JAP Communication

LBNL-59789 Published in J. Appl. Phys., vol. 101, pp. 043304-1-6, 2007. http://dx.doi.org/10.1063/1.2561226

Charge-state-resolved ion energy distribution functions of cathodic vacuum arcs: A study involving the plasma potential and biased plasmas

André Anders a Lawrence Berkeley National Laboratory, University of California, 1 Cyclotron Road, Berkeley, California 94720

Efim Oks State University of Control Systems and Radioelectronics, Tomsk 634050, Russia

Abstract Charge-state-resolved ion energy distribution functions were measured for pulsed cathodic arcs taking the sheath into account that formed between the plasma and the entrance of a combined energy and mass spectrometer. An electron emitting probe was employed to independently determine the plasma potential. All results were obtained by averaging over several individual measurements because the instantaneous energy distributions and the plasma potential show large amplitude fluctuations due to the explosive nature of the arc plasma generation. It was found that the ion energy distribution functions in the plasma were independent of the ion charge state. This is in contrast to findings with continuously operating, direct-current arcs that employ a magnetic field at the cathode to steer the cathode spot motion. The different findings indicate the important role of the magnetic steering field for the plasma properties of direct current arcs. The results are further supported by experiments with “biased a

Author to whom correspondence should be addressed; electronic mail:[email protected]

revised LBNL-59789, submitted to J. Appl. Phys., MS #JR06-3904

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plasmas” obtained by shifting the potential of the anode. Finally, it was shown that the ion energy distributions were broader and shifted to higher energy at the beginning of each arc pulse. The characteristic time for relaxation to steady state distributions is about 100 µs.

Keywords: Cathodic vacuum arc, kinetic energy distribution functions, plasma potential

I. INTRODUCTION It is well known that the ion velocities in cathodic vacuum arcs are supersonic with respect to the ion sound velocity. Motivated by solving the “mystery” of the high ion velocities, and the practical implications for thin film growth, extensive measurements have been done by many authors using a range of methods. Focusing on the methods that can resolve charge and/or mass and provide information on distribution functions, one usually employs either (i) electrostatic field methods,1-4 or (ii) time-of-flight (TOF) techniques.5-9 Some studies deal with the determination of the most likely velocity for a given cathode material, vi* , i.e. the peak in the ion velocity distribution function, which can readily be converted into a most likely ion energy * = mi ( vi* ) 2 . As Rosén and co-workers pointed out in a recent contribution,10 according to Ekin 2

the most likely values of velocity and energy must not be used as average values because the velocity (and corresponding energy) distribution functions are usually not symmetric but have a long tail. More information is provided by those studies that deal with the complete velocity or kinetic ion energy distribution functions.1,2,4,11-13 In the simplest case of these studies, the TOF principle is used without charge and mass resolution. One can simply measure the drift time of the plasma flow over a given macroscopic distance. To create time markers, the plasma production can be either kept short,5 or modulated by oscillating the arc current,9 or by superimposing short current spikes.14 Because peaks in the ion signal were used, the information obtained is the most likely velocity (the maximum of the distribution). Using rapid arc termination by a crow-bar (arc by-pass) switch, Byon and coworkers13 obtained the derivative of the ion current which contains information on the chargestate-averaged velocity distribution function in the flow direction. Using a 2-m-long plasma drift TOF section, a comprehensive collection of charge-state-averaged velocities was created.9 By combining plasma drift and an ion beam time-of-flight system, charge-state-resolved most likely velocities of ions in the flow direction were determined.8,12 It was shown that, for a given cathode material, the most likely drift velocity of ions did not depend on their charge state,


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indicating that the mechanism of ion acceleration is of hydrodynamic nature as opposed to be caused by an electrical potential hump. Electrostatic techniques come in various embodiments such as the retarding field analyzer15 (RFA), or curved sector analyzer (like the EQP by HIDEN Ltd), or cylindrical mirror analyzer (CMA, like the PPM422 by Pfeiffer Vacuum). The RFAs have the disadvantage that they cannot discriminate between ions of different masses and charges. The so-called plasma monitors combine the electrostatic energy analyzer with a mass spectrometer, which, strictly speaking, does not measure mass but the mass-to-charge ratio. Typically, there is an entrance mesh (for RFAs) or a single, small entrance aperture (for plasma analyzers). The potential difference between plasma potential and the entrance plane produces a sheath in which positive ions are accelerated ( V pl > Ventrance ) or decelerated ( V pl < Ventrance ). For V pl > Ventrance the energy gain is ∆Ekin ( Q ) = Qe (V pl − Ventrance )

(1)

provided that there are no collisions in the sheath; Q is the charge state number and e is the elementary charge. If we want to infer about the kinetic energy distribution functions in the plasma (in the direction of measurement), one needs to correct for this energy gain (or loss). The charge-state dependent shift of the energy as per Eq.(1) can be described as a change of the ion’s potential energy to kinetic energy, which is an important concept, as discussed later in this paper. The situation V pl < Ventrance is not as simple because the sheath may not be stable, especially when the sheath voltage is driven to high values.16,17 This applies to the situation when the entrance is grounded and the plasma potential is negative. In this contribution, charge-state-resolved energy distribution functions are measured for pulsed vacuum arc plasmas using an EQP electrostatic energy analyzer. In order to assess energy shifts caused by the sheath at the grounded entrance of the device, the plasma potential was measured using an emitting probe. Additional experiments were carried out by biasing the plasma with respect to the ground potential (entrance of measuring device), which was facilitated by shifting the anode potential. Time resolved results are obtained by using short arcs of different pulse lengths. The distribution functions are also discussed in light of previous results involving metal neutrals generated by the arc and the presence or absence of magnetic fields. The pulsed plasma source used here operates without any applied magnetic field – only the self-field generated by the discharge current is present. This detail is important because it is in contrast to commercial, continuously operating, direct-current (DC) arc sources that employ a magnetic field at the cathode to steer the cathode spot motion (so-called “steered arcs”). While practically all commercial arc sources have a spot steering field, some are additionally equipped with a magnetic macroparticle filter. The filter’s fringe field can have an additional effect on the


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cathode processes. Here, all of these effects are eliminated by using a pulsed source that does not need spot steering, thereby allowing us to investigated the “pure” arc processes and plasma properties.

II. EXPERIMENTAL SET-UP AND MEASUREMENT PROCEDURE The plasma was produced by a cathodic arc plasma source of the “minigun” type18 operating in repetitively pulsed mode. Arcs were “self-triggered” by applying the full charging voltage of the pulse-forming-network (600 V) between cathode and anode.19 In most experiments, the arc pulses had a current amplitude of 220 A for a duration of about 350 µs and a repetition rate of about 2 pulses per second. Power was supplied by a pulse-forming-network and switched by a high current thyristor (T1 in Fig. 1). Aluminum and magnesium used as cathode materials because these are much-studied and industrially relevant materials that allow us to compare our results with those of others. Both materials are characterized by the presence of significant amounts of both singly and doubly charged ions. The cathodic arc plasma was streaming towards the grounded entrance of a differentially pumped plasma analyzer (EQP by HIDEN Ltd., operating in ion mode), placed about 45 cm away, see Fig. 1. The diameter of the entrance aperture was 100 µm. (Probe measurements showed that the peak plasma density is about 1x1016 m-3 at the entrance, resulting in a Debye length of approximately 125 µm; since the sheath at the entrance is several Debye lengths, no plasma can penetrate the analyzer.) The vacuum in the cryogenically pumped discharge chamber was about 5x10-5 Pa and about 1x10-5 Pa inside the analyzer due to differential pumping with a turbo pump.

Data acquisition with the EQP analyzer was synchronized with the pulsed arcs by using the analyzer’s synchronization mode. The analyzer is on standby when the plasma in not present (synchronization port sees 0 V) and resumes work when the plasma is on (synchronization port sees 5 V). The data acquisition was done over the entire arc pulse lengths. Each individual measurement of the energy distribution function was characterized by a large noise on the signal, which is quite common for cathodic arc plasmas. Each measurement was repeated five times and in some experiments even ten times, giving a set of raw data distributions. The set was used to calculate average distribution functions having much reduced noise compared to the raw data functions. The energy was measured with an analyzing voltage in the interval from 0 to 100 V, in steps of 0.1 V. Therefore, to cover the whole interval, 1000 pulsed arcs were used to produce the


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raw data for one distribution function. To appreciate the difficulties, one should recall that 5000 or even 10000 arc pulses are used to determine one average distribution function. The analyzer’s raw data are given as energy per charge, and therefore, when considering multiply charged ions, the raw data need to be multiplied by the charge state number to obtain the energy distribution function. The energy range is therefore 0-100 eV for singly charged ions and 0-200 eV for the doubly charged. To get some information on the temporal development of energy distributions, shorter pulses were used by employing the rapid switch-off (current bypass) method. In essence, the current was re-directed from the arc to a bypass parallel branch, which terminates the arc within about 1 µs. Technically, this was accomplished by closing thyristor 2 after a predetermined delay after arc initiation, which was given by closing thyristor 1 (Fig. 1). The PFN and its charging supply were ground free, allowing us to freely set the absolute potential with respect to ground. In most experiments, the anode was grounded and thereby determined the potentials of the rest of the circuit. For plasma bias experiments, the anode of the vacuum arc discharge was positively biased up to 30 V with respect to ground. An emission probe method20 was used to measure the plasma potential. The probe consisted of a two-hole alumina ceramic tube accommodating the two copper leads for heating and contacting the active part of the probe, a tungsten wire of 0.075 mm diameter and about 5 mm length, which was immersed in the plasma. The active part of the probe was positioned about 1 cm downstream from the annular anode of the plasma source. To obtain the necessary electron emission, the probe was heated by a ground-free DC current of 14 A driven by a voltage of 3 V. The contact between probe and bias supply was on the positive side of the probe circuit (Fig. 1). The current-voltage characteristic of the probe in the plasma was measured with the probe either emitting electrons (hot) or not emitting (room temperature). The plasma potential was determined by finding the voltage at which the two characteristics split.

III. EXPERIMENTAL RESULTS AND PRELIMINARY DISCUSSION A. Energy distribution functions Figure 2 shows the averaged energy distributions for the mass/charge settings 24 and 12, corresponding to Mg+ and Mg2+ ions, respectively. The energy distribution functions have not exactly the same shape for singly and doubly charged ions. While singly charged ions tend to have a rather symmetric (Gaussian) shape, the shape of the energy distribution function of higher charged ions can be generally approximated by a shifted Maxwellian distribution,3,4,21


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fi = ( E ) Cs [ E − ∆E ] exp  − 

(

E − ∆E − Edir

)

2

kT  

(2)

where Cs is a scaling constant, ∆E is the kinetic energy gain given by ∆E is the kinetic energy gain given by Eq.(1), and Edir is the average directed ion energy measured on the axis of the measuring instrument. One striking result from Fig. 2 is that the higher charge state has a lower most likely energy (the peak of the distribution). Apparently, the most likely energy for Mg+ is about 30 eV, while it is 22 eV for Mg2+ (note: the multiplication with the factor 2 for Mg2+ was already taken into account). The same behavior was observed for aluminum plasma: the most likely energies for Al+ and Al2+ were 40 eV and 30 eV, respectively. A reasonable explanation of these ―initially somewhat surprising― results could be the existence of a slightly negative plasma potential. As the ions move towards the grounded entrance aperture of the analyzer, they eventually cross the sheath in front of the aperture. A negative plasma potential leads to electrostatic deceleration which is proportional to the ion charge, see Eq.(1), and hence the measured (remaining) energy can be less for higher charged ions.

B. Plasma potential In order to test this explanation, plasma potential measurements and biased plasma experiments were done. Fig. 3 shows the plasma potential with zero bias, i.e., anode is at ground potential. The probe current-voltage characteristics of the heated and cold probe split at about –5 V with respect to ground. Taking into account that the voltage drop between the ends of the emitting wire is 3 V, the plasma potential may be even lower and we can only say that Vpl is between -5 V and -8 V. For singly charged ions, the corresponding energy of 5 to 8 eV needs to be added to the measurements to correct for the sheath effect, giving for Mg+ about 35 to 38 eV for the most likely energy in the plasma. This is somewhat lower than the previous results of 49 eV obtained by the TOF method,9 but may be qualified as agreeing “reasonably well” given the noisy character of the data. Looking at the doubly charged ions, the correction is 10-16 eV, giving 32-38 eV for Mg2+, i.e., practically the same most likely energy as with the singly charged ions. This provides strong support for the conclusions based on the previous TOF results, which suggested that all ions have the same most likely velocity or kinetic energy in the plasma regardless of their charge state.

C. Plasma biasing


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In the plasma biasing experiment, the anode potential was shifted positively with respect to ground (and hence with respect to the grounded entrance of the analyzer). Figures 4 and 5 show the energy distribution functions when the plasma potential is shifted by biasing the anode potential with respect to ground. As expected, the energy distribution functions are shifted, and the amount of shift depended on the bias voltage multiplied by the ion charge state number. Slight changes in the shape of the distribution could be associated with the fluctuating nature of the arcs and perhaps imperfect energy transmission functions of the analyzer. Figures 6 (a) and (b) illustrate the shifts seen in the probe characteristics. The shifts show that biasing the anode causes a corresponding shift on the voltage axis of the probe and ultimately in the probe plasma potential. The characteristic deviation of the hot probe characteristic from the cold indicates that the plasma potential is always a few volts negative with respect to the anode potential.

D. Time dependence The arc system under investigation is pulsed, and previous results on ion charge states and ion energy showed that the first few 10 µs of an arc discharge are characterized by elevated ion charge22,23 and energy9 compared to the corresponding steady-state (time-averaged) values.24 The most straightforward approach, using the analyzer’s external timing circuit, turned out to be not practical because data acquisition would have taken days for each distribution due to the short data acquisition time combined with our low arc repetition rate. Alternatively, the technique of rapid arc termination13 allowed us to look at arcs of various duration and thereby obtaining a picture on the ion energy evolution –this time measured with an electrostatic energy analyzer– giving us the evolution of the whole distribution function and not just the most likely energy.9 The “price paid” with this faster approach is that the distribution functions are timeaveraged over the (now short and terminated) pulse duration rather than a distribution function at a given time after arc initiation. The second thyristor, electrically parallel to the arc, was triggered (closed) such that the arc is rapidly terminated 12.5 μs, 25 μs, 50 μs, 75 μs, 100 μs, or 125 μs after arc ignition. The analyzer integrates the particle fluxes during these short arcs, showing that the ions have a broader distribution at the beginning of the arc pulse and that the high energy components decays within several 10 µs, in good agreement with previous observations. The specific results for Mg2+ are summarized in Fig. 7, which also indicate a correlation of ion energy with the arc voltage.

IV. DISCUSSION AND CONCLUSIONS


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In the recent discussion by Rosén and co-workers,10 it was argued that conflicting conclusions reported in the literature for the two main characterization techniques, time-of-flight and electrostatic analysis, may originate from the commonly employed data interpretation of energy and velocity, in which peak (i.e. the most likely) values and average values are not carefully distinguished. Although the point is well made, it cannot account for some, still significant differences seen in various reports. For example, if we focus on the peak values only, representing the most likely velocity or energy, we showed here that they are practically independent of charge state, in contrast to the data obtained with a filtered DC arc source where it was stated that “plasma expansion in the absence of a magnetic field leads to higher ion energies for higher charge states.”4 There are three physical factors that may lead to such different conclusions: (i) the strengths and shape of magnetic fields that allow electric fields to exist in the plasma, (ii) collisions, especially charge exchange collisions with metal neutrals produced by the arc, and (iii) shifts in the plasma potential relative to the analyzer’s entrance potential. In the experiments of with DC arc sources, a permanent magnetic field was employed to facilitate steering of the cathode spot. Therefore, even when the magnetic filter field was zero, the magnetic field strength on the cathode surface was not zero. Therefore an electric field can exist in the near-cathode plasma for the “no magnetic field” case4 that will affect the ion energies in a manner proportional to the charge state. The observed ion energies will show a composite of (i) kinetic energy obtained by acceleration very close to the cathode spot, independent of charge states and dominated by hydrodynamic gradients, and (ii) kinetic energy gained in an electric field extending further from the cathode, which is proportional to the charge state. This interpretation is in agreement with findings that magnetic fields modify the kinetic energy of ions in expanding plasmas,4,9 and in particular that ion acceleration occurs when ions move from regions of high magnetic field strength to low field regions. One should note that a similar acceleration principle is used in gridless ion sources such as the end-hall ion source.25 The relevance of the electric acceleration mechanism is underlined by the fact that very high energies have been observed with a magnetically steered source, more than 200 eV for aluminum,4 i.e., much higher than for any of the non-steered arc sources. The second factor, collisions of ions with neutrals produced by the plasma, may have a significant effect on the shape of the distribution function and its evolution associated with the delayed “production” of metal neutrals and the charge exchange collisions caused by them.23 Energetic ions, approaching a solid surface under an acute angle, tend to not stick but to bounce back as a neutralized atoms. Reliable measurements of the neutral-to-ion ratio are rare and therefore not much can yet be said about the relative importance of this effect. If confirmed, one implication is that even streams of filtered arc plasma contain many more neutrals than one would expect. Under the current paradigm one assumes that most of the neutrals are removed


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from the plasma because the electromagnetic filter fields do not assist in the non-line-of-sight transport to the substrate. Research to clarify this question is underway. Finally, we demonstrated here that the plasma potential influences the data as recorded by the analyzer. The plasma potential is affected by the anode potential and a range of other factors such as the shape and size of the chamber, auxiliary anodes (such as filter components, if present), etc. Therefore, it is difficult to compare different systems unless the plasma potential is well known for each of the systems. The specifics of the plasma potential also influenced the energy measurements of ions in a DC boron arc measured by Richter et al.26 This work is unusual because no magnetic steering field was employed, and the anode of the system was not grounded. Boron is a semimetal that needs to be heated (800°C) to have sufficient conductivity for serving as an arc cathode. The arc voltage was high, up to 60 V for a 60 A arc. The cathode potential was measured to be -15 V with respect to ground, and the anode potential was positive in the range 30 V to 45 V above ground.27 A cylindrical mirror energy analyzer with a grounded entrance orifice gave mean values of about 29 eV and 63 eV for B+ and B2+, respectively, for an argon pressure of 0.07 Pa26,28. The 63 eV average value included the factor 2 that must be applied, the raw data signal (energy/charge) was at 31.5 eV for B2+ ions.27 The most likely energies were about 25 eV for B+ and 53 eV for B2+ (cf. Fig.4 of ref.28) Richter and coworkers emphasize that ions are “born” at the cathode and therefore their energy should be expressed with respect to the cathode potential; they concluded that the “kinetic ion energy at low pressure as measured with respect to cathode potential is about 45 eV for B+ and 90 eV for B2+ indicating that electric field influence plays the major role in ion acceleration.”26 The biased plasma experiments presented here confirm that the ion acceleration to high kinetic energy occurs in the sheath at the analyzer’s entrance (as opposed to acceleration near the cathode spot). The values 45 eV and 90 eV refer to the sum of kinetic and potential energy of B+ and B2+, respectively, when the potential reference point is set at cathode potential. Using the most likely values of the distributions, the most likely kinetic drift energy of ions in the plasma can be estimated to about 2 eV and 6 eV for B+ and B2+, respectively, with the sheath voltage being about 23 V (2 eV + 1e * 23 V and 6 eV + 2e * 23 V for B+ and B2+, respectively). One can notice that (a) these kinetic energy values are lower than one would expect for vacuum arc ions,29 and (b) there seems to be a noticeable difference between the charge states. The low kinetic energy in the plasma may be attributed in part to interaction with background gas and non-sticking boron. Additionally, deceleration occurs when the plasma is injected into a magnetic filter: it has been previously shown that the kinetic energy of ions in flowing carbon plasma can be significantly reduced for a similar filter arrangement (see ref9, figure 10, long-coil-case). The charge state dependence in the boron case may be associated with the collisions “seen” be the different charge states: The fact that ions arrive with charge


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state 2 at the analyzer indicates that these ions had less or no collisions with atoms, whereas single charged ions may originate from the cathode spot or may have been produced by collisions of doubly charged ions with neutrals.

IV. SUMMARY In summary, a plasma analyzer comprised of an electrostatic energy analyzer and a quadrupole mass spectrometer was employed to study the charge-state-resolved ion energy distribution functions of pulsed vacuum arcs. Additionally, an electron emitting probe was used to determine the plasma potential. The plasma potential was found to be slightly negative in our system, which required a correction of the analyzer’s raw data to account for a charge-statedependent deceleration of ions in the sheath at the analyzer’s entrance. The corrected data indicated that, for a given cathode material, the most likely ion energy in the plasma is independent of the charge state. This result is in contrast to measurements done with DC arc systems employing magnetic steering fields, which suggests that the magnetic steering field plays an important role for the enhancement of the ion energy. The results were supported by additional measurements in which the plasma potential was intentionally shifted via biasing the anode of the arc discharge. Considering kinetic and potential energy, the findings here can be consolidated with other literature data. Finally, experiments with various short arc durations confirmed previous findings that the ion energy is enhanced at the beginning of an arc; the energy distributions functions are initially broader and extend much further into the high energy range.

ACKNOWLEDGEMENTS The authors thank Prof. F. Richter for stimulating discussions. E.O. acknowledges support by a TUSUR grant of the Russian national program “Education.” This work was supported by the Office of Nonproliferation and International Security, U.S. Department of Energy, IPP project LBNL-196, under Contract No. DE-AC02-05CH11231.


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Figure Captions FIG. 1 Electrical schematic of the experimental setup with a pulsed cathodic arc plasma source of the “minigun” type, ejecting vacuum arc plasma towards an emitting probe and the entrance of a differentially pumped plasma analyzer; the bypassing thyristor T2 is only used in the experiments with rapid arc termination. FIG. 2 Energy distributions for the mass/charge settings 24 and 12, corresponding to Mg+ and Mg2+ ions, respectively, with the anode of the arc plasma source at ground. Each energy distribution function was normalized to its peak value for easier comparison. The charge state multiplier 2 for the energy of Mg2+ was taken into account but no correction was yet made for the sheath effect at the analyzer’s entrance. FIG.3 The probe current-voltage characteristics of the heated and cold probe in a Mg plasma with the anode at ground potential. FIG. 4. Energy distribution function as in Fig. 2 but with the arc anode shifted to +10 V with respect to ground. FIG. 5 Energy distribution function as in Fig. 2 but with the arc anode shifted to +30 V with respect to ground. FIG. 6 Part of the probe characteristic for (a) room temperature and (b) hot (electron emitting) probe immersed in biased Mg plasma; the anode bias voltage with respect to ground is indicated at each curve. FIG. 7 Influence of the arc duration on the peak (most likely value) and full width at half maximum (FWHM) of the energy distribution; each energy distribution function is integrated over the arc pulse duration. Additionally, the temporal development of the arc voltage is shown (not integrated but the value just before arc termination).


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Fig. 1


14

Fig. 2


15

Fig. 3


16

Fig. 4


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Fig. 5


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Fig. 6 (a) and (b)


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Fig. 7


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