Plasma Sources Science and Technology

Plasma Sources Sci. Technol. 23 (2014) 025014 (11pp) doi:10.1088/0963-0252/23/2/025014

A dc plasma source for plasma–materialinteraction experiments

T S Matlock, D M Goebel, R Conversano and R E Wirz

University of California Los Angeles, 420 Westwood Plaza, Los Angeles, CA 90095, USA

E-mail: tmatlock17@ucla.edu

Received 3 September 2013, revised 10 February 2014Accepted for publication 27 February 2014Published 24 March 2014

AbstractA new device has been constructed for the investigation of interactions between engineeredmaterials and a plasma in regimes relevant to electric propulsion and pulsed power devices.A linear plasma source, consisting of a hollow cathode, cylindrical anode, and axial magneticfield, delivers a 3 cm diameter beam to a biased target 70 cm away. The ion energy impactingthe surface is controlled by biasing the sample from 0 to 500 V below the local plasmapotential. This paper discusses the major aspects of the plasma source design and presentsmeasurements of the plasma parameters achieved to date on argon and xenon. Experimentsshow that splitting the gas injection between the hollow cathode and the anode region providescontrol of the discharge voltage to minimize cathode sputtering while providing ion fluxes tothe target in excess of 1021 m−2 s−1. Sputtering rate measurements on a non-texturedmolybdenum sample show close agreement with those established in the literature.

Keywords: plasma interactions, sputtering, sputter deposition, molybdenum

(Some figures may appear in colour only in the online journal)

1. Introduction

The plasma interactions (Pi) facility is being developedat UCLA for the testing of advanced, micro-architecturematerials [1] for applications in harsh environments, similarto that produced in electric propulsion (EP) and pulsed powersystems. A 250 A hollow cathode plasma source is integratedwith guiding solenoidal magnets running across a vacuumchamber to provide a roughly 3 cm diameter plasma to adownstream target material with target-directed, xenon orargon ion fluxes. Material coupons may be installed in thepath of the plasma beam and biased to provide energeticion bombardment, and then examined post-irradiation byremoving them from the chamber and sending them to aseparate laboratory for analysis, though a suite of in situdiagnostics is under development.

The dynamic interactions between plasmas and materialsfar from equilibrium are a critical and currently not wellunderstood aspect of EP and pulsed power device design.Facilities dedicated to the examination of phenomena arisingwhen materials are exposed to extreme plasma environmentsare in ongoing use for research vital to magnetic confinementfusion [2–6] and hypersonic vehicles [7, 8] among other fields.The Pi facility is designed to investigate partially ionizedplasmas in argon and xenon of moderate electron temperature

(2–10 eV) and plasma density (1016–1019 m−3) and overallconditions similar to those found in EP devices. In contrast tothe more canonical experiments cited above, the interactionsbetween EP plasmas and exposed materials have largely beeninvestigated within the device of interest, where the deviceoperation (and generated plasma) is intrinsically tied to theproperties of the plasma-facing materials [9, 10]. The Pifacility is designed to minimize feedback between the plasmasource and material under study in order to enable a lessdevice-specific investigation of how material properties andsurface architecture affect resilience to EP-relevant plasmabombardment.

This paper presents the design and operational metrics ofa plasma source intended to enable fundamental experimentsto characterize both global and microscopic interactions ofplasma–material systems. The plasma provided must besimple enough to promote accurate numerical modeling andflexible enough to capture the range of phenomena occurringin the plasma regimes of interest.

2. Experimental apparatus

The Pi facility at UCLA is comprised of a 1.8 m diameter by2.8 m long vacuum chamber evacuated by dual cryopumps

0963-0252/14/025014+11$33.00 1 © 2014 IOP Publishing Ltd Printed in the UK

Plasma Sources Sci. Technol. 23 (2014) 025014 T S Matlock et al

Figure 1. (a) Pi facility sketch (top view) with cathode flow indicated by red arrow, anode flow indicated by blue arrows. (b) Pi facility inoperation on xenon (front view).

with a combined pumping speed of 5000 l s−1 on argon,allowing base pressures as low as 5 × 10−7 Torr. The plasmasource is mounted on one flange of the chamber, diametricallyopposed to the flange which supports the sample manipulatorarm. Intermediate guide magnets are mounted to struts lyingchordally across the bottom of the chamber. All componentsof the plasma source and delivery system lie within the vacuumchamber with small axial gaps between system elementsallowing for the insertion of plasma diagnostics in a flexiblemanner. A sketch of the facility layout is given in figure 1(a)and a picture of plasma bombardment of a graphite target isshown in figure 1(b).

2.1. Plasma source design

The plasma source consists of a lanthanum hexaboride (LaB6)hollow cathode coupled to a water cooled, cylindrical copperanode. The cathode has a 1.3 cm inner diameter LaB6 insertinside a graphite cathode tube with a 1 cm aperture tungstenorifice plate. A graphite keeper electrode positioned around thecathode tube aids in starting the discharge and helps to protectthe orifice plate and graphite tube end from ion bombardmentfrom the cathode plume plasma. This size cathode is capableof running continuously at 250 A of discharge current [11, 12],and has been used in the Pi facility up to the maximum 125 Arating of the present discharge power supply. The anode has anapproximately 6 cm inner diameter and is 30 cm long. A water-cooled magnetic field coil positioned around the cathode anda solenoid coil wound on the anode provide an axial magneticfield that both confines the electrons to improve the ionizationand guides the plasma to the target region. The magnetic fielddiverges from the cathode face to the anode solenoid regionto better match the cathode exit diameter to the anode, andthe axial strength can be selected in the range 100–500 G tooptimize the discharge parameters for plasma generation andtransport. Simulated magnetic field strengths and flux lines areshown in the appendix, for solenoid settings which maximizedtarget current at a discharge condition in argon.

The hollow cathode plasma source differs significantlyfrom the previous plasma source (PISCES [13, 14]) developedfor the purpose of plasma–surface interactions experiments.In that case, a large area LaB6 disk cathode coupled toa cylindrical anode produced the plasma in a quasi-reflexdischarge mode. That source required large discharge powerlevels (10–50 kW) to generate a relatively large area hydrogenplasma (50–75 cm2) capable of delivering a high flux to thetarget region downstream of the anode. The new Pi sourcedesign is optimized to produce a smaller-diameter argonor xenon plasma (≈10 cm2) while operating at manageabledischarge power levels in the 5–10 kW range. The systemincludes a gas injector positioned between the cathode and theanode to provide direct control of the discharge voltage at agiven discharge current and cathode flow rate. This anode gasinjector is also known to reduce the oscillation level in thecathode plume and the local production of energetic ions thattend to sputter the keeper face and anode wall [15, 16]. Thearea expansion ratio of the plasma from the hollow cathodeorifice to the anode is on the order of 20 to 30, so the dischargeis stable and well behaved over a large range in dischargecurrent and plasma densities. In addition, the higher neutralgas pressure downstream of the cathode orifice in the newPi, compared with the constant axial pressure in the flat diskPISCES cathode source, provides additional protection of theinsert from contamination by metallic components that mightbe sputtered or evolved in the system.

The plasma from the source region is coupled throughtwo 10 cm diameter water-cooled ‘chamber solenoids’ to thecooled target located inside the sample magnet coil. Theplasma transport region through the chamber solenoids isintended to provide isolation between the target being sputteredand the plasma source. The ionization mean free path forparticles sputtered from the target is typically less than thedistance from the target to the anode, and the ions created fromthe target material then diffuse to the walls of the solenoidspools or fall back down the axial potential gradient in theplasma to the target region.

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Plasma Sources Sci. Technol. 23 (2014) 025014 T S Matlock et al

The plasma source components (anode and cathode) floatrelative to the vacuum facility and the grounded chambersolenoids. Because of the large area of the grounded solenoids,the plasma tends to float within an electron temperature(<10 eV) of the ground potential over the entire range ofdischarge currents. Since the bias applied to the target is maderelative to chamber ground, this provides a stable referencepotential from which the ions are accelerated through thesheath to the biased sample.

2.1.1. Source collisionality analysis. The long intermediateregion between the plasma source and the material under testis one of the discerning features of the device design. Thisregion is designed to be sufficiently long such that the particlessputtered from the target do not stream back to the anode regionand contaminate the cathode or anode surfaces. For example,if the sputtered target material is ionized in the anode regionthen it is likely to accelerate toward a cathode surface causingcontamination and limiting the life of the plasma source. Theability of the device to provide long duration plasma exposureto target materials relies on the ionization of sputtered targetparticles downstream of the anode, where they are likely toredeposit on the target (a process similar to the recyclingwhich occurs at tokamak divertor targets) or grounded chambermagnet surfaces. This effectively isolates the plasma sourceand target regions of the device.

It is convenient to refer to electrons within the facility asbelonging to one of two classes. So-called primary electronsare those which enter the anode region with an energy close tothe discharge voltage, gained through the potential differencebetween the cathode and the anode. Primary electrons arefree to stream along the para-axial magnetic field, and inthe absence of significant collisionality to randomize theirvelocities, may be treated as a mono-energetic population withnegligible temperature. The second class of electrons, referredto as plasma electrons, are those which are created when aprimary electron suffers an inelastic collision. An ionizingcollision, for example, results in a low-energy electron beingliberated from the atom and in a large drop in the energyof the ionizing electron while randomizing the direction inwhich both electrons leave the collision, thus creating twoplasma electrons, in essence. These plasma electrons areapproximated here as belonging to a Maxwellian distribution:

λC+ = vC

ne〈σC+ve〉 . (1)

The distance a sputtered carbon atom can travel in abackground of ionizing electrons can be estimated using (1),where σC+ is the ionization cross section for carbon, ve andne the ionizing electron speed and density, vC the speed of thesputtered carbon, and with 〈. . .〉 denoting an ensemble average.In order for the majority of sputtered carbon atoms to be ionizedbefore reaching the anode region roughly 70 cm away, theaverage density of plasma electrons in the long intermediateregion must be greater than 2.5 × 1018 m−3 (assuming anelectron temperature of 7 eV), using the calculated electronimpact ionization cross sections from Kim and Desclaux [17]which we have integrated over a Maxwellian distribution.

The above estimate assumes the sputtered carbon isejected with an average axial speed of 7.3 km s−1 basedon LIF measurements of carbon sputtered by 1.5 kV argonions [18, 19] and gives a conservative upper bound for theelectron density required to ionize sputtered atoms. Othermaterials, such as molybdenum and tungsten, will requiremuch lower electron densities for the same ionization meanfree path. Ground state ionization rates from the ADASdatabase [20] for molybdenum and tungsten are much higherthan those calculated by us for carbon; with rates listed as5.15 × 10−14 m3 s−1 and 4.3 × 10−14 m3 s−1, respectively,compared with 4.16 × 10−15 m3 s−1 for carbon. The ADASrate coefficient for ionization of ground state carbon is listed as3.69 × 10−15 m3 s−1 for comparison. The speed of the ejectedparticles may also be substantially lower for these refractorymetals, due in part to an order of magnitude increase in massover carbon. The axial speed of molybdenum sputtered byargon ions is expected to be around 1.7 km s−1, based on theassumption that the most probable energy is roughly half thesublimation energy (6.85 eV/atom for Mo [21]), leading toan electron density of only 5 × 1016 m−3 needed to ensureionization in under 70 cm.

The reverse situation, of material sputtered from thecathode contaminating the target, must also be considered.In order for carbon sputtered from the cathode keeper, forexample, to be ionized before streaming past the anode, theplasma electron density in this region ought to be at leasttriple that estimated above (i.e. >7.5 × 1018 m−3), neglectingionization due to primary electrons in order to find an upperbound for the threshold density. Double probe measurementsshow the plasma density at the downstream exit of the anoderegion approaches 4 × 1018 m−3 during operation of thedischarge at 85 A and 43 V on 20 sccm of xenon. The electrondensity between the anode exit and cathode is expected toexceed this measurement and may certainly lead to sputteredcarbon ionization lengths less than the anode length, however,the peak on-axis plasma potential must occur downstream ofmost carbon ionization events in order to ensure recycling to thekeeper. The location of the maximum on-axis plasma potentialis not known at this stage of development and will changewith the parameters of operation, but the conservative natureof the above estimates (e.g. neglects slowing of the sputteredcarbon by high neutral gas pressures and the off-normal peakin sputtered particle angular distribution [22]) allows us toreasonably expect that cross-contamination may be avoidedat the proper operating conditions.

The preceding analysis demonstrates how the effectiveseparation of the source and test region can be obtained, withthe dense plasma and long intermediate section minimizingthe possibility of cross-contamination of sputterants from oneregion to the other. Similar estimates may be made of theimportant collision scale lengths for plasma species in thedevice in order to gauge the relative importance of specificprocesses to the physics of source operation. A list of theselengths, and corresponding collision frequencies, are givenin table 1, where momentum exchange collisions are listedby participating species abbreviated i–j, with e for plasmaelectrons, p for primary electrons, i for singly charged xenon

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Plasma Sources Sci. Technol. 23 (2014) 025014 T S Matlock et al

Table 1. Collisional frequencies and mean free paths at the exit ofthe plasma source for operation on xenon.

Collision type Frequency (MHz) Mean free path (cm)

e–n [23] 11 15.8e–i [24] 4.6 38.9Ionization, e [25] 0.38 470i–i [24] 0.12 0.7i–n [26] 0.013 17Ionization, p [25] 2.5 130Slowing [24] 1.3 250

ions and n for neutral xenon atoms. Electron impact ionizationcollisions are presented for primary electrons, with an assumedenergy of 30 eV, and plasma electrons (by integrating availablecross sections over a Maxwellian distribution), with anassumed temperature of 7 eV; ionization collision mean freepaths are given for the electrons rather than neutrals. Theeffective slowing of primary electrons by the backgroundplasma electrons is also presented, even though this processhas a mean free path greater than twice the length of the device.

Sources for the collision cross sections used are givenin the table. Plasma and neutral densities of 2.5 × 1018 and2×1019 m−3 are assumed, with the prior based on measurementand the latter based on a 20 sccm flow of xenon travelingthrough a 6 cm diameter tube with an ensemble speed of140 m s−1. An ion temperature of 1 eV is assumed (though theactual temperature may be significantly lower) for the ion–ioncollisions presented in the table, while the ion–neutral meanfree path is calculated assuming the ions are streaming throughthe neutrals at the ion sound speed.

The mean free paths listed in table 1 may be comparedwith the electron and ion Larmor radii in order to asses theirdegree of magnetization. The magnetic field strength nearthe anode is usually around 300 G, corresponding to an iongyroradius of 1 cm (again using a presumed upper bound of1 eV) and an electron gyroradius of 0.2 mm. This field strengthcorresponds to ion and electron Hall parameters, defined as theratio of cyclotron to neutral collision frequency, of 1.7 and 470,respectively, indicating that electrons are highly magnetized,while the ions are in an intermediate magnetization regimewhere their motion is strongly affected by the magnetic field,though they are not well confined:

νe–n ≈ 6.6 × 10−19 Te/4 − 0.1

1 + (Te/4)1.6, (2)

νe–i = 2.91 × 10−12ne ln �T −3/2e , (3)

νi–i = 1.96 × 10−27m−1/2i ni ln �T

−3/2i , (4)

νi–n = 3.13e

4ε0m

−1/2i nnα

−1/2, (5)

νslowing = e4 ln �ψne

2πε20m

2ev

3p

, (6)

ln � = 29.91 − ln

(n

1/2e

T3/2

e

), (7)

ψ = erf

(√Ep

Te

)− 2

√Ep

πTeexp−Ep/Te . (8)

The collision frequency equations used are reproduced in(2)–(6). In these equations, ne is the density of Maxwellianelectrons, ln � is the Coulomb logarithm (given in SI in (7)),mi is the mass of the ionic species, Ti the ion temperature, nn

the neutral density, e is the elementary charge, α is the dipolepolarizability of the neutral atom (taken as 4.5 × 10−40 F m−2

for xenon [27]), vp is the speed of the primaries, ε0 is thepermittivity of free space, and ψ is a function of the primaryelectron energy, Ep, and the Maxwellian electron temperature,Te. The function ψ is given in (8) where erf is the errorfunction, which approaches unity at values of Ep/Te greaterthan 1.2. Of the equations listed, only (2), which providesa fit to numerically integrated experimental cross sections, isspecific to xenon. The form of (4) shown is based on theassumption, which we rely on throughout this article, that ionsare singly charged. Validation of this assumption is left forfuture work, but we expect only minor corrections to arisefrom consideration of higher charges, due to the low electronenergies involved. The electron–electron collision frequencyis identical to νe–i for singly charged ions.

3. Plasma source performance

The discharge current–voltage characteristics are presented forboth xenon and argon in figure 2(a) at various flow splitsbetween the cathode and the anode (through the ring injector).The discharge requires higher voltages during operation onargon, despite higher total volumetric flow rates (26 sccm Ar,compared with 20 sccm Xe), while a higher cathode-to-anodeflow fraction is observed to lead to a decrease in dischargevoltage at all discharge currents.

A 3.8 by 5.1 cm coupon of Duocel vitreous carbon foam(100 PPI, 21–24% density) is used as a sample target materialand biased 200 V below ground. The current collected by thetarget is shown in figure 2(b) as a function of the dischargecurrent. The target current is observed to increase withdischarge current in an approximately linear manner. Targetcurrents obtained on argon are higher for all discharge currentswhen the majority of the flow is introduced through the anodering injector rather than the cathode, even when normalized bythe input power.

Representative results showing the change in dischargeparameters versus the anode mass flow rate are given in figure 3at several values of the cathode flow rate for each gas species.In all cases an increase in anode flow allows operation at alower discharge voltage for a given discharge current (95 A forthe xenon data and 115 A for the argon settings shown). Effectsfrom increasing the anode flow rate appear to diminish at hightotal flows. Ion currents at the target increase nearly linearlywith anode flow rate according to the data of figure 3(b), withsome saturation occurring a high total flow rates.

The same general dependences of the discharge voltage onflow rate are observed when the anode flow rate is held constantand the cathode flow varied instead. This may be observed in

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Plasma Sources Sci. Technol. 23 (2014) 025014 T S Matlock et al

Figure 2. (a) Discharge voltage and (b) target current as a function of discharge current for different cathode and anode (in parenthesis)mass flow rates given in sccm.

Figure 3. (a) Discharge voltage and (b) target current as a function of anode flow rate for different cathode mass flow rates given in sccm.

figure 4(a), where again the discharge is able to operate atlower voltages when the neutral injection is supplemented.

On the other hand, the effect of increased cathode flowrate on the target current, shown in figure 4(b), is dramaticallydifferent from that displayed in figure 3(b) for anode flow rate.Instead of increasing proportional to cathode flow rate, thetarget current tends to tail off at higher flows (with non-zeroanode flow). In argon, for example, the target current reachesa maximum near 13 sccm and begins to decline as the cathodeflow is increased further. The existence of target currentmaxima in figure 4(b) is expected to be due to the competingtrends of increased plasma density with increased gas feedand the drop in energy available to electrons as the dischargevoltage lowers affecting the ability of the plasma to bridge theneutral-dominated region between the anode and the target.

Similar plots are given in figures 5(a) and (b), but with thetotal mass flow rate into the system held constant (at 26 sccmfor argon, and 20 sccm for xenon) while the ratio of anode-to-cathode flow is altered. Figure 5(b) reveals the somewhatunexpected trend of dramatic gains in target current at highanode flow fractions. The target current obtained is limited by

the ability of the discharge power supply to support the highvoltages necessary at low cathode flow rates. Another practicallimit to the useful anode flow fraction is the increased cathodewear expected when the cathode flow is low and ions born inthe anode region impact cathode potential surfaces with higherenergies. Higher anode voltages can also be expected to leadto higher fractions of multiply charged ions (the desirability ofwhich depends on the experiment). It is clear figures 4(b) and5(b) that the addition of an auxiliary neutral flow near the anodeallows us to attain significantly higher target currents than canbe delivered with cathode flow alone. It should also be notedthat the steady increase in discharge voltage at high anode-to-cathode flow fractions in figure 5(a) is expected to be drivenby a dearth in neutrals in the cathode rather than an excess ofneutrals near the anode, as figure 3(a) shows that an increasein anode flow alone helps to lower the discharge voltage.

Constant magnet settings are used in the experimentsdescribed above for each gas species. The magnetic field is30% stronger at the cathode when operating on argon ratherthan xenon, and 20% weaker in the anode region. Finite-element simulations of the field near the target surface suggestit is roughly 200 G during operation on either gas.

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Plasma Sources Sci. Technol. 23 (2014) 025014 T S Matlock et al

Figure 4. (a) Discharge voltage and (b) target current as a function of cathode flow rate for different anode mass flow rates given in sccm.

Figure 5. (a) Discharge voltage and (b) target current as a function of anode-to-cathode flow rate ratio for constant total mass flow rates.

All discharge voltage measurements are made at thepower supply and reduced to account for an average resistancein the cabling between the supply and the electrodes of27 m. Changes in the cabling resistance with heating arenot monitored and are estimated to lead to a discharge voltageuncertainty of 1.35 V, corresponding to a 50% variability in theresistance. Accuracy of the target current and target floatingpotential measurements are limited by the resolution of thepower supply, resulting in uncertainties of ±5 mA and ±0.5 V.

4. Plasma profiles

A preliminary survey of the plasma has been undertakenusing a planar Langmuir probe to measure plasma density,temperature and potential. The molybdenum probe is 4 mmin diameter with ceramic paste insulating the downstream sideand an alumina probe holder. Measurements displayed here areperformed with the probe 8 mm upstream of the target materialsurface and translated laterally and vertically by motor drivenball-screw stages. The target is biased to −200 V while aKepco BOP 100-1M power supply is used to bias the planarprobe to −100 V for measurements of the spatial distributionof ion saturation current in front of the target. A representativeion current distribution is shown in figure 6(a). Integrating theion current density shown in figure 6(a) roughly yields a total of

1 A and about 0.54 A in the area projected to the target surface,while the actual current collected by the target is 0.26 A. Thereason for this discrepancy is not yet known, but is expected tobe due in large part to an increase in the probe collection areaby the sheath [28], with the coarseness of the data collectionmesh also contributing to uncertainty in integration.

A finer spatial scan of the ion flux across the vertical centerof the target is shown in figure 6(b) for the same dischargeconditions. An ion current profile taken at the same dischargeconditions used for the sputter yield measurements describedbelow is also presented in figure 6(b). Standard deviationsin ion current collected within a 1.27 cm radius of the samplecenter are below 11% for argon and below 7% for xenon.

5. Sputter yield measurement

Accurate sputter yield measurement is a critical benchmark forany plasma–surface interaction testbed and as such we haveattempted to validate the Pi facility using materials with well-known sputter rates. To this end, a flat molybdenum sample(initial mass and thickness of 6.7731 g and 0.254 mm) wasinserted in the Pi target holder and its weight loss measuredafter a 1 h exposure to a previously characterized plasma.

The target is covered by a Mo plate with a 2.54 cm diameteraperture, constricting the plasma exposure on the sample to a

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Plasma Sources Sci. Technol. 23 (2014) 025014 T S Matlock et al

Lateral Position, x (cm)

Ver

tica

l Pos

itio

n, y

(cm

)Ion Flux, Γ

i (m2 s−1 )

−3 −2 −1 0 1 2 3−3

−2

−1

0

1

2

3

1.2

1.4

1.6

1.8

2

2.2

2.4x 10

21

−6 −4 −2 0 2 4 60.5

1

1.5

2

2.5x 10

21

Lateral Position, x (cm)

Ion

Flu

x, Γ

i (m

2 s−1

)

XeAr

Figure 6. Ion flux measured 8 mm upstream of a −200 V biased target (a) across the target plane (b) along the vertical center (Y = 0). Thedischarge is operated at 112 A and 73 V with a cathode flow of 15 sccm Ar and zero auxiliary anode flow. Operation on xenon at 100 A and40 V with the cathode and the anode flows of 6 and 14 sccm is shown in (b) along with a smoothing spline used for sputter yield estimates.

known area with limited edge effects. The discharge is run at100 A with the cathode and the anode flow rates of 6 sccmand 14 sccm xenon, respectively. Time-averaged values ofdischarge voltage, target current and background pressure of39.8 ± 0.4 V, 270 ± 11 mA, and (1.0 ± 0.26) × 10−4 Torr(corrected for xenon) are obtained over the course of materialsputtering. The target is biased 200 V below ground, whilethe plasma potential measured 8 mm upstream of the guardplate is 3 ± 2.5 V. Plasma potential is measured using theplanar Langmuir probe described above and the relation, φpl =Te(1/2 + ln[

√mi/2πme]) + φfl, with the stated uncertainty

due mainly to the accuracy of Te, which is measured here as5.8 ± 0.4 eV. This relation for plasma potential, φpl, basedon electron temperature, Te (in eV), floating potential, Vfl,and the ion-to-electron mass ratio, mi/me, assumes a two-component plasma (i.e. no high-energy primaries or low-energy secondaries) exists near the probe surface.

Integrating the current collected from a prior run atthe same discharge conditions over the 2.54 cm diameterexposed area leads to a particle current estimate of1.11(+0.34/ − 0.21)1018 ions s−1 impinging on the sample,with the uncertainty evaluated by integrating the currentincluding one standard deviation of the measurement (2000samples are obtained at 200 kHz for each position). Theresult of a 60 min plasma exposure was a loss of 81.8 ±0.5 mg, corresponding to a sputter yield (with no correctionfor redeposition of sputtered atoms) of 0.132(+0.047/ −0.028) atoms/ion.

As noted in the previous section, sputtered molybdenumatoms are readily ionized in the plasma near the target andmay by guided back by the plasma potential distribution toredeposit on the target. Mass loss measurements are then onlyan indicator of the net sputter yield, which is the differencebetween the actual sputter rate and redeposition rate on thetarget. Redeposition is accounted for by Doerner et al usinggeometric arguments along with spectroscopic measurementsof the sputtered molybdenum energy and ionization mean free

path [29]. Their calculations yield a correction factor of 1.7,multiplied by the measured net yield to find the gross sputteryield, at conditions very similar to the present experiment(target radius, electron temperature and electron density areclose to those found here). This correction factor assumes thatthe sputtered molybdenum is ejected from the surface witha cosine distribution while (as noted by Doerner) the actualsputter yield is expected to be primarily at angles near 45◦ offnormal for the conditions here of low-energy ions (200 eV)with normal incidence [22].

Here we present a similar analysis of redeposition ratesthat extends to include the angular and energy distributions ofsputtered particles. We frame our analysis on the assumptionthat (almost) all sputtered particles that are ionized somewherewithin the projected area of the target surface are entrainedby the electric field to be redeposited on the target. Taking aspherical coordinate system fixed at some radial location on thetarget surface, r , we can find the maximum velocity angle fromsurface normal, θmax, for a sputtered particle of speed v to travela distance λ and still be within the projected target area using(9) for a given azimuthal angle ψ (on the target surface plane)

sin θmax(r, v, ψ) = −r cos(ψ) +√

r2 cos2(ψ) − (r2 − R2t )

λ(r, v).

(9)

Here we are taking the target radius, Rt , as the maximumradial distance from axis a sputtered particle can be ionized andstill redeposit on the target, however, an ion-confining radialelectric field often exists in cylindrical plasmas which mayeffectively funnel particles ionized at higher radii back to thetarget area. This effect is disregarded for now, but is easilyhandled by replacing Rt in (9) with some larger Reff .

The characteristic distance a sputtered particle travelsbefore being ionized is calculated assuming a Maxwelliandistribution of plasma electrons (with density ne andtemperature Te) using (10), where the cross section forelectron impact ionization of the sputtered particle σ+, is a

7

Plasma Sources Sci. Technol. 23 (2014) 025014 T S Matlock et al

function of relative velocity of the electron and sputteredatom. Equation (10) may equivalently be expressed asλ = v/(ne(r)R+(v)). Integrating over the theoreticaltotal ionization cross-sections of ground state and metastablemolybdenum from Kwon et al we find the atomic velocity-dependent ionization rate is well fit by R+ = 1.978×10−25v2−2.062×10−19v+3.044×10−14(m3 s−1) when Te = 5 eV [30].

λ(r, v)

= v

ne(r)

(me

2πTe

)3/2∫exp

(−mec

2

2Te

)|c − v|σ+(|c − v|) d3c

.

(10)

We assume that the distribution of sputtered particlevelocities can be split into angular and energy-dependentfunctions as f (v) = f0(v)h(θ) so the fraction of the axial fluxof sputtered particles from a given location that redeposit onthe target can be calculated by (11) below, where the radialdependence enters through θmax. An upper bound on theintegration over v is introduced to account for the ability offast sputtered particles to continue a roughly ballistic trajectorydespite the plasma electric field and avoid entrainment backto the target. Here we set vmax equivalent to 20 eV, whichis roughly half the discharge voltage (note that for this smallrange of energies the ionization rate is essentially independentof atom velocity):

�(r) =∫ vmax

0 f0(v)v3 dv∫ 2π

0

∫ θmax

0 h(θ) cos(θ) sin(θ)dθdψ∫ ∞0 f0(v)v3 dv

∫ 2π

0

∫ π/20 h(θ) cos(θ) sin(θ) dθ dψ

.

(11)

In the present experiment, the surface area being sputteredthat can contribute to redeposition on the target area includesboth the target itself and the molybdenum guard plate. Theguard plate is a square with 5.08 cm sides, but is considered asa disk of radius Rg = 5.08/

√π cm to simplify analysis. The

gross sputter yield, γ , can then be estimated from the measurednet sputter yield, γnet, using the radial distribution of incidention flux, �i(r):

γ = γnet∫ Rt

0 �i(r)rdr∫ Rt

0 �i(r)r dr − ∫ Rg

0 �i(r)�(r)r dr(12)

Equation (12) is easily solved numerically with knowledgeof the sputtered particle velocity distribution. Linear cascadetheory of particle sputtering leads to ejected particles with anenergy distribution function, attributed to Thompson [31], of

gT (E, θ) ∝ E cos θ

(E + Eb)3, (13)

where Eb is the surface binding energy which is takenas 6.82 eV for molybdenum [32]. The energy distributionfunction can be split as before to g(E, θ) = g0(E)h(θ)

and converted to velocity space by the relation g0(E) dE =2πv2f0(v) dv, yielding f0 ∝ v(v2 + v2

b)−3. Use of the

Thompson distribution results in (11) reducing to

�(r) = 8vb

3π2

∫ vmax

0

∫ 2π

0

v4

(v2 + v2b)

3(1 − cos3(θmax)) dψ dv.

(14)

The measured incident ion flux profile is fit to a radialdistribution function of the form �i = �i0J0(2.4048r/Rw),where Rw is the radius at which the flux goes to zero (taken as5.08 cm here to match the solenoid inner radius) and J0 is thezero order Bessel function of the first kind, while maintainingthe net ion current to the target found by integrating themeasured profile (�i0 = 2.29 × 1021 m−2 s−1). The electrontemperature is assumed constant across the target (at 5 eV)to yield an electron density profile of the same shape, ne =2�i0J0(2.4048r/Rw)/

√Te/mi. The electron density and ion

flux are inserted in (10) and (12), resulting in a gross sputteryield estimate of 0.145 atoms/ion, a roughly 10% increase overthe net yield. The low redeposition fraction estimated by thismethod is a result of the high energy, most probably, of (13)corresponding to a long mean free path for ionization (3.6 cmon axis) and thus a small solid angle subtending the target area.

The energy distribution function of Thompson is knownto be inaccurate at low incident ion energies (i.e. sub-keV),where narrower distributions peaked at lower energies are oftenfound [33, 34]. Stepanova and Dew suggest an alternativeenergy distribution at low incident energy based on theoreticalconsiderations, shown in (15) below, where mt is the targetatom mass, a ≈ 2 − mt/(4mi), Emax is the maximum energyfor a sputtered atom and Ei is the incident ion energy [34]. Themaximum sputtered particle energy is (Ei/Eth)Eb, where Eth

is the threshold incident energy for sputtering to occur, takenas 46.8 eV for Xe+ on Mo [32]

gS(E, θ) ∝ E

(E + Eb)3exp

[−13

(mi(E cosa θ + Eb)

mtEi

)0.55]

×(

1 − E + Eb

Emax + Eb

). (15)

To continue the simple analysis we neglect the angulardependence of the energy distribution in (15) as a secondorder effect and instead maintain h(θ) = cos θ . The energydistribution of Stepanova and Dew then leads to a gross sputteryield estimate of 0.304 atoms per ion (2.3γnet).

The assumption of a cosine distribution of sputteredparticles also breaks down at low incident energies. To capturethis effect we use a rough model of the angular sputter yieldof molybdenum as h(θ) = cos θ(1 + 2 sin θ), which has thedesired properties of a peak yield 45◦ off normal and a localminimum at 0◦ [22]. This more realistic angular distributionleads to a gross sputter yield estimate of 0.264 atoms/ion(2γnet). A comparison of this value and several gross sputteryields found in the literature is made in table 2, where theaverage value of tabulated yields is 0.24 ± 0.07 atoms/ion,showing close agreement with our adjusted measurement.

The analysis presented allows a simple evaluationof the degree to which redeposition affects sputter yieldmeasurements obtained through mass loss. An accurateredeposition evaluation, however, requires an accurate energydistribution function for sputtered particles, for which we haverelied on theory-based curve fits, and an accurate evaluation ofthe ionization frequency (neR+). For example, a 25% increasein the electron density over the value assumed here results inan estimate of nearly double the sputter yield. This analysisneglects collisions of the sputtered particles with neutral atoms

8

Plasma Sources Sci. Technol. 23 (2014) 025014 T S Matlock et al

Table 2. Gross sputter yield (atoms/ion) for Xe+ on Mo at 200 eV from various sources, with ∗ signifying a model output.

Present Rosenberg [35] Yamamura* [32] Doerner [29] Kolasinski [36] Tartz* [37]

0.264 0.28 0.182 0.162 0.314 0.277

(a) (b)

(c) (d)

Figure 7. SEM images of Mo surface post-exposure showing (a) the interface of the exposed (lower left) and guarded (upper right) regionsof the sample at 68× and (b) 456× magnification. (c) Exposed portion of sample at 929× and (d) guarded portion of sample at 346×magnification.

(neutral xenon densities are lower at the target than the sourcewhere the mean free path is long), magnetic field effects (Mo+

gyroradius is Rt ), and takes the ionization mean free pathbased on ne(r) at the surface rather than a more complicated,angle-dependent, path length integral value of ne. We alsoneglect the incomplete ionization of sputtered Mo flux in oneionization mean free path, but note that though we erroneouslycount the 36% of particles that are not ionized within λ asredeposited we simultaneously discount the particles that areionized in a distance <λ that would exit the projected targetarea after traveling λ.

The molybdenum sample was imaged with a scanningelectron microscope (SEM) after the sputter yield experiment,the results of which are shown in figure 7. SEM imagesof the interface between the guarded portion of the sample

and that exposed to the plasma, such as those of figures 7(a)and (b), show a lighter, more textured surface where the samplewas guarded from ion bombardment. Energy dispersivespectroscopy (EDS) analysis of the sample in the exposedregion indicates a surface composition identical (within 0.6%by weight) to that of a pristine molybdenum sample similarlyanalyzed confirming a lack of significant contamination ofthe target by the plasma source. There is not a discernablelanthanum peak in the energy spectrum of the exposed sampleobtained by EDS.

6. Conclusion

A facility has been designed, constructed and operated thatis intended to provide a stable plasma to a downstream

9

Plasma Sources Sci. Technol. 23 (2014) 025014 T S Matlock et al

target, while avoiding coupling between the plasma–materialinteractions at the target and the operation of the upstreamplasma source. A simplified plasma environment local to thetest article is desired for investigation, both experimentally andnumerically, of the response of micro-architectured materialsto propulsion-relevant plasmas.

The design of the plasma source has been discussed andcontextualized by scale length arguments in section 2.1. Theconfiguration described here has provided desirable operation,but is as yet unoptimized. The use of four independentsolenoids and two flow injection paths allows substantialflexibility during plasma source operation, though componentdimensions and spacings are based on best estimates and adesire for diagnostic accessibility during this developmentalstage. Further testing, coupled with numerical modeling,will be necessary to reach a more finalized design, but themeasurements described herein have shown that the initialoperation of the source is near the desired levels. A modelingeffort is currently underway to aid in optimization of the flowinjection locations and distribution, magnetic field profile, anddevice dimensions.

Ion currents of up to 0.5 A were achieved on a 20 cm2,negatively biased graphite target plate, at a discharge powernear 7.5 kW. Such high target currents were enabled by theaddition of a auxiliary flow injector placed between the cathodeand the anode, providing a source of cold neutrals directly tothe main ionization region. Ion fluxes of over 1021 m−2 s−1

on argon were measured at the target, where spatial Langmuirprobe scans reveal an ion beam size of roughly 2.5 cm diameter.

A sputter yield measurement was performed on an as-received sample of molybdenum that matched results in theliterature well. The accuracy of sputter yields obtained in thePi facility through mass loss may be augmented in the futureby spectroscopic measurements that could aid in estimatingthe rate of material redeposition on sample surfaces. Somediscrepancy exists in the ion currents measured through spatialscans with a Langmuir probe and those collected by thebiased target, the resolution of which should also increase theaccuracy of sputter yield estimates.

Several important plasma parameters remain to becaptured before testing on micro-architectured materials canbegin in earnest. The ion energy distribution, and ion speciesfractions need to be identified at the intended dischargeconditions in order to accurately assess sputtering rates andimportant mechanisms. Spatial profiles of the plasma potentialand electron energy distribution will be necessary to properlyaccount for interactions in the near-surface plasma. Theacquisition of such data is the focus of ongoing work,which also includes an investigation of the plasma fluctuationcharacteristics.

Acknowledgments

This work is funded by the US Air Force Office of ScientificResearch under grant nos FA9550-11-1-0282 and FA9550-11-1-0029 and the UCLA School of Engineering and AppliedSciences. The authors would like to thank Professor NasrGhoniem for support of this effort and David Rivera forproviding the SEM images and EDS analysis.

Appendix. Magnetic field

Figure A1. (a) Maxwell simulation of magnetic field utilized foroperation on argon with close-ups of (b) the target region and (c) theanode region.

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