Temporal evolution of ion energy distribution functions and ion charge states of Cr and Cr-Al pulsed arc plasmas

Composite (alloy) films have been widely used for many industrial applications. Compared to pure metal coatings, alloy coatings can deliver a lot of advanced features. For example, Cu-W or Cu-Mo films show good thermal stability.¹ Besides metallic and intermetallic coatings, coatings of ternary nitrides are even more important for applications. It is well known that ternary nitrides such as (Al, Cr)N have been employed as modern protective coatings for cutting tools.² The coatings processes often make use of composite cathodes such as Al-Cr cathodes in a reactive deposition process.

The cathode physics using composite cathodes, however, has not been clarified well and there is a need for deeper investigations. In a work by Savkin et al.,³ it was shown that a charge state distribution (CSD) depends on whether the ions originate from a pure elemental cathode or from a composite cathode due to the difference of electron temperature in the corresponding cathode spot plasma.³ In the case of filtered arc plasma from a Ti-Al composite cathode, as reported by Bilek et al., it was shown that the charge state distribution of Ti is affected by the Al content in the cathode composition while Al is insensitive to the atomic fraction of Ti.⁴ The sensitiveness of Cr and insensitiveness of Al toward addition of a second element on CSDs were also reported with Cr-Al alloy cathodes by Franz et al.⁵ In the Ti-Hf system, in contrast, charge state distributions of Ti and Hf were found to be unaltered by the presence of the other element.⁶ 

The composition of a cathode material affects not only ion charge state distributions but also the ion energy distribution functions (IEDFs). Recently, measuring dc arc plasmas, Zhirkov et al. argued that ion acceleration is primarily based on the gas-dynamic mechanism.⁷ In a follow-up work, they proposed a “velocity rule,” based on experimental data, which states that the most likely velocities of ions of different mass are equal.⁸ They also found that IEDFs of Ti ions and Al ions from composite cathodes do not have high energy tails, which were observed on pure element cathodes, rather, the IEDFs assumed a more symmetrical shape.⁸ Clearly, the addition of an extra element into a pure metal cathode affects the plasma characteristics in terms of the plasma-chemical balance as determined by the generation and transport of ions in plasmas. Plasma characteristics such as CSDs and IEDFs are reported to be quite different for multicomponent cathodes such as Ti-Al (Refs. 4 and 8) or Cr-Al (Ref. 5) compared to characteristics when using single element cathodes. It is safe to say that research in this field is incomplete in terms of data and underlying physics.

In order to reveal the physics in the evolution of plasma in low pressure cathodic arc discharges, time-resolved measurements with probe analysis,⁹ time-of-flight (TOF) mass analysis,¹⁰ quadrupole mass analysis,¹¹ electrostatic energy analysis,¹¹ and optical spectroscopy¹² have been carried out. On cathodic arc discharges, the average velocities obtained by TOF analysis and the mean charge state of ions flying from cathodes show a characteristic decay with a time constant of a few hundred microseconds.^10,13 In all cases, the peaks of intensity of higher charge states occur early in the pulse and they are followed by lower charge states and neutrals; the latter was confirmed with optical spectroscopy.¹² In our previous work measuring time-resolved IEDFs of pulsed Cu arc plasma, it was found that the ion signal intensity of Cu¹⁺ ions slightly increases for times after 100 μs after ignition.¹⁴ The phenomenon was more pronounced at a longer distance of 0.38 m than of 0.18 m from the cathode.¹⁴ We concluded that charge exchange reactions are more likely to take place after 100 μs because more neutral atoms appear in the chamber space, presumably the atoms coming from the wall as not all ions stick when arriving at a wall but bounce back as neutrals. Additionally, until about 50 μs after ignition, when less charge exchange reaction occur due to the lack of neutrals, the kinetic energies of ions were found to be proportional to the ions' charge states. This suggests that acceleration of ions at cathode spot is at least in part electrostatic, i.e., driven by a potential hump mechanism.

Improving the temporal resolution of ion energy and charge state measurements enables deeper insights in the physics of cathodic arc plasma and the particle collisions and related plasma-chemical reactions as the plasma expands from cathodes spots. In our related work¹⁴ we introduced the concept for pure copper plasma, whereas here we apply this approach to plasma from a composite cathode.

In this paper, to clarify the influence of an additional material to a pure elemental cathode on kinetic energies of ions and CSDs, ion energy-time distribution functions of Cr arc plasmas and mixed Cr-Al arc plasmas have been studied.

The general experimental setup in this experiment is similar to that of our previous work¹⁴ and shown in Fig. 1.

An arc plasmas source of the miniature gun type¹⁵ was used with either a Cr or a Cr_0.75Al_0.25 alloy rod as the cathode, with the rod front face as the area where cathode spots can burn. The cathode had a diameter of 6.35 mm and a length of about 20 mm. The arc plasma gun was set in front of the entrance orifice of a mass and energy analyzer (EQP300 by Hiden Analytical Ltd.), which was differentially pumped down to the low 10⁻⁶Pa range. No working gas was added during the measurements, i.e., the cathodic arc was operated as a vacuum arc, with the operational pressure close to the base pressure. Pulsed arc discharges with a pulse duration of approximately 600 μs were generated with a repetition rate of 3 pulses/s by using a system comprised of a pulse forming network (PFN)¹⁶ with nine LC-sections and one RC-section. Charging was done by a dc power supply (KL Series by Glassman High Voltage Inc., maximum 1 kV and 3 A). A silicon controlled rectifier switch unit and two pulse delay generators (TGP110 by TENMA and MODEL-214 A by Hewlett Packard) were used to start and terminate the arc pulse as indicated in Fig. 1. The arc discharge current was approximately 190–200 A with a charging voltage of 380 V. Voltage of the cathode (with respect to the grounded anode) and discharge current were measured using a wide-band oscilloscope (TDS5054B-NV by Tektronix) via 1:100 voltage probe (P5100 by Tektronix) and current transformer (Model 101X by Pearson Inc.), respectively.

In order to determine kinetic energy of ions in the plasma region, plasma potential was measured by an emissive probe. Such measurements allow us to account for ion acceleration in the sheath at the entrance orifice of the ion energy analyzer. The principle of the measurement is essentially the same as in our previous work on copper plasmas.¹⁴ A tungsten filament with diameter of 0.075 mm connected to a DC power supply (72–7295 by TENMA, maximum 40 and 5 A) via a switching unit was positioned at a distance of 21 mm from the cathode surface. Since the heating currents of 1.5 and 1.8 A did not deliver any difference in potential measurements, we verified that we have sufficient electron emission; the heating current was set to 1.7 A. The filament was isolated from the heating circuit while the arc pulse is on: this was arranged using a MOSFET switching unit providing an isolation resistivity of more than 2 MΩ, which is higher than the impedance of the oscilloscope recording the potential. The potential of the probe was measured on the oscilloscope directly.

Principle and practical method of obtaining IETDFs with high time resolution from the ion detection signal taken directly from the mass spectrometer interface unit of an EQP300 energy analyzer and mass spectrometer was fully described in our previous paper.¹⁴ Therefore, here we describe only the concept and summarize the essence of the measurement principle. The ion detection signal for a given reference voltage $V reference$ and mass-per-charge ratio $m / Q$ was acquired from the control unit via its auxiliary output port and averaged through 50 individual pulses on an oscilloscope. The averaged waveform as a function of time $V ¯ ( t )$ was transformed into a signal intensity $I ( t )$⁠, which is equivalent to a count rate, defined as

where $V off$ is the potential measured in the absence of plasma (about 5 V). $V reference$ was varied from 6/Q V with an increment of 6/Q V per step until no significant signal was obtained, where Q is the charge state of measured ion species. Since $I ( t )$ can be measured with variation of $V reference$ and mass filter (⁠ $m / Q$⁠) settings, $I ( t )$ is a function of not only time t, but also of kinetic energy of an ion in the plasma region, $E 0$⁠, and m and Q, thus we have $I ( t , E 0 , m , Q )$⁠. Corrected IETDFs were obtained by multiplying with Qe and including a correction to account for the potential difference in the sheath between plasma and the instrument, as follows:

where $V plasma$ is the plasma potential. The most abundant stable isotopes of Cr and Al were used, namely, ⁵²Cr and ²⁷Al. The ratio of m/Q was set to 52.00 (Cr¹⁺), 26.00 (Cr²⁺), 17.34 (Cr³⁺), 13.00 (Cr⁴⁺), 27.00 (Al¹⁺), 13.50 (Al²⁺), and 9.00 (Al³⁺). The electron multiplier voltage $V M$ of the ion detector was set to 1.6 kV. $V M$ was set to 1.9 kV occasionally to measure the low-signal ion species such as Cr¹⁺. In any case, $V M$ is mentioned in the caption of each figure.

The signal of ²⁷Al¹⁺ (m/Q = 27.00) contains that of ⁵⁴Cr²⁺ (m/Q = 27.00). The abundance ratio α of ⁵⁴Cr to ⁵²Cr is approximately 3%. Therefore, the intensity of Al¹⁺ was corrected by assuming that the signal intensity of ²⁷Al¹⁺ contains that of ⁵⁴Cr²⁺, the intensity of which should contain 3% of ⁵²Cr²⁺, as follows:

Similarly, ²⁷Al²⁺ (m/Q = 13.5) is slightly affected by ⁵⁴Cr⁴⁺ (m/Q = 13.5): however, the intensity of ⁵²Cr⁴⁺ is relatively low (less than 0.1 V) through the pulse and the influence of ⁵⁴Cr⁴⁺ on the Al²⁺ signal is limited to less than 3 mV, which can be neglected. The contribution of ⁵⁴Cr⁶⁺ (m/Q = 9) has practically no influence on the Al³⁺ signal at all.

Time axes of each curve were corrected by subtracting the time-of-flight values

where $t raw$ is the time in raw waveform on the oscilloscope. The total time-of-flight τ_TOF can be described as the sum of times spent in each sector

where $τ plasma$⁠, $τ ext$⁠, $τ E – sec$⁠, $τ m – sec$⁠, and $τ det$ are the time of flight of an ion in the plasma region, extractor, E-sector, m-sector, and detector region, respectively. Each time of flight is calculated according to Eqs. (10)–(14) of Ref. 14. In this experiment, $L ext$⁠, $L E – sec$⁠, $L m – sec$⁠, and $L det$ were 0.059, 0.265, 0.179, and 0.041 m, and $V transmission$⁠, $V ext$⁠, and $V dynode$ were set to 3, −12, and −1200 V, respectively. For an ion to be detected, the equation

must be satisfied, where $E kin E – sec$ and $E filter$ are the kinetic energy of ion in the energy filter sector and a constant of energy of Q × 40 eV, respectively. The kinetic energy in the instrument is dependent on the ion charge state, but independent of the kinetic energy which ions originally had in the plasma.

The voltage and current of the pulse discharge are shown in Fig. 2.

Since the impedance of the PFN is higher than that of arc plasmas, the discharge current is primarily determined by the impedance and charging voltage of the PFN. The discharge voltage (i.e., the voltage between anode and cathode, not to be confused with the PFN's charging voltage) is a slightly material dependent value. We measure that the differences in voltage, current, and power are small (less than 10%) when using a Cr versus a Cr_0.75Al_0.25 cathode. Plasma potentials drop immediately (a few μs) after ignition and recover within 50 μs to −5.5 and −2.5 V, depending of use of Cr and Cr_0.75Al_0.25 cathode, respectively, and are constant for the rest of the pulse. These latter potentials were used as representative values for the kinetic energy calculations.

When using the pure Cr cathode, the ion signals of Cr²⁺ and Cr³⁺ are clearly observed while small signal voltages were obtained for Cr¹⁺ and Cr⁴⁺ with the intensity scale from 0 to 3 V as shown in Figs. 3(a)–3(d).

In both cases of Cr²⁺ and Cr³⁺, the range of ion energy shifts to low energies as time elapses. The kinetic energy of Cr³⁺ at 50 μs after ignition is higher than that of Cr²⁺ and the IEDF of Cr³⁺ has a tail in the higher energy region throughout the pulse. The signal of Cr¹⁺ decreased as shown in Figs. 4(a) and 4(b) at a greater measuring distance.

Furthermore, the temporal evolution of IEDFs in Cr-Al mixed plasmas is quite different from the evolution using a pure Cr cathode as shown in Figs. 5(a)–5(d) and 6(a)–6(c).

A small, but not negligible amount of Cr¹⁺ is observed in the latter part of the pulse even for the close distance of 0.18 m. As with a pure Cr cathode, Cr²⁺ and Cr³⁺ are observed. The range of their kinetic energies is slightly lower when using the Cr_0.75Al_0.25 cathode than when using the Cr cathode. It is clear that Cr³⁺ appears only at the very beginning of the pulse: within 100 μs after ignition, the relative intensity of Cr³⁺ rapidly decreases leaving just a small signal of kinetic energy of about 60 eV.

The evolutions of the Al²⁺ and Al³⁺ distributions, Fig. 6, show the same tendencies as the distributions for Cr²⁺ and Cr³⁺, respectively, albeit with smaller signal amplitudes.

In order to access the IEDFs for certain time intervals, the intensity of ion signals obtained in Figs. 3, 5, and 6 with the same electron multiplier voltage of V_M of 1.6 kV were integrated over time (practically done by summing up the digital data in 200 ns steps), namely, at the beginning of the pulse, from 50 to 70 μs, and at the later part of the pulse, from 500 to 520 μs

and

The thus-obtained IEDFs are shown in Figs. 7(a)–7(e).

In both Cr and Cr-Al plasmas, high energy tails are observed at 50 μs after ignition. Tails of the higher charge state distributions exists in the high energy region to a greater extent than for lower charge states; Cr³⁺> Cr²⁺> Cr¹⁺. Later in the pulse, ion energy distributions reach approximate steady-state. While the high energy tails still show sufficient intensity in Cr plasma, the tails disappear in Cr-Al plasmas and IEDFs of different charge states approach a distribution that appears universal for all species.

To see the evolution of total intensities of each ion species and the time dependence of mean ion charge state $Q ¯ ( t )$⁠, the intensities at a given time were summed up for all energy values under consideration of Q as follows:

Then, $Q ¯ ( t )$ is calculated as

In both cases, the intensities of Cr²⁺, Cr³⁺, and $Q ¯ ( t )$ decreased as shown in Figs. 8(a)–8(c) and 9.

Compared to Cr plasmas, a faster decay of Cr²⁺ and Cr³⁺ occurs in Cr-Al plasmas than in pure Cr plasmas. An increase in Cr¹⁺ signal correlates corresponding to a faster decrease of Cr²⁺ and Cr³⁺ (Fig. 8). Furthermore, the increase of Al¹⁺ ions is greater than the increase of Cr¹⁺ in Cr-Al plasmas although the composite balance of Al:Cr is 1:3 and Al²⁺ and Al³⁺ show less intensity than Cr²⁺ and Cr³⁺. The value of $Q ¯ ( t )$ at t = 50 μs does not show significant difference between Cr and Cr-Al plasmas; however, $Q ¯ ( t )$ decreases more rapidly in Cr-Al plasma than in Cr plasma as the discharge continues (Fig. 9).

In our previous paper on Cu, it was found that the intensity of Cu¹⁺ increases as with increasing distance from the cathode.¹⁴ Compared to Cu, Cr plasma does not show this feature rather intensity of Cr¹⁺ decreases as the distance become longer. As described in Ref. 10, the generation of singly charged ion in the latter part of the pulse is driven by charge exchange reactions between ions and neutral atoms, i.e.,

The difference of the cross sections of these reactions in two different elements, Cr and Cu, will affect the frequency of charge exchange reaction in the plasmas. Cross sections of charge exchange reactions have been discussed.^17–21 For the case of Q = 1, which is known as resonant charge exchange, the cross section of the reaction of each element reported by Smirnov shows larger cross section for Cr, 16–23 × 10⁻¹⁵ cm², than for Cu, 13–19 × 10⁻¹⁵ cm², in the energy range of 0.1–10 eV.¹⁸ Previous experimental data showed that the decay time constants of the mean ion charge states depend on the cathode element,¹⁰ which agrees with the differences found between Cr plasmas (this experiment) and Cu plasmas.¹⁴ 

Similar to single element plasmas, Cr-Al plasma also contains ions with high charge state and high kinetic energy within the first 100 μs after ignition, and ions of higher charge state have higher energies. The mean ion charge state $Q ¯$ of Cr ions exhibit close values at 50 μs after ignition regardless if the Cr cathode or the Cr_0.75Al_0.25 cathode was used but $Q ¯$ evolves differently, depending on the cathode composition, as the pulse evolves. These results provide good evidence for the role of particle collisions, which increase as the plasma fills the chamber space in several hundred μs. Since the timescale of the decay, considering IEDF or $Q ¯ ( t )$⁠, is of the order 100 μs and therefore much longer than the lifetime of a cathode spot of 10–40 ns,²² cathode spot phenomena cannot explain this long term decay.

Generation of singly charged ions and the rapid decrease of $Q ¯ ( t )$ indicate that charge transfer from high charge state ions to neutral atoms is more likely to happen in Cr-Al plasmas than in pure Cr. Therefore, in addition to charge exchange reaction between particles of the same element such as

charge exchange reaction between particles of different elements, here Cr-Al hetero-element pairs

should play a major role. As mentioned above, the decays of the mean ion charge states of different elements are element-specific. One should expect that the cross sections for reactions of Eqs. (13) and (14) are different from the cross sections applicable to Eq. (12). The hetero-element interactions can explain the significant change of IETDFs caused when adding an additional element. Internal energy deficits $Δ E$ of Eqs. (12)–(14) with Q = 2 can be calculated as

and with Q = 3

from the cumulative ionization energy of each ion species listed in Table B4 in Ref. 23. The cross section is negligibly small when ΔE < 0.²⁴ A positive energy defect allows these reaction at n = 2 and n = 3 to occur. From Fig. 5(b), Cr³⁺ is the ion species that is influenced most strongly by the presence of Al. Increased intensity of Cr²⁺ and insensitiveness of Cr¹⁺ corresponding to the reduction of Cr³⁺ in Fig. 8 suggest that the reduction of Cr³⁺ is driven by reactions of Eq. (19) rather than by reactions of Eq. (18). Al¹⁺ showing greater intensity increase than Cr¹⁺ in Fig. 8(c) even though the atomic fraction of Al in cathode material is smaller than Cr supports this further, i.e., the presence of Al neutrals enhances charge exchange reaction and a reduction of the charge states of Cr ions. This is evidence that neutrals are generated by self-sputtering and nonsticking on the chamber wall. Then the kinetic energies of atoms are a fraction of the energies of ions causing them so the velocities of neutral atoms are much slower that the velocity of ions. Thus, frequency of the reactions of Eq. (11) is

where $v M 1 Q +$ is the velocity of an ion, $λ M 1 Q +$ is the mean free path of an ion with respect to charge exchange collisions, $N M 2 0$ is the density of neutral atoms, and $σ M 1 Q + − M 2 0$ is the cross section of $M 1 Q + − M 2 0$ collisions. The evolution of $N M 2 0$ depends on the filling time of the near cathode space with neutrals. The filling time t_a depends on the velocity of ion and characteristic length scale of the chamber

where s is a characteristic length of chamber. The velocity of Al is $m Cr / m Al$ (≈1.4) times faster than Cr of the same kinetic energy. The magnitude of $t a$ is 10–100 μs for the kinetic energy of atoms of 1–50 eV with s = 0.2 m. As described above, the velocity of Al is 1.4 times faster Cr. Shorter t_a offers faster increase of $N M 2 0$⁠, resulting in higher collision frequency f. Regarding this point, a heavier ion pair, Ti and Hf, as described in Ref. 6, may have a longer decay time for $Q ¯ ( t )$⁠. Insensitiveness of the charge state distribution of Ti and Hf to the cathode composition in Ref. 6, in contrast to the significant effect of Al in the Ti-Al (Ref. 4) and the Cr-Al (Ref. 5) systems, can be explained by the filling time being not short compared to the pulse length of 250 μs, which was used in their experiment. Since the cross sections vary corresponding to the elements pair and their ion energies and the generation of neutral atoms depends on many factors, such as the ion sticking coefficient and the thermal conductivity of cathode material,¹⁰ it is not easy to predict the timescale of the decay for an individual element. As shown in the Table I of Ref. 10, the characteristic time constants of the mean ion charge state decay is not proportional to the ion mass. However, adding an extra element, which has a short decay time, can play an important role for particle collision reactions in plasmas, resulting in a significant influence on CSDs and IETDFs as explained here.

Finally, a comment should be made on finding slightly negative plasma potentials relative to ground (anode). In most plasmas, the plasma potential is positive, which is related to a negative anode fall. In arc plasmas, the situation is a bit more complicated as we have positive ions moving away from the cathode to the anode. To balance the charged particle flux at the anode, the anode fall can be positive or negative depending on size and position of the anode relative to the main plasma flow. It is therefore not uncommon that cathodic arc plasma has a plasma potential that is slightly negative relative to the grounded anode.

Measurement of ion energy-time distribution functions of pulsed arc plasmas from Cr and Cr-Al cathodes revealed the effects of a second element in a composite cathode, like Al in Cr, on CSD and IETDF. Both Cr single-element and Cr-Al multi-element plasmas showed the decay of ion energies and mean charge states as explained by particle collisions and charge exchange reaction according to Eq. (11); however, the Cr³⁺ fraction and the mean charge state function $Q ¯ ( t )$ showed faster decrease in Cr-Al than in Cr plasmas. Since the initial mean ion charge state of Cr in pure Cr and in Cr-Al plasmas showed approximately the same value, the addition of Al to a Cr cathode strongly affects the decay time primarily by particle collisions and charge exchange reactions more than by ionization phenomena at the cathode spot. In addition to Cr-Cr pairs of ion-atom collisions, collision of ions and atoms of Al-Cr can occur. Stronger changes of Al¹⁺ than Cr¹⁺ ions suggest that neutrals of Al play an important role in the plasma chemistry. The lower mass of Al suggests that Al neutrals can fill the volume between cathode and detector faster than the neutrals of Cr. Neutrals are produced, e.g., by ions not sticking to a wall even as they are condensable, film-forming ions. Considering cross sections and energy deficit in ion-neutral collisions, we found that Al neutrals lead to significant charge exchange reaction rates followed by a rapid reduction of the fraction of multiply charged Cr ions, especially Cr³⁺. We note that there are other factors that determine the production of neutrals such as the thermal conductivity of the cathode material so that it is not easy to predict the decay time for individual elements. The significance of the effect of a second element in a composite cathode varies depending on the elements in question, both of matrix and additive, the time scale of the process after start of plasma generation, and the length scale between cathode and substrate or detector.

The authors gratefully acknowledge the Mitsubishi Materials Corporation for supporting this study under Contract No. WF010678. The authors gratefully acknowledge Robert Franz for providing Cr-Al alloy cathodes. Work at Berkeley Lab was supported by the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.