solely recorded for Al under identical conditions as presented in the current paper, i.e. 400 μs long pulses at 1.8 Pa argon pressure for a two inch diameter magnetron. From Figure 4 it is clear that in the case of Al, the sputter wind contribution is rather small as compared to other metals which agrees with the conclusion by Huo et al. [33]. However, Figure 4 also shows that the conclusion cannot be generalized. Moreover, it is clearly necessary to analyze sufficient materials. Based on a seven element study (Al, C, Cr, Cu, Nb, Ti, and W) Anders et al. [22] conclude “The very large differences between materials cannot be ascribed to the different sputter yields but they indicate that generation and trapping of secondary electrons play a major role for current-voltage-time characteristics.” When a similar plot of the peak current as Figure 4 is made but now as a function of the sputter yield, a significant correlation is found (r² = 0.5795, for 17 elements, degree of confidence 99.981%). When the plot is however restricted to the same six elements as in the study of Anders et al. no significant correlation is found. Hence, within their experimental framework, the conclusion of Anders et al. is correct according to our study, but clearly when the dataset is expanded, another conclusion can be drawn.

The peak is followed by a stabilization of the discharge current. The constant current in this regime is referred to as the plateau current. According to Wu et al. [21], the current waveform can be understood as follows. Before the maximum the argon ions are already replaced by metal ions, and the secondary electron yield decreases because the metal ions contribute less to the target secondary electron emission. When equilibrium is reached, the plasma is a mixture of metal and argon gas ions. When no highly charged metal ions are produced, the discharge current will stabilize, and the waveform will show a plateau until the end of the pulse. Again a simple conceptual calculation can be performed to test this hypothesis. As the current decrease is the result of the replacement of argon by metal ions, the relative current decrease should scale with the ionization rate of the metal atoms. Also, the magnitude of the current decrease will depend on the steepness of the I-V characteristic, i.e. the sharper the I-V characteristic, the stronger the effect. As mentioned before, the sharpness of the I-V characteristic scales almost linearly with the electron yield. As such the following test parameter is derived,

The ionization rate can be calculated from the cross section for electron impact ionization, and the electron energy distribution. The latter is assumed to be Maxwellian with an electron temperature of 6 eV. This approximation is also used in advanced models for high power impulse magnetron sputtering (HiPIMS) [27, 40, 41]. The exact electron temperature has however little impact on our analysis. The cross section for electron impact ionization was calculated according the Deutsch-Mark semi-classical formalism [42–45]. The input data for this formalism, such as the ionization energy in the (nl) subshell, and the radius of maximum radial density of the atomic subshell characterized by the quantum numbers n and l, were taken, as suggested in the papers by Deutsch et al., from Desclaux [46]. Figure 5 shows the test parameter p_test,2 as a function of the metal ionization rate. A linear correlation is found which confirms the above reasoning. When the DC like results (Ag, Cu, and Zn) are removed from the analysis (see gray line) the relation correlation is hardly affected.

Again, one outlier, i.e. magnesium, is observed (based on a studentized residual analysis with a significance level 0.05). This is not surprising as the opposite reasoning as related to Figure 4 can be made. In Figure 4, Pb was observed to deviate from the found correlation. It was argued that the large cross section for impact ionization is probably the cause. In the present case, the replacement of argon by magnesium will be small because the momentum transfer between magnesium and argon is not efficient. This also agrees with the fact that this test parameter is almost constant for Mg, irrespective of the steepness of the I-V characteristic. Indeed, both the peak and the plateau current increase with the erosion groove depth (see Figure 2). As discussed before, the deposition rate for Mg scales linearly with the erosion depth. So despite more Mg atoms are sputtered, the effect on the decrease of the plateau is minimal because the sputtered Mg atoms do not replace the argon atoms, and only a limited impact of gas rarefaction is observed.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.