Measurements of Ar + and Xe + velocities near the sheath boundary of Ar–Xe plasmausing two diode lasersDongsoo Lee, Noah Hershkowitz, and Greg D. Severn Citation: Applied Physics Letters 91, 041505 (2007); doi: 10.1063/1.2760149 View online: http://dx.doi.org/10.1063/1.2760149 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/91/4?ver=pdfcov Published by the AIP Publishing

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Measurements of Ar+ and Xe+ velocities near the sheath boundary of Ar–Xeplasma using two diode lasers

Dongsoo Lee and Noah Hershkowitza�

Department of Engineering Physics, University of Wisconsin at Madison, Madison, Wisconsin 53706

Greg D. SevernDepartment of Physics, University of San Diego, San Diego, California 92110

�Received 31 May 2007; accepted 25 June 2007; published online 27 July 2007�

The Bohm sheath criterion in single- and two-ion species plasmas is studied with laser-inducedfluorescence �LIF� using two diode lasers in Xe and Ar–Xe plasmas. The plasmas are generated ina low pressure unmagnetized dc hot filament discharge confined by surface multidipole magneticfields. Two LIF schemes are employed to measure the argon and xenon ion velocity distributionfunctions near a negatively biased boundary plate. The results show that the argon and xenon ionvelocities approach the ion sound speed of the system near the sheath-presheath boundary andsatisfy the generalized Bohm criterion. © 2007 American Institute of Physics.�DOI: 10.1063/1.2760149�

In weakly collisional plasmas with single-ion species,when the ion collisional mean free path is significantly largerthan the Debye length, the Bohm criterion gives a solution tothe ion’s velocity at the sheath-presheath boundary.1 Apresheath forms in the plasma so as to accelerate the ions tothe Bohm velocity Cs at the boundary,

Cs = �kTe/mi, �1�

where Te is the electron temperature and mi is the ionmass.2,3 Here, Te is assumed to be much greater than the iontemperature Ti. On the other hand, how ions attain their en-ergy and how their velocities are determined at the sheath-presheath boundary in plasmas with multiple-ion specieshave been unsolved questions. Riemann derived a general-ized Bohm criterion for weakly collisional plasmas,4

�i� ni0

ne0�Csi

2

vi02 � 1, �2�

where the i numbers the ion species, the zero subscript refersto the sheath edge, v is the ion drift velocity, n is the iondensity, and ne denotes the electron density. However, thecriterion is still unclear in multiple ion species plasmas sincean infinite number of possible solutions can be found.Among these solutions, two simple solutions are apparent.One is that all ions reach the sheath edge with the samevelocity, the ion sound speed of the system, and the other isthat each ion species has its own Bohm velocity at the sheathedge.

Our previous publications, which employed ion acousticwave �IAW� measurement or a combination of IAW andlaser-induced fluorescence �LIF� measurements of argonions, were consistent with the former solution in two-ionspecies plasmas.5–9 A preliminary particle simulation foundqualitative agreement with the experimental data only nearthe sheath edge.7 However, no experiments were made todirectly measure the velocities of two ions near the sheathedge in the two-ion species plasmas. In this letter, both theAr+ and Xe+ velocities were directly measured in Ar–Xe

plasmas with two tunable diode lasers for the first time. Theresults showed that both the Ar and Xe ions approached theion sound speed of the system near the sheath edge.

A schematic diagram of the experimental arrangement isshown in Fig. 1. The experiments were carried out in a dcmultidipole plasma chamber. The cylindrical surface of thechamber was surrounded by 12 rows of permanent magnetsto enhance the plasma density and uniformity. Neutral argonand xenon were ionized by energetic electrons boiling fromhot thoriated-tungsten filaments biased at −60 V with respectto the grounded chamber wall. A stainless steel plate of7.5 cm in radius was held in the middle of the chamber andbiased at −30 V to generate an ion sheath. The center of theplate had a 1 cm diameter hole, and a razor blade stack wasattached behind the hole to prevent the laser reflection. Theplate was displaced from the optical axis of the light collec-tion assembly to collect the LIF signals as a function ofdistance z from the electrode plate.

Two tunable diode lasers were used in our LIF experi-ments to measure the Ar+ and Xe+ velocities. In the case ofthe Ar+, the laser of 668.614 nm �in vacuum� excited the Ar+

metastable level �3d4F7/2� to the 4p4D5/2 level, and fluores-cence emitted with a wavelength of 442.72 nm �in air� was

a�Electronic mail: hershkowitz@engr.wisc.eduFIG. 1. �Color online� Schematic of the dc multidipole chamber and mea-surement systems.

APPLIED PHYSICS LETTERS 91, 041505 �2007�

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measured during the state change from 4p4D5/2 to 4s4P3/2.10

A recently developed Xe+ LIF scheme with a tunable diodelaser was employed to measure the Xe+ velocity.11 Thescheme utilizes the Xe+ metastable level �5d4F7/2�, which isexcited by a wavelength of 680.574 nm �in air�. The com-plete scheme is 5d4F7/2→6p4Do

5/2→6s4P3/2, and the fluo-rescence has a wavelength of 492.15 nm �in air�. This letteris the first test of the Xe+ LIF scheme to measure the Xe+

velocity distribution function.The LIF measurement system used in this experiment is

described in detail elsewhere.9 The laser passed through aniodine cell to measure the iodine spectra and the Ar+ or Xe+

fluorescence at the same time. The iodine spectra were usedfor a wavelength calibration.12–14 The fluorescence of Ar+

and Xe+ was filtered by a 0.3 nm bandwidth filter centered at442.7 nm �Ar+� and 492.2 nm �Xe+�. The filtered fluores-cence was amplified by a photomultiplier tube and recoveredby a mechanical chopper rotating at 3.1 kHz and a lock-inamplifier. The signal to noise ratio was limited by the tem-poral stability of the laser.11 The LIF signal obtained whilechanging the laser frequency ��� was converted to an ionvelocity distribution function �IVDF� f�vz ,z� from the Dop-pler equation,

vz =c��

�0 + ��

c��

�0= �0�� , �3�

where vz is the ion velocity, c is the speed of light, �0 is theexcitation wavelength, �0 is the excitation frequency�=c /�0�, and �� is the frequency shift ��−�0�. The ionvelocities were calculated from the second moment of theIVDFs,

vz2� = �

−�

�

vz2f�vz,z�dvz �

−�

�

f�vz,z�dvz, �4�

which gives the root mean square velocity vrms= vz2�0.5.

An emissive probe measured the plasma potential �Vp�using the inflection point method in the limit of zeroemission.15 It was moved along the central axis to obtain Vpprofiles. The sheath-presheath boundary was identified at theposition where the voltages of the inflection points changedfrom increasing to decreasing with emission.16 A Langmuirprobe was used to obtain the electron density and tempera-ture in the bulk plasma. The probe data revealed that theelectrons had a bi-Maxwellian distribution in our plasmas.The effective electron temperature �Te� used for Eq. �1� wascalculated as a density-weighted harmonic average of thetwo temperatures,17

1

Te= �nc

ne� 1

Tc+ �nh

ne� 1

Th, �5�

where nc and nh are the cold and hot electron densities, andTc and Th denote the cold and hot electron temperatures,respectively. Ion acoustic waves were generated by a metalmesh immersed in the plasma.9 The ion sound speed of thesystem, which is equal to the IAW phase velocity in the bulkplasma, was calculated from the slope of the receiving Lang-muir probe positions versus the phase delays. Each ion’s ra-tio can be obtained from the measured IAW phase velocity�vph� in the bulk Ar–Xe plasmas expressed as18

vph = ��nAr/ne�CAr2 + �nXe/ne�CXe

2 . �6�

Figure 2�a� shows the xenon IVDFs and Fig. 2�b� plotsthe plasma potential and Xe+ velocity as a function of thedistance z in the pure Xe plasma. The Xe pressure was0.45 mTorr and the filament emission current was 0.75 A.The electron density is 5.4�109 cm−3 and the effective Te is0.61 eV, which yields the Bohm velocity Cs=675 m/s. Thesheath edge is determined to be z=0.32±0.02 cm. The Xe+

rms velocity at the sheath edge is 640±60 m/s, which isclose to its Bohm velocity. The measured IAW velocity vph is685±20 m/s in the bulk, so the three velocities agree withintheir experimental uncertainties.

Figure 3 shows the argon and xenon IVDFs in the Ar–Xeplasma. The argon and xenon partial pressures were 0.5 and0.2 mTorr, respectively. Close to the plate, it is observed thatthe IVDFs are distended on the slow velocity side of thepeak of the distribution. The plasma potential and Ar+–Xe+

velocities calculated from Fig. 3 are plotted in Fig. 4 as afunction of the distance z. The electron density is 8.4�109 cm−3 and the effective Te is 0.69 eV, which givesBohm velocities CAr=1290 m/s and CXe=710 m/s �indi-cated by arrows in Fig. 4�. The IAW velocity vph is measuredto be 1030±50 m/s, so the relative ion concentrations fromEq. �6� are nAr/ne=0.48 and nXe/ne=0.52 in the bulk. Thesheath edge is determined to be z=0.27±0.03 cm. The Ar+

velocity measured from the LIF data at the sheath edge is

FIG. 2. �Color online� �a� Xe IVDFs and �b� the spatial profiles of theplasma potential and Xe+ velocity in the pure Xe plasma as a function ofdistance z from the plate.

041505-2 Lee, Hershkowitz, and Severn Appl. Phys. Lett. 91, 041505 �2007�

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1100±60 m/s, which is close to the vph and is not consistentwith its own Bohm velocity. On the other hand, the xenonion velocity is 940±50 m/s at the sheath edge. This is muchfaster than CXe and is just barely in agreement with the IAWvelocity within experimental uncertainties. From the two ve-locity measurements, it is evident that the results exclude oneof the simple solutions, i.e., the ions do not have their ownBohm velocities near the sheath edge. The data appear tosupport the other simple solution that the ions approach theIAW velocity near the sheath edge. Substituting the mea-sured values into the left hand side of Eq. �2� gives 0.97,which satisfies the generalized Bohm criterion in two-ionspecies plasmas.

This work was supported by DOE Grant No. DE-FG02-97ER54437. One of us �G.D.S.� expresses thanks for thesupport by DOE �DE-FG02-03ER54728� and NSF�CHEM0321326�.

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FIG. 3. �Color online� �a� Ar and �b� Xe IVDFs as a function of distance zfrom the plate in the Ar 0.5+Xe 0.2 mTorr plasma.

FIG. 4. �Color online� Spatial profiles of the plasma potential and Ar+–Xe+

velocities in the Ar 0.5+Xe 0.2 mTorr plasma.

041505-3 Lee, Hershkowitz, and Severn Appl. Phys. Lett. 91, 041505 �2007�

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