Dynamics of bipolar HiPIMS discharges by plasma potential probe measurements

Measurements were performed in a cylindrical stainless-steel vacuum chamber, see figure 1(a), (42 cm in diameter, height of 30 cm, i.e. a surface area of approx. 6800 cm² and a volume of approx. 42 liters) pumped by a turbomolecular pump down to a base pressure of 3 × 10⁻⁴ Pa. During operation, 30 sccm of Ar (99.997%) gas was injected into the chamber and the working pressure was adjusted by a gate valve located between the chamber and the turbomolecular pump. All the measurements, except for those described in section 2.4 and discussed in section 3.2, were obtained with a planar circular magnetron (TORUS Circular, Kurt J. Lesker Company) with a two-inch 3 mm thick Cu (99.99%) target mounted in the top lid of the chamber with the magnetron axis coinciding with the central axis of the chamber. Prior to the experiments, the magnetic field components (B_r, B_z) were mapped in a half-plane using a Gaussmeter probe (420 Gaussmeter, LakeShore), see figure S2(a) in the supplementary material. The B_r component above the racetrack at the target $\left(z,r\right)$ = (0, 9) mm was approx. 100 mT. The magnetic field was characterized as unbalanced type-2 with a null point located at z = 14 mm from the target. For mounting of the magnetron, an electrically insulated vacuum feedthrough was used, so that the magnetron body (together with the anode shield) was not conductively connected to the chamber. The magnetron body (together with the anode shield) was connected to the grounded vacuum chamber via a copper strip (see the violet wire in figure 1(a)), which made it possible to measure the corresponding current I_ch. The cathode was connected through a coaxial cable to a HiPIMS pulsing unit (Bipolar HiPSTER, Ionautics AB) fed by two dc power supplies, one that delivered a negative potential U₋ for initiating classical HiPIMS pulses and a second one used to apply a positive potential U₊. The outer and inner conductors of the coaxial cable were separated at approximately mid-length to enable measuring the target current I_t (inner conductor) and the returning current I_cr (outer conductor). The currents I_t, I_cr and I_ch were sensed by Chavin Arnoux C160 current clamps. The current through the anode shield I_as could not be directly measured but it was obtained numerically as I_as = I_cr − I_ch, see figure 1(a). The target voltage U_t was sensed at the same place as the target current by means of a High Voltage Differential Probe (Testec) (70 MHz) with an attenuation ratio of 1:100. All the signals were recorded on a digital oscilloscope (PicoScope 4444, Pico Technology) in an averaging mode averaging over 100 consecutive pulse periods. A stainless-steel substrate table (diameter of 5 cm) was positioned in the middle of the chamber with a target-to-substrate-table distance of 11 cm. During the experiments the substrate table (together with the supporting rod) was floating.

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For the study of the phenomena occurring during the positive pulse, we have chosen a positive pulse length of τ₊ = 400 μs. As discussed later in section 4.5, the minimum delay time τ_± between the negative and positive pulse is limited by the intrinsic properties of the bipolar HiPIMS unit and depends on discharge conditions. During measurements we aimed at achieving the lowest possible delay time τ_±. The positive voltage applied to the target U₊ was typically set to 100 V. However, for some discharge conditions, the target voltage U_t at the beginning of the positive pulse was lower, as the positive voltage power supply was not able to deliver the high currents needed. Typically, the pulsing frequency was maintained constant at around 50 Hz. Our measurements, however, indicate that changes of the frequency and hence average discharge power, are not affecting the presented results obtained during the positive pulse as long as the shape of the HiPIMS discharge (negative pulse) current waveform (I_D,peak and τ_−,eff) is kept unchanged. The HiPIMS discharge current waveform is here quantified by I_D,peak, and by the full width at half maximum denoted as τ_−,eff, as discussed later in section 3.1.

Seven circular flat probes (diameter of 30 mm) were positioned at various places along the chamber walls, see figure 1(a). The probes were constructed from aluminum foil, insulated from the chamber walls by Kapton tape, and stuck to the chamber wall by using a copper two-side-adhesive tape. The probes were connected to the electrical feedthroughs by coaxial cables with the shields connected to ground, see figure 1(b). During measurement of the current through a given probe, the probe was biased at −40 V and the other probes were grounded. As the probe was biased at −40 V and the plasma potential was higher than 0 V during the positive pulse, the measured current corresponds to the ion saturation current. Two passive 1:10 oscilloscopic probes (TPP0101, Tektronix) connected to a differential input of the oscilloscope were used to measure the voltage drop over a 10 Ω resistor, from which the probe ion saturation current ${I}_{\mathrm{n},\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{b}\mathrm{e}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$ for a particular probe numbered by n was estimated. Due to a slight mismatch of the resistances of the two passive probes, a significant dc offset was present in the signal (linearly related to the probe biasing voltage). During the data analysis the offset was subtracted by assuming that the probe current before the start of the negative pulse is negligible. By dividing ${I}_{\mathrm{n},\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{b}\mathrm{e}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$ by the probe area, the ion saturation current density ${J}_{\mathrm{n}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$ was obtained. In order to approximately determine the total chamber ion saturation current ${I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$, cylindrical symmetry of the chamber was assumed. For each probe, a specific region of the chamber wall with an area of ${A}_{\mathrm{w}}^{\mathrm{n}}$ was selected, see figure 1(a), and the total ion saturation current through this area ${I}_{\mathrm{n},\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$ was estimated as ${I}_{\mathrm{n},\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}={A}_{\mathrm{w}}^{\mathrm{n}}{J}_{\mathrm{n}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$. Only one probe (No. 7) was used on the upper lid of the cylindrical chamber. The total chamber wall ion saturation current ${I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$ was estimated by summing all the seven ${I}_{\mathrm{n},\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$ currents and multiplying the sum by a constant factor of 0.75. The factor of 0.75 was found to fit the ${I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$ data to the −I_t data in the 0.3 Pa case shown in figure 10. The factor can be justified by the fact that the extrapolation of the probe currents ${I}_{\mathrm{n},\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{b}\mathrm{e}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$ to the total chamber wall current ${I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$ is only approximative and because the geometry of the chamber deviates from the cylinder approximation due to the presence of various vacuum ports (not shown in figure 1(a)). Moreover, the same factor of 0.75 was used also for the other discharge conditions studied and resulted in a very good correspondence with the target current data, see figure 10, which further justifies this approach of estimating ${I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$.

For the measurement of the plasma potential an emissive probe was placed at the magnetron axis at a distance of z = 10 cm from the magnetron (1 cm above the substrate holder). The emissive probe was constructed using a tungsten wire loop (W + 1% Th wire of 150 μm in diameter), protruding 4 mm out of a double-bore ceramic tube. The floating potential of the emissive probe was measured by a passive oscilloscopic probe (1:10, 10 MΩ, 12 pF, TPP0101, Tektronix) between two 100 Ω resistors connected in parallel to the wire loop, see figure 1(a). The wire loop was continuously ohmically heated by supplying a heating current I_h of 3.5 A by means of an in-house-built floating dc power supply using the push-pull topology, where the capacitance of the floating part to the grounded part was less than 40 pF. A reasonably small capacitance of the probe to ground is needed in order to achieve a small RC time constant of the probe charging [33]. The RC constant of the probe is also decreasing with increasing probe collecting area, plasma density and/or probe electron emission current when the probe is heated. The increase of the electron emission current from the emissive probe when increasing the heating current I_h is significantly decreasing the time needed for the probe to charge up to more positive voltages, which is shown in the supplementary material figure S3. The data in figure S3 show that a saturation of the plasma potential signal rise time in the beginning of the positive pulse was achieved even at low plasma density conditions, which implies that the influence of probe charging on the plasma potential measurement during the positive pulse can be neglected.

A spatial map of the plasma potential discussed in section 3.2 was measured for a three-inch circular magnetron (Gencoa) with a 5 mm thick Cu (99.99%) target, which was mounted from the side of the same cylindrical vacuum chamber so that the axis of the magnetron was perpendicular to the cylindrical chamber axis and at the same time perpendicular to the he emissive probe holder, see the schematics in figure 2. The magnetic field lines of the magnetron are depicted in figure S2(b) in the supplementary information. It is an unbalanced type-2 magnetic configuration, with a null point located at z = 44 mm from the target and a radial component of the magnetic field B_r = 70 mT at the target above the race track $\left(z,r\right)$ = (0, 23) mm. In this configuration, the substrate table, the wall flat probes, and the two-inch magnetron were not mounted. The radial position was adjusted by radial movement of the emissive probe, while the axial position was changed by axial movement of the magnetron. A separate large flat floating probe (diameter of 5 cm) was positioned more than 20 cm from the target, outside of the magnetic trap region, and was used to measure the floating potential in order to evaluate possible influence of the emissive probe on the discharge, when located inside the magnetic trap. The waveforms during the spatial mapping were not averaged than in the other measurements, and a different oscilloscope was used (Tektronix TDS 520 C).

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In this section we describe the evolution of the plasma potential measured at a typical position of a substrate holder, specifically 10 cm from the target at the magnetron axis. As can be seen from the magnetic field map of the two-inch magnetron in figure S2(a), the emissive probe was positioned in the plasma bulk region well outside of the magnetic trap. The temporal evolution of the plasma potential during the positive pulse is observed to be highly dynamic and dependent on the discharge conditions. We have identified three process parameters that are significantly influencing the plasma potential evolution during the positive pulse: (i) working gas pressure p, (ii) peak HiPIMS discharge current I_D,peak and (iii) length of the HiPIMS discharge current pulse τ_−,eff. These individual effects are demonstrated in figures 4–6, respectively. The effects of changing the positive pulse voltage U₊ are less pronounced and are shown in figure 7. In the text we use the symbol t to denote a time instant, while τ denotes a length of a time interval.

Let us first look at the general temporal evolution of the plasma potential before addressing the individual effects of the investigated external process parameters. Figure 3 shows the recorded plasma potential U_p,subst.(t), target current I_t(t) and target potential U_t(t) waveforms using a working gas pressure of 0.3 Pa. The target current I_t during the negative pulse sharply increases, attains a peak value I_D,peak, and till the end of the negative pulse stays at a value close to I_D,peak. This close-to-rectangular shape of the target current during negative pulse allows us to approximately characterize this discharge current regime by two values—the peak HiPIMS discharge current I_D,peak and the length of the HiPIMS discharge current pulse τ_−,eff, see figure 3(a). Note, that τ_−,eff is smaller than the set negative pulse length τ₋. The difference is mainly caused by the formative time lag, which is the time needed for the primary Townsend ionization avalanche to occur and during which only negligible current flows to the target [34]. In the present example I_D,peak = 48 A, τ_−,eff = 55 μs, and τ₋ = 105 μs. At the onset of the discharge current rise, the plasma potential attains values of around −25 V, however, then increases to a value close to 0 V. This observation agrees qualitatively with other works studying the plasma potential in HiPIMS in more detail [35]. The end of the 105 μs long negative pulse corresponds to time 0 μs in the figures. Figure 3(b) shows a close-up at the transition from the negative pulse to the positive pulse. All the discharges studied show similar behavior at this transition. There is a delay time τ_± between the end of the negative pulse and onset of the positive pulse of around 6 μs, which, at the given conditions, was the lowest possible delay given the bipolar HiPIMS power supply used. During this delay time the target current decreases sharply, while the measured target voltage reverses polarity, peaks at around 60 V and stabilizes at around 15 V. We attribute this measured positive voltage during the delay interval to an artefact caused by a voltage induced along the coaxial cable between the target and the voltage measuring spot (see the inductance L_c shown schematically in figure 1(a)) due to the fast target current decrease. Additional target potential measurements (not shown) using an external wire attached directly to the target, revealed that the target voltage is in fact close to zero in the delay time interval. The plasma potential measured during the delay time interval is also close to zero, as seen in figure 3(b).

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For the typical discharge shown in figure 3(a) we can clearly distinguish four different phases during the positive pulse which are labelled A, B, B/C, and C. After the delay time τ_±, the target potential U_t rapidly rises and attains a value close to the applied voltage U₊ = 100 V. A short overshoot of U_t to around 115 V is observed during the first few μs, as seen in figure 3(b). We also see that the plasma potential very closely follows the target voltage in the beginning of the positive pulse with no detectable delay between the target voltage and plasma potential rise. The fact that the plasma potential closely follows the target potential in the beginning of the positive pulse applies to all the other discharge conditions studied. We denote this early transient phase A with a time duration of τ_A. The difference between the measured target and plasma potentials is not more than 6 V during phase A. This difference is likely an artefact of the measurement. Because of the high-density HiPIMS plasma, it is possible that the emissive probe was not emitting enough, i.e. not operating in the potential saturation region, and hence the measured plasma potential can be slightly underestimated. This measurement error would be of the order comparable to the electron temperature. Besides these features in the potential measurements, a large negative target current is observed in figure 3, attaining a peak value of I_tA = −20 A, during phase A.

Beyond phase A, the evolution of the plasma potential largely depends on the discharge conditions. The onset of phase B is marked by a sharp drop of the plasma potential, which attains a value close to 0 V. The time instant of the transition from phase A to phase B we denote as t_A→B = τ_± + τ_A, see figure 3(b). The plasma potential remains fairly constant around 0 V throughout the entire phase B. At the transition from phase A to phase B the target current rapidly decreases towards 0 A (at the end of phase B it attains −0.3 A). The high target potential of (∼170 V) in the beginning of phase B is likely related to a voltage induced by the sharp decrease of the target current and caused by the inductance L_i, see figure 1(a). Additional direct target potential measurements taking into account induced voltage on L_i + L_c (not shown) confirmed that this target potential peak is not an artefact, but a real voltage present on the target.

After phase B the plasma potential seems to be highly unstable and exhibits high-amplitude oscillations, in this case with a period of around 12 μs. This phase is labeled B/C, as it resembles several transition attempts from phase B to a following stable phase C, in which the plasma potential rises to a level of around 50 to 65 V, well below the applied target potential of 100 V. It should be noted that the waveforms shown, which have been averaged over 100 consecutive discharge pulses (discharge periods), correspond well to non-averaged single-shot discharge waveforms. This fact suggests that the observed oscillations are of non-stochastic origin. The plasma potential oscillations during phase B/C correlate with oscillations of the target current. These target current oscillations are likely inducing the observed small target potential oscillations as well, as seen in the recorded target potential waveform. The transition phase B/C is followed by phase C during which the plasma potential stabilizes at close to a constant potential of around 57 V and a negative current of roughly −1.5 A is flowing through the target with a decreasing magnitude. At the end of the positive pulse, the target is left floating and discharges rapidly to 0 V, closely followed by the plasma potential.

In the following subsections we will investigate some trends with the working gas pressure, the HiPIMS peak current, the HiPIMS pulse length, and the amplitude of the positive pulse. The interpretation of that quite extensive data becomes simplified by keeping in mind the purpose of this work: to find experimental conditions for ion acceleration in the plasma volume between the target and the substrate. An upper limit to such acceleration is the potential difference between the target and the substrate position which we denote as ΔU = (U_t − U_p,subst.). This quantity is given by the difference between the black and the red curves in the following graphs, which is what to keep track of from the aspect of ion acceleration. For the case study in figure 3, we can see that ΔU is below 6 V during phase A (only a marginal ion acceleration is possible) and close to the applied 100 V in phase B (possibly full acceleration). Then ΔU oscillates between 50 and 100 V in phase B/C, and finally approaches around 35 V towards the end of phase C. However, it is important to keep in mind that ΔU only gives an upper limit to the ion acceleration. The ions positions at the time when the reversed pulse is applied, and their times of crossing from the magnetic trap to the substrate, both come into play. We will return to these issues in section 4.5.

3.1.1. Variations with working gas pressure

Figure 4 shows the recorded plasma potential, target current and target potential waveforms for four different working gas pressures. The shape of the target current during the negative pulse (i.e. I_D,peak and τ_−,eff) was maintained almost unchanged. Due to the decrease of the formative time lag with increasing working gas pressure, slight adjustments of the negative pulse voltage and changes of the negative pulse length τ₋ were needed. The observed changes in plasma potential during the positive pulse can therefore be attributed predominantly to the different working gas pressures investigated. Due to the intrinsic properties of the bipolar HiPSTER power supply (discussed in section 4.5), the delay time τ_± was only slightly decreasing with the increase of the pressure; τ_± = 5.6 μs for 0.3 Pa and τ_± = 3.4 μs for 1.9 Pa.

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A clear trend in the length of the different phases during the positive pulse can be observed as the working gas pressure is altered. It follows from figure 4, that by increasing the pressure, phase A lengthens which leads to an increase of the phase A to phase B transition time t_A→B from 19 μs at 0.3 Pa to 37 μs at 1 Pa. At the same time, the transition from phase B to phases B/C and C occurs sooner for higher pressure, which effectively decreases τ_B from 90 μs at 0.3 Pa to 7 μs at 1 Pa. For working gas pressures >1 Pa, phase B disappears altogether and the time of transition from phase A to phase C, t_A→C, occurs later with increasing pressure (see the 1.6 Pa case shown in the supplementary information in figure S4). For 1.9 Pa, phase A lasts over the whole positive pulse duration.

The target current evolution during the positive pulse correlates with the plasma potential evolution as described previously, i.e. during phase B, the target current value is much smaller than during phases A or C. The magnitude of the target current during the positive pulse decreases with increasing working gas pressure. During phase A the target current attains a value of I_tA = −20 A for 0.3 Pa, while it reaches only I_tA = −3.6 A for 1.9 Pa.

3.1.2. Variations with HiPIMS target current

We also observed significant changes in the behavior of the plasma potential and target current during the positive pulse when changing I_D,peak or τ_−,eff of the negative HiPIMS. The results of these changes, keeping the pressure constant at 0.3 Pa, can be seen in figures 5 and 6, respectively. As can be seen from figure 5(a), the increase in I_D,peak leads to an increase of the negative target current during phase A, I_tA. A closer look at the data shows an increase of the negative target current during phases B/C and C and a slight increase during phase B. For I_D,peak of 8 A, the maximum current during phase A, I_tA, is around −0.5 A. On the other hand, for I_D,peak of 70 A, I_tA attains −70 A. Due to this large current drawn during phase A and limitations of the positive voltage power supply (dc driving unit), the applied positive voltage during most part of phase A is lower than the desired 100 V for high I_D,peak (for I_D,peak of 70 A the target voltage is around 45 V for most part of phase A). That is also reflected in lower plasma potential values during most part of phase A as shown in figure 5(b). The set target potential of 100 V was quickly recovered at the beginning of phase B. Due to the intrinsic properties of the bipolar HiPIMS power supply (discussed in section 4.5), the delay time τ_± was increasing with the increase of I_D,peak; τ_± = 9.5 μs for I_D,peak of 70 A and τ_± = 0.8 μs for I_D,peak of 8 A.

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From the plasma potential waveforms in figure 5(b) we see that increasing I_D,peak has qualitatively similar desirable effects as decreasing the working gas pressure, i.e. shortening τ_A and prolonging τ_B. For the highest I_D,peak of 70 A the A/B transition time t_A→B = 15 μs and τ_B = 120 μs. For I_D,peak of 30 A, t_A→B = 23 μs and τ_B = 57 μs. For the lowest peak current I_D,peak of 8 A, phases B and B/C disappear and phase A transits directly to phase C at t_A→C = 35 μs. For the I_D,peak = 8 A case, one can also notice, that the plasma potential decay time after the end of the positive pulse is longer, compared to the higher I_D,peak cases. That is caused by a slower discharging of the floating target due to a lower plasma density in the low peak current case.

The effect of changing width of the negative discharge current pulse τ_−,eff on the positive pulse dynamics was studied while maintaining a constant I_D,peak of around 48 A. As is shown in figure 6, the effect is qualitatively similar as decreasing I_D,peak. That means when shortening τ_−,eff the magnitude of the target current during the positive pulse is decreasing, τ_A is increasing, and τ_B is decreasing. For τ_−,eff of 5 μs, phase B does not seem to fully develop and the transition from phase A to C, t_A→C, occurs at around 50 μs.

3.1.3. Variations with the positive pulse voltage U₊

The measurements shown above have been performed with a constant positive voltage U₊ of 100 V. Here we study the influence of U₊ on the plasma potential evolution during the positive pulse, see figure 7. The measurements were performed at a pressure of 0.3 Pa, a I_D,peak of 48 A and a τ_−,eff of 55 μs. The delay time τ_± was decreasing with increasing U₊, which is further discussed in section 4.5. For U₊ of 150 V the delay time τ_± is 3.6 μs, however, for U₊ of 40 V the delay time τ_± is 16 μs.

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The transition from phase A to phase B occurs almost at the same time, which, seen up close, increases only slightly with higher U₊. For U₊ of 40 V, t_A→B = 19.7 μs, for U₊ of 150 V, t_A→B = 19.9 μs. We can clearly see phase B for all U₊ studied, yet its length, τ_B, is decreasing when increasing U₊. The observed changes in t_A→B and τ_B, we attribute mainly to the increase of U₊ as the effect of changing τ_± has an opposite effect on the changes of t_A→B and τ_B (see supplementary information S5). In phases B/C and C the plasma potential increases following the increase of U₊, however, a voltage difference between the target potential and the plasma potential, ΔU_C, is present. For U₊ of 150 V, ΔU_C = 20 V. For U₊ of 100 V, 80 V and 60 V, ΔU_C ≈ 40 V at the end of the positive pulse. For U₊ of 40 V, phase C cannot be easily distinguished from phase B as the plasma potential is close to 0 V till the end of the positive pulse.

No obvious trend of the target current change with U₊ during phase A can be seen. Only a slight rising trend of the target current (in absolute value) with increasing U₊ for U₊ ⩾ 60 V is seen in close-up (not shown) during phases B and C. During phases B/C and C for U₊ of 40 V only very small negative target current flows, around six times smaller than for the larger U₊.

In summary, the desired trends of shorter τ_A and longer τ_B, which gives a longer time window in the positive pulse for possible ion acceleration, are seen for lower working gas pressure (figure 4), higher HiPIMS pulse discharge current (figure 5), and longer HiPIMS pulse length (figure 6). The amplitude of the negative pulse on the other hand has only a small effect. This is a good sign. It opens the possibility to choose a desired accelerated ion energy, independent of optimizing discharge parameters for a long acceleration time window.

Mapping of the plasma potential was carried out to gain insight into the spatial variations inside and outside the magnetic trap. A reliable spatial mapping of the plasma potential in the case of the two-inch magnetron proved difficult to perform, since the presence of the emissive probe inside the magnetic trap significantly affected the discharge conditions—the target current during the negative pulse—and hence also the behavior during the positive pulse. The spatial scan of the plasma potential was therefore performed using a three-inch magnetron, where only a minor influence of the emissive probe was observed. As follows from the magnetic field lines map of the three-inch magnetron, the magnetic trap region is substantially larger than for the two-inch magnetron (see supplementary information, figure S2). Besides the emissive probe, another (large flat non-emitting) probe was used to simultaneously record the floating potential outside of the magnetic trap, in order to detect any possible influence of the emissive probe on the discharge. The discharge conditions (p = 0.35 Pa, I_D,peak = 238 A, τ_−,eff ≈ 130 μs) were selected to observe formation of phases B and C. Figure 8(a) shows a measurement when the emissive probe was positioned far away from the magnetic trap at $\left(z,r\right)=$ (120, 20) mm, i.e. a comparable configuration as investigated in the two-inch magnetron case. The characteristic times derived from figure 8(a) are: τ_± = 15 μs, τ_A = 7 μs, t_A→B = 22 μs, τ_B = 148 μs, t_B→C = 170 μs. We see a similar behavior of the plasma potential measured by the emissive probe and of the floating potential measured by the non-emitting probe. The small difference between the two probes during phase C, attaining 15 V at the end of the positive pulse, is likely due to the different location of the probes.

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Figure 8(b) shows the situation when the emissive probe was located inside the magnetic trap above the erosion track at position $\left(z,r\right)$ = (16, 20) mm and the non-emitting flat probe was positioned outside the trap. The emissive probe reveals that the plasma potential inside the magnetic trap is around 50 V during the first 35 μs of phase B, which together with the measurement from the non-emitting flat probe indicates a significant electric field present in the plasma. During phase C, the emissive probe measures a plasma potential close to the target voltage, whereas the non-emitting flat probe shows a lower voltage of around 50 V, leading to ΔU_C ≈ 50 V, which also indicates that a significant electric field is present in the plasma during phase C.

Several measurements were performed at different locations of the emissive probe outside and inside of the magnetic trap, from which the spatial profiles of the plasma potential at a given time were reconstructed, see figure 9 (full video can be found in the supplementary material). At the beginning of the positive pulse the plasma potential closely follows the target potential and reaches the applied 100 V throughout the entire mapped region (not shown). At t = 23 μs the plasma potential outside the magnetic trap drops to close to 0 V, corresponding to the beginning of phase B, see figure 9(a). The plasma potential is close to 0 V also inside the magnetic trap along the center axis of the magnetron. On the other hand, the plasma potential is elevated inside the magnetic trap with the highest values recorded above the target racetrack. The plasma potential remains stable at 0 V outside the magnetic trap during the whole phase B, which lasts until t = 170 μs. The potential structure inside the magnetic trap shows a much more dynamic behavior, as seen when comparing figures 9(a)–(c), recorded during phase B. First, an increase of the plasma potential at the axis of the magnetron is observed, see figure 9(b). This is followed by an overall decrease of the plasma potential to 0 V inside the magnetic trap at t ≈ 70 μs to 80 μs, as seen in figure 9(c). During the rest of phase B from around 80 μs to 170 μs some cases of a short spontaneous increase of the plasma potential are observed only at a few localized positions inside (and at the edge) of the magnetic trap (shown only in the video in the supplementary material).

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During phase C, when the plasma potential outside the magnetic trap is elevated to around 60 V, we clearly observe a stable potential structure resembling a double layer [36] located inside the magnetic trap and protruding slightly out of the magnetic trap along the magnetron axis, see figure 9(d). Above the target racetrack, the plasma potential is close to the full target potential of 100 V. This structure slightly evolves in time, spreading somewhat outside the magnetic trap and lasts until the end of the positive pulse at t = 400 μs.

To analyze the evolution of measured plasma potential at the substrate, we here describe a simple theory relating U_p,subst. to the electron saturation current at the target ${I}_{\mathrm{t}}^{\mathrm{e},\mathrm{s}\mathrm{a}\mathrm{t}}$ and ion saturation current at the grounded chamber wall ${I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$ in a highly simplified case, in which no magnetic field is present at the target. For this theoretical discussion, the grounded magnetron anode ring is considered a part of the grounded wall. We treat the target and the grounded chamber wall as ordinary electrodes immersed in the afterglow plasma during the positive pulse and separated from the bulk plasma by sheath regions. The potential of the target is fixed at U_t = U₊ and the potential of the grounded wall is 0 V. We consider a steady-state situation, where the sheaths at the target and wall have been established. We apply a basic theory of a sheath current in the absence of magnetic fields with no collisions and ionization for a case of a flat surface [38], which is well-known as the flat Langmuir probe theory. The target current I_t and wall current I_w can then be written as:

$$\begin{align}\hfill {I}_{\mathrm{t}}& ={I}_{\mathrm{t}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}-{I}_{\mathrm{t}}^{\mathrm{e},\mathrm{s}\mathrm{a}\mathrm{t}}\enspace \mathrm{exp}\left(\frac{{U}_{\mathrm{t}}-{U}_{\mathrm{p}}}{{k}_{\mathrm{B}}{T}_{\text{e}}/e}\right)\quad \mathrm{f}\mathrm{o}\mathrm{r}\enspace {U}_{\mathrm{p}} > {U}_{\mathrm{t}}\quad \mathrm{a}\mathrm{n}\mathrm{d}\quad {I}_{\mathrm{t}}=-{I}_{\mathrm{t}}^{\mathrm{e},\mathrm{s}\mathrm{a}\mathrm{t}}\quad \mathrm{f}\mathrm{o}\mathrm{r}\enspace {U}_{\mathrm{p}}< {U}_{\mathrm{t}}\hfill \end{align} \tag{ 1 }$$

$$\begin{align}{I}_{\mathrm{w}}& ={I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}-{I}_{\mathrm{w}}^{\mathrm{e},\mathrm{s}\mathrm{a}\mathrm{t}}\enspace \mathrm{exp}\left.\frac{-{U}_{\mathrm{p}}}{{k}_{\mathrm{B}}{T}_{\mathrm{e}}/e}\right.\quad \text{for}\enspace {U}_{\mathrm{p}} > 0\quad \text{and}\quad {I}_{\mathrm{w}}=-{I}_{\mathrm{w}}^{\mathrm{e},\mathrm{s}\mathrm{a}\mathrm{t}}\quad \text{for}\enspace {U}_{\mathrm{p}}< 0,\end{align} \tag{ 2 }$$

where ${I}_{\mathrm{t}}^{\mathrm{e},\mathrm{s}\mathrm{a}\mathrm{t}}$, ${I}_{\mathrm{t}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$ and ${I}_{\mathrm{w}}^{\mathrm{e},\mathrm{s}\mathrm{a}\mathrm{t}}$, ${I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$ are the electron and ion saturation currents at the target and grounded wall, respectively. For simplicity, we also assume that the electron temperature T_e is equal near the target and the wall. We neglect any voltage drops in the bulk plasma caused e.g. by ambipolar diffusion or plasma resistivity and therefore we use a single value of the plasma potential U_p.

The electron and ion saturation currents at the wall can be expressed according to these formulae:

$$\begin{equation}{I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}=0.6{A}_{\mathrm{w}}{\langle {n}_{e}\rangle }_{{A}_{\mathrm{w}}}e\sqrt{\frac{{k}_{\mathrm{B}}{T}_{\mathrm{e}}}{{m}_{\mathrm{i}}}}\end{equation} \tag{ 3 }$$

$$\begin{equation}{I}_{\mathrm{w}}^{\mathrm{e},\mathrm{s}\mathrm{a}\mathrm{t}}={A}_{\mathrm{w}}{\langle {n}_{\mathrm{e}}\rangle }_{{A}_{\mathrm{w}}}e\sqrt{\frac{{k}_{\mathrm{B}}{T}_{\mathrm{e}}}{2\pi {m}_{\mathrm{e}}}},\end{equation} \tag{ 4 }$$

where n_e is the plasma density (assuming plasma quasi-neutrality) and ${\langle {n}_{\mathrm{e}}\rangle }_{{A}_{\mathrm{w}}}$ symbolizes an average value of the plasma density along the wall surface with total area A_w. The ion saturation current is expressed according to the Bohm criterion assuming that the ion temperature is small compared to T_e, i.e. T_i ≪ T_e. The expressions for the target saturation currents, ${I}_{\mathrm{t}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$ and ${I}_{\mathrm{t}}^{\mathrm{e},\mathrm{s}\mathrm{a}\mathrm{t}}$, are analogous to equations (3) and (4), but ${A}_{\mathrm{t}}{\langle {n}_{\mathrm{e}}\rangle }_{{A}_{\mathrm{t}}}$ is used instead.

In a steady-state situation, no capacitive currents flow through the sheaths, the total charge inside the chamber is constant, and hence from the continuity equation it follows, that the target and wall currents must be equal (balanced):

$$\begin{equation}{I}_{\mathrm{t}}=-{I}_{\mathrm{w}}.\end{equation} \tag{ 5 }$$

The steady-state situation is reached by charging of the plasma and adjustment of the sheath potentials until an equilibrium value of the plasma potential U_p is established.

In figure 10 we illustrate how the target and wall currents depend on the plasma potential according to equations (1) and (2). Following equation (5), the steady-state plasma potential can be found at the intersection of the two curves. Two relevant scenarios can be distinguished in figure 10: (a) ${I}_{\mathrm{t}}^{\mathrm{e},\mathrm{s}\mathrm{a}\mathrm{t}}$ > ${I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$ and (b) ${I}_{\mathrm{t}}^{\mathrm{e},\mathrm{s}\mathrm{a}\mathrm{t}}$ < ${I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$. In scenario (a) ${I}_{\mathrm{t}}^{\mathrm{e},\mathrm{s}\mathrm{a}\mathrm{t}}$ > ${I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$, the steady-state plasma potential is slightly (to the maximum a few times T_e) higher than U_t. The potential drop is located in the sheath at the grounded wall. The target current I_t is limited and given by the ion saturation current at the wall, ${I}_{\mathrm{t}}=-{I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$. In scenario (b) ${I}_{\mathrm{t}}^{\mathrm{e},\mathrm{s}\mathrm{a}\mathrm{t}}$ < ${I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$, the plasma potential is only slightly higher than 0 V. The potential drop is mainly located in the target sheath and the target current I_t is limited and given by the electron saturation current at the target, ${I}_{\mathrm{t}}=-{I}_{\mathrm{t}}^{\mathrm{e},\mathrm{s}\mathrm{a}\mathrm{t}}$. Note, that the potential drop occurs at the electrode at which the total current is limited.

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In the presence of the magnetic field in front of the target, the electrons are magnetized (for typical values of B = 10 mT and T_e = 0.5 eV, the gyroradius of electrons is around 0.3 mm) and the description of the target sheath region and electron current at target I_t is highly complicated and differs from that defined by equation (1). Moreover, more complicated potential structures in the form of a double layer can exist in front of the target as shown in figure 9(d), and as discussed further in section 4.3, non-negligible electron impact ionization can be present. Because the electron current at the target is not well theoretically defined, we will from hereon not directly use the expression electron saturation current, ${I}_{\mathrm{t}}^{\mathrm{e},\mathrm{s}\mathrm{a}\mathrm{t}}$, but rather refer to this conceptualized quantity as an available target electron current. Nevertheless, we believe, that the same principle of balanced currents, with a modified formula for I_t, is to a large degree defining the bulk plasma potential during the positive pulse.

The experimental results presented in section 3.1 have shown a very interesting behavior of the target current. The target current (with our sign convention) during the positive pulse is clearly anti-correlated with the evolution of the plasma potential distinguishing the different phases A, B, B/C and C. Moreover, the magnitude of the target current during the positive pulse is strongly dependent on the external factors studied (p, I_D,peak, τ_−,eff). It is therefore of interest to understand the observed features of the target current during the positive pulse.

As the target is at positive potential during the positive pulse, it acts as an anode and is attracting electrons, while positive ions are attracted to the wall. Another contribution to the wall current involves secondary electron emission (typically contributing less than 10% [39]), which we neglect for the sake of simplicity. As discussed in section 4.1, when neglecting capacitive currents in the sheath regions, the target current I_t must be equal to the current to the grounded electrodes, I_g, i.e. −I_t = I_g = I_w + I_as, where we further distinguish current to the grounded chamber walls I_w and current to the grounded anode shield of the magnetron I_as. To provide an experimental verification of the current equality, the ion saturation current at the wall ${I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$ and anode shield current I_as has been measured (as explained in section 2.2) for the four different working gas pressures discussed in section 3.1.1. The discharge currents, and the target and plasma potentials, are shown in figure 4. In figure 11 the ion saturation current at the wall ${I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$, the sum ${I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}+{I}_{\mathrm{a}\mathrm{s}}$ and the target current −I_t are compared during bipolar HiPIMS discharges. More detailed current data from each wall-probe together with the anode shield current can be found in the supplementary information S6.

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For the case p = 0.3 Pa, figure 11 shows only minor differences between ${I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$ and ${I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}+{I}_{\mathrm{a}\mathrm{s}}$ and hence, in this case, I_as is insignificant during the positive pulse. The target current −I_t corresponds to the data shown earlier in figure 3. During phase A, the target current reaches a peak value of around −I_tA = 20 A. We observe a good agreement between ${I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$ and −I_t during phase A, during which the plasma potential U_p,subst. is close to the target potential U_t. Hence, the situation during phase A corresponds well to scenario (a) as described in section 4.1. It can be expected that the available electron current at the target (theoretical ${I}_{\mathrm{t}}^{\mathrm{e},\mathrm{s}\mathrm{a}\mathrm{t}}$) is higher than the ion saturation current at the wall ${I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$, but due to the requirement of balancing the currents, the target current is limited by ${I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$, i.e. ${I}_{\mathrm{t}}=-{I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$, during phase A. The rapid decrease of the target current during the phase A to B transition is accompanied with a decrease of U_p,subst. close to 0 V. At the same time, we do not observe any changes in ${I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$, which continuously follows a trend expected from unipolar HiPIMS discharge (see section 4.3). Since the target current is smaller than ${I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$ during phase B, the target current is limited by the available target electron current (theoretical ${I}_{\mathrm{t}}^{\mathrm{e},\mathrm{s}\mathrm{a}\mathrm{t}}$) during this phase. As we observe changes in I_t and not ${I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$, we can assume that the processes involved in the phase A to B transition cause a significant decrease of the available target electron current much below ${I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$. As the plasma potential is close to 0 V, this situation during phase B corresponds well to scenario (b), as described in section 4.1. During the oscillatory phase B/C the target current is oscillating roughly between 0 A and ${I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$. Following the theory on balanced currents in section 4.1, the oscillations of the plasma potential during the B/C phase are caused by rapid changes of the available target electron current, because the changes in ${I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$ are negligible. (The small peaks observed in ${I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$ are likely due to a capacitive current flowing through the wall-probes as the sheath at the particular probe is expanding and shrinking.) During phase C the target current is stabilized at ${I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$, i.e. ${I}_{\mathrm{t}}=-{I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$. However, the plasma potential does not reach U_t as predicted by the simple theory in scenario (b) but is stabilized at a value of U_p,subst. = U_t − ΔU_C. This fact is likely related to the presence of a double layer in front of the target during phase C, which is addressed in more detail in section 4.3.

When the working gas pressure p is increased (while maintaining constant I_D,peak and τ_−,eff) the magnitude of ${I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$ decreases. The decrease of ${I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$ when increasing p can be explained by a lower plasma density at the chamber walls [40] due to a slower plasma diffusion at higher p. For p of 0.3 Pa and 0.6 Pa we observe only one peak in the ${I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$ waveform occurring at around t = 35 μs. For the higher p of 1 Pa and 1.9 Pa, the ${I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$ waveform reveals additional smaller peak/peaks at later times during the positive pulse (and also after the positive pulse, not shown) of unknown origin. In [41], a similar behavior of the plasma density was attributed to an ion acoustic wave in the plasma, reflecting off the chamber walls. For all the four pressures, the magnitude of the current flowing through the anode shield I_as during the positive pulse is very small. I_as ≈ 2–3 A in the first 10 μs of the positive pulse, and I_as < 1 A during the remainder of the positive pulse (see the supplementary information S6). I_as increases slightly with increasing p. Comparison of ${I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}+{I}_{\mathrm{a}\mathrm{s}}$ data with the ${I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$ data in figure 11 shows, that the contribution of I_as during the positive pulse is small for the lower p of 0.3 Pa, 0.6 Pa and 1 Pa. On the other hand, for the 1.9 Pa case, I_as contributes roughly 50% to the total ground current I_g, since ${I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$ is small.

For all the four pressures investigated we observe a very good agreement between the target current −I_t and the wall and anode shield currents ${I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}+{I}_{\mathrm{a}\mathrm{s}}$ during phases A and C, as was already described for the 0.3 Pa case. These results further support the above described understanding of the dynamic behavior during the positive pulse. The increase of I_D,peak or τ_−,eff at constant pressure, see figures 5 and 6, respectively, leads to an increase of the negative target current during the positive pulse. That agrees with the fact that a denser plasma diffuses to the chamber walls for higher I_D,peak and longer τ_−,eff, as confirmed by additional wall-probe measurements (not shown). The results in figure 7 show, that the negative target current during the positive pulse is only negligibly increasing with increasing U₊. That agrees with the fact, that the ion current at the wall is saturated and only negligibly increases with the increase of the chamber wall sheath voltage during phases A and C.

The same wall-probe measurements to those shown in figure 11, were performed also for unipolar HiPIMS discharges. In figure 12 we show a comparison of the ion saturation current density ${J}_{1}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$ measured by probe No. 1 in unipolar and bipolar HiPIMS. The same trends as discussed here are observed also for all the other wall-probes (not shown). The same discharge parameters for both unipolar and bipolar discharge were used; p = 0.3 Pa, I_D,peak = 48 A, τ_−,eff = 55 μs, i.e. the same as in figure 3. During the negative pulse and the delay time, we do not observe any significant difference in ${J}_{1}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$ between the unipolar and bipolar discharge. During phases A and B, we observe only a small increase of ${J}_{1}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$ during the bipolar discharge (can be seen only with a linear scale, not shown). On the other hand, during phase B/C and C, the magnitude of ${J}_{1}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$ significantly increases and its slope of decay is smaller. Interestingly, during the off-time after the positive pulse, ${J}_{1}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$ measured in the bipolar discharge decays faster than that measured in the unipolar discharge.

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The higher ion saturation current at the wall during phases B/C and C in the bipolar discharge can be related to an increased plasma density, which is likely caused by additional electron impact ionization occurring during phase C (and to smaller degree during phase B/C). This increased ionization is likely related to the formation of the double layer in front of the target as shown in figure 9(d) and connected to a secondary reversed plasma discharge. The ignition of this reversed discharge is supported by the remaining afterglow plasma from the negative HiPIMS pulse. In this work and also in [19, 21] (and derived from mass-spectra of other works [15, 19–21, 23]), the potential drop ΔU_C was observed to be slightly larger than the ionization potential of the argon working gas, i.e. ΔU_C > 15.76 V, and usually is observed to be around ΔU_C ≈ 20 V (in this work ΔU_C ≈ 20–40 V). In [20] a sudden increase in light emission of neutral and ion species (Ar⁺ and Ti⁺) was observed right after a plasma potential drop of 20 V (i.e. during phase C). The light emission in [20] originated close to the target, however, not directly inside the magnetic trap. This is in agreement with our measurement of the double layer structure shown in figure 9(d), where the gradient of the plasma potential, i.e. electric field, is located rather at the edge of the magnetic trap. From our additional measurements (not presented), it is clear, that the plasma potential oscillations during the B/C phase are related to an attempt to ignite a reversed discharge (B → C$\left.\right)$ but does not succeed immediately and is thereby quenched (C → B$\left.\right)$. It is, however, not fully clear, why the reverse discharge exhibits such an unstable behavior during the B/C phase.

Based on our discussion on the measured ion saturation current density in unipolar and bipolar HiPIMS from figure 12, it is clear that the high target current measured during phase A at low pressures (0.3 Pa) is mainly due to a plasma generated during the negative HiPIMS pulse and any possible contribution to the target current from a secondary discharge is negligible.

In sections 4.1 and 4.2 we have suggested that the quasi-stationary plasma potential in the bulk plasma is established to balance the electron current at the target and ion current at the grounded electrodes. Hence, knowing both the available target electron current (theoretical ${I}_{\mathrm{t}}^{\mathrm{e},\mathrm{s}\mathrm{a}\mathrm{t}}$) and ${I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$ is the key for understanding and further tuning of bipolar HiPIMS. We have experimentally evaluated ${I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$ during the whole positive pulse. However, we could not easily obtain the value of the available target electron current (theoretical ${I}_{\mathrm{t}}^{\mathrm{e},\mathrm{s}\mathrm{a}\mathrm{t}}$). It can only be measured directly during phase B and is given as the target current I_t. It is, however, very likely that the available target electron current is larger than ${I}_{\mathrm{w}}^{\mathrm{i},\mathrm{s}\mathrm{a}\mathrm{t}}$ during phases A and C. Different possible paths for the electrons to reach the target should be distinguished (outer part of the target not covered by magnetic trap, current through the magnetic trap, current through the null point), which is, however, out of scope of this paper.

The transition from phase A to phase B is related to the rapid decrease of the available target electron current. The physical explanation of this phenomenon is, however, not clear. During the transition from phase B to phase C the available target electron current increases. We speculate, that this phenomenon could be coupled with the working gas dynamics in front of the target and thereby related to gas rarefaction and gas refill. Significant gas rarefaction is expected at the high HiPIMS peak discharge currents at the end of the negative pulse in the present experiments, typically I_D,peak = 48 A (corresponding to a peak discharge current density of J_D,peak ≈ 2.5 A cm⁻²). For example, Huo et al [42] report a maximum decrease of the argon density in the IR of Δn_Ar/Δn_Ar,0 ≈ 50% at J_D,peak ≈ 0.6 A cm⁻² and the rate of gas rarefaction was the fastest at I_D,peak. Kozák and Lazar [43] as well as Huo et al [42] later found that the depletion of neutral argon increases with increasing peak current with values of Δn_Ar/Δn_Ar,0 of up to 70%. The reduction in argon density is not compensated by sputtered neutrals, since the sputtered neutral density is generally more than an order of magnitude smaller than the working gas density [44]. A consequence of the lower density of neutral particles in the IR at the early stage of the positive pulse is likely the difficulty to ignite a reversed discharge, which is in line with our discussion at the end of section 4.3. The transition to phase C, however, could be associated with a working gas refill which increases the probability for electron–argon ionization collisions in the IR. In [42] the characteristic time associated with working gas refill is roughly around 100 μs, which is in reasonable agreement with the here-observed times of transition from phase B to C, t_B→C. For higher I_D,peak and stronger gas rarefaction, longer refilling times can be expected, which could be the reason for the increasing t_B→C values observed in figure 5(b). In order to use the same explanation also for the data shown in figure 6(b), longer τ_−,eff would need to have a similar effect on the gas rarefaction as increasing I_D,peak, which is, however, less obvious. Further studies are likely needed to provide more information on the electron density and ion and neutral gas dynamics close to the target. Still, the ionization in the IR/magnetic trap during phase C increases the electron density at the target and hence likely contributes to the increase of the available target electron current above the ion saturation current at the walls.

As discussed in the beginning of section 4, one can expect ion acceleration in the magnetic trap region during phases B and C. Furthermore, only those ions, which, at the beginning of these phases, are located at a position of high plasma potential can be accelerated. As a consequence, ions which leave the magnetic trap before time t_A→B (see figure 3(b)) will not be significantly accelerated, as there is little to no electric field in the DR outside the magnetic trap.

To quantify these timing constraints, we here make rough estimates of the characteristic time for a majority of the ions to leave the magnetic trap. It follows from energy and time-resolved mass spectrometry measurements in HiPIMS discharges, that the kinetic energy of most metal ions arriving at the substrate (peak in the energy distribution function) is typically in the range 2–20 eV [5]. In the case of ⁶³Cu⁺ ions, this energy range results in speeds of 0.2–0.8 cm μs⁻¹. This range of speeds corresponds well with the typical metal ion time-of-flight data from target to substrate [45]. The size of the magnetic trap region (in the axial direction towards the substrate) can be approximated by the distance of the magnetic null point from target. As such, it depends on the magnetron size and the degree of unbalance with typical values around a few centimeters for small circular magnetrons, see for example [46]. In the present case we find that the null point is situated at 1.4 cm and 4.0 cm from the target for the two-inch and three-inch magnetrons, respectively. The characteristic times for the metal ions to leave the magnetic trap is then around 2–7 μs for the two-inch magnetron and 5–20 μs for the three-inch magnetron. These times are likely a lower estimate when looking at the working gas ions, such as ⁴⁰Ar⁺, since recorded energy distributions of these ions generally exhibit a peak at around 2 eV without an energetic tail [5].

Let us now compare the characteristic times for ions escaping the magnetic trap with the time required to achieve ion acceleration during the positive pulse. The shortest phase A to B transition time achieved with the two-inch magnetron is t_A→B = 15 μs for the discharge in figure 5 at the highest peak current investigated (I_D,peak = 70 A, τ_−,eff = 55 μs, p = 0.3 Pa). This is at least a factor 2 longer compared the ion escape time found above. We therefore expect only a limited fraction of Cu⁺ ions to be accelerated using the experimental conditions of the two-inch magnetron in this work. In the three-inch magnetron discharge in figure 8, t_A→B = 22 μs which means also only limited fraction of Cu⁺ ions to be accelerated. Moreover, because of the long negative pulse length, τ_−,eff, it is expected that a significant fraction of the ions (both Cu⁺ and Ar⁺) will leave the magnetic trap even during the negative pulse. This latter effect was studied by Viloan et al [22] for Ti/Ar bipolar HiPIMS discharges in a wide range of negative and positive pulse lengths. They found that the fraction of ions (Ti⁺ and Ar⁺) accelerated in the grounded substrate sheath (8.5 cm from a target) decreased from ∼100% to ∼10% when increasing the negative pulse length τ₋ from 20 μs to 200 μs. As the acceleration region during phase B in the present work is even closer to the target, given by the magnetic trap size, the needed τ₋ can be expected to be proportionally smaller.

Based on these considerations of timing the ion acceleration we find that it would be beneficial to achieve a lower t_A→B = τ_A + τ_± to accelerate a larger fraction of the ions during the positive pulse. Ideally this means eliminating phase A entirely, i.e. τ_A = 0, and at the same time maintain a low τ_±. During our experiments we aimed at achieving the lowest τ_± possible given the experimental setup. However, a finite τ_± might sometimes be desirable. The reason is that energetic ions are produced already during the negative HiPIMS pulse [47, 48], and that too energetic ions can be detrimental to the growing film due to the risk of high intrinsic film stress. A finite τ_± can allow these energetic ions to escape from the magnetic trap without such extra acceleration. As mentioned in the result section, the observed delay time τ_± varied depending on the discharge conditions and is seen to depend mainly on the HiPIMS peak current I_D,peak (figure 5) and positive pulse voltage U₊ (figure 7). This can be explained by the inductance L_i + L_c ($\approx$10 μH) in the path from the output of the transistors of the bipolar HiPSTER unit to the target, as depicted in figure 1(a). Although the transistors themselves are open during the delay time and the output voltage is clamped at the positive voltage U₊, a voltage drop occurs at these inductive elements due to the fast decay of the target current, see figure 3(b), causing the target potential to be close to 0 V. At larger positive voltage U₊, the energy stored in L_i + L_c can be dissipated faster, leading to a faster target current decay and smaller delay time τ_±, see figure 7. Hence lower τ_± than those presented should be possible to achieve by lowering L_i + L_c.