Influence of the magnetic field on the extension of the ionization region in high power impulse magnetron sputtering discharges

We here suggest an indirect measurement to determine the size of the IR. For this, we assume the emission intensity of the Ar I line at λ = 763 nm to be a good measure for the argon ionization rate. The idea is based on the fact that the emission intensity at 763 nm is proportional to the population rate of the upper 4p[3/2]₂ level (at 13.17 eV), with the correspondent lower one being the metastable 4s[3/2]₂ level (at 11.54 eV). If the level populates proportionally to the ionization rate, the emission at 763 nm can be taken as a measure for the ionization rate.

First, let us discuss the population pathway of the 4p[3/2]₂ level. For this, there are two principal possibilities, the direct population from ground state and the step-wise population via one of the 4s levels. To quantify the estimates, we take an argon model by Bultel et al [31] who lists cross sections from each of the four 4s levels and from the ground state to the combined (4p[3/2]$_{1,2}$, 4p[5/2]$_{2,3}$) level, which contains the 4p[3/2]₂ state. Considering the combined level is justified here as strong mixing can be expected within the 4p manifold. Figure 1 shows the rate coefficients for these processes. Considering that the density of the Ar 4s levels is typically at least two orders of magnitude below the ground state density in HiPIMS discharges [32, 33], for an electron temperature above 2 eV, direct population from the ground state is the dominant population mechanism. This finding agrees with the analysis by Stancu et al [34] (see appendix D in Stancu et al [34]).

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Next, we discuss the proportionality between the 4p[3/2]₂ population and the electron impact ionization rate coefficient from the ground state. Figure 2 shows the ratio of the rate coefficients for electron impact excitation to electron impact ionization. One can see that for electron temperatures at 3 eV the rates are equal, and above 4 eV the ratio is rather flat. For HiPIMS discharges, electron temperatures above 4 eV have indeed been observed in modeling [32, 33, 35], and this is expected to represent the electron temperature next to the target surface. Experimentally, however, usually lower electron temperatures are determined, which is typically explained by the fact that they are measured at some distance from the target surface for various target materials [36–41]. Dubois et al [12] applied Thomson scattering measurements and determined the electron temperature to be 1.3 eV at 5 mm from a titanium target surface. This is lower than what has been observed by Langmuir probe measurements at 40 mm and 100 mm away from a titanium target, 3.5 eV [40] and 2 eV [41], respectively. In the most recent study by Held et al [42] the Langmuir probe is placed 8 mm above the target surface, parallel to the target surface, and the electron temperature is determined to be roughly 4 eV and agree very well with IRM calculations. The IRM calculations consistently give an electron temperature of 4 eV and higher for a discharge with a titanium target [34, 43]. So it is safe to assume that the electron temperature is around or above 4 eV during the pulse within the IR. We therefore conclude that the emission intensity from the 4p[3/2]₂ level to the 4s[3/2]₂ level is a good indicator for the presence of ionization, and therefore a good measure of the IR volume.

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The experiments were carried out in a custom-built cylindrical vacuum chamber (height 50 cm and diameter 45 cm) made of stainless steel, with a VTech$^{\mathrm{TM}}$ (Gencoa Ltd, United Kingdom) magnetron assembly with a 4 inch (100 mm) diameter titanium target, installed. A base pressure of $4 \times 10^{-6}$ Pa was achieved using a turbo molecular pump backed by a roughing pump. Argon was used as the working gas and maintained at 1 Pa. The discharge was operated in HiPIMS mode. The pulses were 100 µs long, delivered by a pulsing unit (HiPSTER 1, Ionautics, Sweden), which in turn was fed by a regular DC power supply (1.5 kV and 2 A, Technix, France). Micrometer screws placed at the back of the magnetron assembly allow for accurate displacement of each magnet without breaking the vacuum. Here, optical emission spectrometery is applied to determine the shape and size of the IR for the same magnet configurations as explored experimentally by Hajihoseini et al [44]. Thus, seven magnet configurations have been systematically studied by varying the position of the center (C) and edge (E) magnets, namely, C0E0, C0E5, C0E10, C5E0, C5E5, C10E0, and C10E10. The numbers indicate the displacement of each of the magnets from the back of the target, in millimeters. For example, C10E0 means that the center (C) magnet is shifted back 10 mm away from the target backplate. The shifting of the magnets is shown schematically in figure 3(a). The edge (E) magnet has the north pole facing the target back side, while the C magnet is reversed. Except for the C10E10, the peak discharge current was maintained at about 40 A ($J_{\mathrm{D,peak}} \approx 0.5$ A cm⁻²) by adjusting the discharge voltage figure 4. This is what we have referred to as the fixed peak current operating mode [44, 45]. The repetition frequency was adjusted as well to keep the averaged discharge power $\langle P_{\mathrm{D}} \rangle$ constant, when the magnetic configuration is varied.

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Figure 3(a) also shows the arrangement of the optical system with respect to the cathode target and the IR. A camera (VEO 710L, Phantom) was radially positioned 70 cm away from the axis normal to the target surface. The recorded light emission came from half of the torus-shaped IR, the half on the right side of the axis (figure 3(a)). The light then passed through a window (viewport). A photo lens (Nikkor 50 mm 1:1.2, Nikon, Japan) and an interferential bandpass filter centered on the 763 nm line (10 nm bandwidth) completed the arrangement. The camera was triggered with the onset of the pulse voltage and two recordings per pulse were captured with 45 µs and 5 µs of acquisition and readout time, respectively. The second image of each pulse was used for the analysis presented in the current study, recorded between 50 and 95 µs from the pulse initiation. This time range included the part with the high discharge currents that are characteristic for a HiPIMS discharge and therefore most interesting. The raw images had a size of $399 \times 356$ pixels and a resolution of 0.15 mm pixel⁻¹.

For each magnetic field configuration, the camera recorded 13 images. The images displayed in this work are single frames, but the quantitative results presented are average values over all the sampled images, and the associated errors are the corresponding standard deviation. An example of a raw image is shown in figure 3(b). Each image was processed by inverse Abel transformation or Abel inversion [46], which yielded localized information on the light emission above the guard ring of the magnetron. By Abel inversion line-of-sight intensity measurements are transformed, to give information on the internal radial distribution of the emission from the plasma. The assumption of azimuthal symmetry around the symmetry axis holds since time variation due to spoke motion occur on a much shorter time scale (typically hundreds of ns).

It can be clearly seen in figure 6 that the shape of the magnetic field lines matches the contours of the IR. This observation can be explained in terms of electron confinement. Due to a high electron conductivity along the magnetic field lines, the electron properties, notably the density and temperature, are close to being constant along a magnetic field line. Conversely, the electron conductivity across the magnetic field lines is limited [48–50], so that electron properties can change drastically in the direction orthogonal to the magnetic field lines. It is therefore understandable that the shape of the IR closely follows the magnetic field lines.

Electrons in a magnetic field gyrate around the field lines with a gyro radius ($r_{\mathrm{ce}}$) that is inversely proportional to the magnetic field strength $B_{\mathrm{r}}$, i.e. $r_{\mathrm{ce}} \propto 1/B_{\mathrm{r}}$ [51]. The classical (collisional) cross-B transport speed is proportional to $r_{\mathrm{ce}}$ [4, 48]. The electron mobility across the magnetic field lines therefore changes with the magnetic field strength [4, 48]. We see in figure 8(a) that in the range $B_{\mathrm{r}} \lt 18$ mT, the IR axial extension ($z^{^{\prime}}_{\mathrm{IR}}$) is close to being inversely proportional to $B_{\mathrm{r}}$, i.e. proportional to $r_{\mathrm{ce}}$. Therefore, the shrinking size of the IR should be due to a reduction in electron mobility from a stronger $B_{\mathrm{r}}$.

Figure 8(b) shows that the width of the IR exhibits the same behavior as the axial extension. It has been suggested and confirmed experimentally in a dc magnetron sputtering discharge that the width of the racetrack region $w^{^{\prime}}_{\mathrm{rt}}$ scales as $w_{\mathrm{rt}} \propto r_{\mathrm{ce}}^{1/2 } \propto B_{\mathrm{r}}^{-1/2 }$ [52], which supports our hypothesis that the shrinking size of the IR is related to the electron mobility.

For a decreasing $B_{\mathrm{r}}$, a higher voltage is necessary to sustain the discharge, as can be seen in figure 4(b). Note that the highest discharge voltage was needed for our weakest magnetic field, the C10E10 configuration, as seen in figure 4(a), but the peak discharge current could not reach 40 A. In the extreme case of no magnetic field, i.e. in the case of dc diode sputtering, electrons are not confined at all. What is found with lower $B_{\mathrm{r}}$, in figure 6, is therefore the beginning of the 'loss of electron confinement'. The IR, its shape and size is therefore intrinsically connected to the magnetic trap.

For a magnetic field strength $B_{\mathrm{r}}$ in the range 18 to 22 mT, the IR axial extension $z^{^{\prime}}_{\mathrm{IR}}$ stays almost constant as the magnetic field strength is increased. The plasma volume thus shrinks with increased magnetic field strength until it reaches a certain limit. The IR does not shrink below this limit when the magnetic field is further increased. This could indicate that the electron confinement is not further improved by strengthening the magnetic field B. The pulse power barely changes for those conditions, as can be seen in table 1, meaning that the electron density and temperature might be roughly the same.

For the strongest magnetic field, $B_{\mathrm{r}} = 23.8$ mT, corresponding to the magnet configuration C0E0, the IR axial extension $z^{^{\prime}}_{\mathrm{IR}}$ increases and thereby deviates from the reported trend, as seen in figure 8(a). Note also its large errors bar. The nature of the discharge might here change due to enhanced instabilities induced by electric and magnetic cross field ($\mathbf{E} \times \mathbf{B}$) drifts or spokes [12, 13, 53]. Note that on shorter time scales than those used to record the images, one can observe plasma instabilities, so called spokes. They can be observed with gated cameras looking laterally and axially onto the discharge [50, 53, 54] and through simulations [55, 56]. Such instabilities further complicate the description of the IR. It is important to point out that the IR width $w^{^{\prime}}_{\mathrm{rt}}$ and cross-sectional area ${\cal A}^{^{\prime}}_{\mathrm{IR}}$ do not show such a deviation from saturation (figures 8(b) and (c)). Regarding the symmetry of the IR, Kanitz et al [13] observed something similar to the one presented in this study. They observed a distribution of metastable argon atoms Ar$^{\mathrm{m}}$, with the difference that they see it beyond the $z_{\mathrm{null}}$, indicating their diffusion [57].

We can think of the electrons, to a first approximation, as being trapped along the magnetic field lines, bouncing between the magnetic mirrors at both ends of the magnetic field lines, as these approach the target. This means that we can assume the same electron energy distribution (EEDF) along each flux tube. This is why we observe an agreement between the optical emission and the magnetic field line structure as shown in figure 6. We now consider a cloud of electrons within such a flux tube. The question is what the temporal evolution of the EEDF is during their drift away from the target. For simplicity we consider an initially Maxwellian EEDF. For this electron population the electron temperature is determined by the opposing processes of Ohmic heating and energy loss by collisions. The heating rate is proportional to the electric field E, and is therefore stronger close to the target surface, and drops with the distance away from the target surface. The cooling rate is proportional to the working gas density and remains more constant with increasing distance from the target. This means that at a certain distance the cooling mechanism takes over. If the population remains Maxwellian the drifting electron cloud would be characterized by an electron temperature which gradually decreases as it moves away from the target, which has indeed been observed experimentally, as discussed above [12].

Regarding the variation of electron density and electron temperature with distance from the target surface, Dubois et al [12] investigated the drop in electron density and electron temperature above the racetrack using Thomson scattering measurements. The spatial variation in electron density was found to show a bi-exponential dependence while the variation in electron temperature could be described by a simple exponential function. For a pulse length of 70 µs, an argon working gas pressure of 1 Pa, and a peak discharge current of 40 A, for the C5E5 magnetic configuration, they determined the electron density 3 mm above the guard ring to be $1.81 \times 10^{19}$ m⁻³ and to fall to half of this value at roughly 12 mm above the guard ring and drop by about 70% at roughly 22 mm above the guard ring. This is roughly of the same distance as what we determine to be the axial extension of the IR using OES. They also found the electron temperature to drop, from 1.3 eV 3 mm above the guard ring, to about 0.7 eV 40 mm above the guard ring. However, in similar conditions, other investigations have determined higher electron temperatures, ${\sim}4$ eV (8 mm from the target surface) [42], 3.5 eV (40 mm from the target surface) [40] and 2 eV (100 mm from target surface) [41], thus higher than measured by Thomson scattering [12]. Also, just above the sheath, facing the target, particle-in-cell Monte Carlo collision simulation results show electron temperature of ∼7 eV [55], where most of the ionization is suggested to occur [42, 58]. Then, it is expected that the electron temperature drops across the IR. The effect of a drop in electron temperature with increasing distance from the cathode, by collisions with the atoms, would be that the IR appears larger in images recording the emission from the 4p level, than it actually is. In other words, if the electron temperature drops below 3 eV, the electron impact excitation rate coefficient will become larger than the electron impact ionization rate coefficient, and the excitation and ionization cannot be considered proportional any more, as can be seen in figure 2. Consequently, the IR will be smaller than presented in figure 6. Nevertheless, in such case, the trends seen in figure 8 will remain the same. Notice all iso-contours (blue lines) seen in figure 6 follow the same trend. Further out in the IR, where electron temperatures are lower compared to the target vicinity, the ionization rate can therefore be expected to be low. Assuming an electron temperature of 1 eV at the here-determined border of the IR, we expect an excitation rate that is a factor of 10 to 20 higher per ionization rate, compared to the target vicinitiy with electron temperatures ${\gt}4$ eV. Combining this with the 50% cut-off in emission intensity at this border, we note that the ionization rate at the here-determined border will be factor of 20–40 lower compared to the near-target vicinity.

The magnet configurations explored here were the same as in the experimental work of Hajihoseini et al [44], where the ionized flux fraction and deposition rate was reported for the various magnet configurations, while keeping the average power constant, by either maintaining fixed discharge voltage or fixed peak discharge current. The discharges explored by Hajihoseini et al have been studied extensively, including exploring the influence of magnetic field on the discharge current, the electron density and the ionization probability [35], to determine the transport parameters of the neutrals and ions of the sputtered species [59], as well as demonstrate how to minimize variations of the flux parameters, the deposition rate and the ionized flux fraction, as the target erodes [45]. The size of the IR is an input parameter when modeling the HiPIMS discharge, using models such as the IR model [26, 27]. When modeling the HiPIMS discharge, the IR has been assumed to extend up to several tens of millimeters from the cathode target [25, 60]. In the IRM, to calculate the plasma chemistry in a volume given by a rectangular torus with radii r₁ and r₂, which set the width of the racetrack $w_{\mathrm{rt}} = r_2 - r_1$. In the IRM study of the discharges explored using the same magnetron assembly and cathode, the IR was assumed to be 28 mm wide and extend 25 mm away from the target surface [27]. The results presented in figure 8 show the axial extension $z^{^{\prime}}_{\mathrm{IR}}$ to be in the range 7–14 mm (i.e. 10–17 mm from the target surface) and the width of the IR at the guard ring $w^{^{\prime}}_{\mathrm{rt}}$ to be 23–29 mm. The volume of the IR is ${\cal V}_{\mathrm{IR}} = 2\pi {\cal A}^{^{\prime}}_{\mathrm{IR}} R_{\mathrm{IR}}$, with $R_{\mathrm{IR}} \approx$ 25 mm [44] as the radial position of the racetrack from the center of the target, is here determined to be 2.1–$4.2 \times 10^{-5}$ m³, compared to $1.0 \times10^{-4}$ m³ used in the IRM calculations [27]. We note that the measured volume from this work matches well with the assumed volume of the IR. However, for more precise global models of the HiPIMS discharge, the shape of the IR and the gradient in electron temperature and density are likely parameters to be optimized in future developments.