Diagnostics and two-dimensional simulation of low-frequency inductively coupledplasmas with neutral gas heating and electron heat fluxesK. N. Ostrikov, I. B. Denysenko, E. L. Tsakadze, S. Xu, and R. G. Storer

Citation: Journal of Applied Physics 92, 4935 (2002); doi: 10.1063/1.1510598 View online: http://dx.doi.org/10.1063/1.1510598 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/92/9?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Two-dimensional particle-in-cell Monte Carlo simulation of a miniature inductively coupled plasma source J. Appl. Phys. 108, 093309 (2010); 10.1063/1.3506536 One- and two-dimensional modeling of argon K-shell emission from gas-puff Z-pinch plasmas Phys. Plasmas 14, 063301 (2007); 10.1063/1.2741251 Diagnostics and Simulation of LowFrequency Inductively Coupled Plasmas AIP Conf. Proc. 669, 71 (2003); 10.1063/1.1593868 Modeling argon inductively coupled plasmas: The electron energy distribution function and metastable kinetics J. Appl. Phys. 91, 3539 (2002); 10.1063/1.1452772 Hysteresis and mode transitions in a low-frequency inductively coupled plasma J. Vac. Sci. Technol. A 18, 2185 (2000); 10.1116/1.1286142

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JOURNAL OF APPLIED PHYSICS VOLUME 92, NUMBER 9 1 NOVEMBER 2002

[This a

Diagnostics and two-dimensional simulation of low-frequency inductivelycoupled plasmas with neutral gas heating and electron heat fluxes

K. N. Ostrikova)

Plasma Sources and Applications Center, NIE, Nanyang Technological University, 1 Nanyang Walk,637616 Singapore and School of Chemistry, Physics and Earth Sciences, The Flinders University of SouthAustralia, Adelaide SA 5001, Australia

I. B. DenysenkoPlasma Sources and Applications Center, NIE, Nanyang Technological University, 1 Nanyang Walk,637616 Singapore and School of Physics and Technology, Kharkiv National University, 4 Svobody sq.,61077 Kharkiv, Ukraine

E. L. TsakadzePlasma Sources and Applications Center, NIE, Nanyang Technological University, 1 Nanyang Walk,637616 Singapore and Optics and Fluid Dynamics Department, RISOE National Laboratory, P.O. Box 49,DK-4000 Roskilde, Denmark

S. Xub)

Plasma Sources and Applications Center, NIE, Nanyang Technological University, 1 Nanyang Walk,637616 Singapore

R. G. StorerSchool of Chemistry, Physics and Earth Sciences, The Flinders University of South Australia,Adelaide SA 5001, Australia

~Received 9 April 2002; accepted 29 July 2002!

This article presents the results on the diagnostics and numerical modeling of low-frequency~;460KHz! inductively coupled plasmas generated in a cylindrical metal chamber by an external flat spiralcoil. Experimental data on the electron number densities and temperatures, electron energydistribution functions, and optical emission intensities of the abundant plasma species in low/intermediate pressure argon discharges are included. The spatial profiles of the plasma density,electron temperature, and excited argon species are computed, for different rf powers and workinggas pressures, using the two-dimensional fluid approach. The model allows one to achieve areasonable agreement between the computed and experimental data. The effect of the neutral gastemperature on the plasma parameters is also investigated. It is shown that neutral gas heating~at rfpowers>0.55 kW) is one of the key factors that control the electron number density andtemperature. The dependence of the average rf power loss, per electron–ion pair created, on theworking gas pressure shows that the electron heat flux to the walls appears to be a critical factor inthe total power loss in the discharge. ©2002 American Institute of Physics.@DOI: 10.1063/1.1510598#

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I. INTRODUCTION

In recent years, there has been a steadily growing inest in the ‘‘fine engineering’’ of low-temperature plasmasnumerous high-tech applications in low-temperature plasenhanced synthesis of nanocomposite and biocompatibleterials, nanoscale assemblies, ultra-fine etching, patterand microstructuring of semiconductor wafers in ultralarscale integration large-scale manufacturing, micromachindevelopment of active elements in photonic devices,many others.1 The fine engineering concept involves the dvelopment of sophisticated means of generating the plato comply with the specific requirements, and controlling tplasma species composition, number densities and fluxe

a!Also with: Division of Microelectronics, School of Electrical and Eletronic Engineering, Nanyang Technological University, 639798 Singap

b!Author to whom correspondence should be addressed; electronicsyxu@nie.edu.sg

4930021-8979/2002/92(9)/4935/12/$19.00

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wards surfaces being processed.2,3 In particular, the commonrequirements for the suitability of low-temperature plasmfor most high-tech applications are high uniformity of ionand active neutral species over the discharge cross seand volume, high product yield with low damage, proceselectivity, and reproducibility.4,5 Sources of inductivelycoupled plasmas~ICPs! with external flat spiral coils6 domeet the above requirements and as such are widely adoby the semiconductor industry as reference plasma reacfor microelectronic circuitry fabrication.

In applications, the operating conditions of ICPs cvary over broad ranges, e.g., the plasma needs to remfairly stable when the gas feedstock pressure varies frofew mTorr to a few atmospheres. However, low-pressureerating regimes still remain favorable for most of the existiapplications of ICPs. It is remarkable that the rf power trafer efficiency in low-pressure ICP devices is usually vehigh thus making it possible to generate dense (ni;8

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5 © 2002 American Institute of Physics

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4936 J. Appl. Phys., Vol. 92, No. 9, 1 November 2002 Ostrikov et al.

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31011– 831012 cm23, whereni is the ion density! plasmaswith moderate rf input powers.4,6–8

Most of the existing modeling and experimental effoare focused on 13.56 MHz inductively coupled plasmwidely used nowadays by the semiconductor and otherdustries. However, sources of lower frequency rf plasmasgaining rapidly increasing attention due to a number ofdisputable advantages. In particular, operating ICP devwith frequencies in the range 0.46–0.5 MHz has provedexpectedly efficient in producing highly uniform, highdensity plasmas in large volumes.9–16 Moreover, low-frequency rf plasma devices have great potentialupscaling9,10 and for controlling the electron energy distribtion functions ~EEDFs!,16 rates of the major gas-phasreactions,17 optical emission intensity, and mode transitiothresholds,15 as well as various thin film deposition14 andnanoassembly18 processes. This certainly makes the sourof low frequency ICPs~LF ICPs! attractive as prototypes olarge-volume commercial plasma reactors.

To date, most modeling studies of the electromagneffects and particle/power balance in ICPs have been musing either the fluid model19–22 or the particle-in-cellmethod23,24 with Monte Carlo collisions,25 or hybridmodels.26 The nonlocal kinetic approach27 can also be usedto simulate the plasma parameters at low gas pressuresremarkable that, despite relative modeling simplicity, tfluid models appear to be able to resolve much of theevant physics with reasonable accuracy within a toleracomputational cost.28

Most recently, it has been recognized that heating ofneutral gas in low-temperature ICP sources during plasprocessing can result in notable distortions of the uniformof the neutral number densities across the chamber leadinvariations of the plasma parameters, composition, temptures, and number densities of the reactive species, as wechemical reaction rates.29 Similarly, gas heating strongly affects the discharge electrodynamics and particle kineticmicrowave surface wave sustained plasmas.30,31

Here, we aim at incorporating the neutral gas heateffects into the two-dimensional~2D! fluid simulation oflow-frequency ICPs and verify the model experimentally uing Langmuir probe and optical emission spectrosco~OES! techniques. Thus, the key internal discharge paraeters, such as the plasma density, electron temperatureEEDF are examined by Langmuir probe diagnostics. Thigh-resolution OES technique is used to study the optemission intensity~OEI! of the abundant plasma speciesdifferent ranges of the working gas pressure. The modework is based on an improved 2D fluid model for an argplasma, accounting for the heating of the neutral gas andelectron heat flux to the walls. The computed electron/number densities, electron temperatures, and optical esion intensities of the excited argon species appear toconsistent with the experimentally measured values. Thependence of the average power loss per an electron–ioncreated on the working gas pressure is studied as well.

The paper is organized as follows. In Sec. II, we descrthe experimental setup, ancillary equipment, and diagnotools. The basic assumptions, equations and boundary co

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tions of the 2D model are presented in Sec. III. In Sec.the profiles of the plasma parameters are computed forferent rf powers, working gas pressures and temperaturescompared with the results of the Langmuir probe measuments. A satisfactory agreement between the results of ocal emission spectroscopy and the computed OEI profilealso reported. The results obtained and pathways for furimprovement of the model and experimental techniquesdiscussed in Sec. V. A brief summary of this work and toutlook for future research are given in the Conclusion, SVI.

II. EXPERIMENTAL DETAILS

Experimental measurements have been carried out inlow-frequency ~;0.46 MHz! inductively coupled plasmasource described in detail elsewhere.12,15 The plasma is gen-erated in a cylindrical, stainless steel vacuum chamber winner diameter 2R532 cm and lengthL520 cm ~Fig. 1!.The chamber is cooled by a continuous water flow in btween the inner and outer walls of the chamber. The top pof the chamber is a fused silica disk, 35 cm in diameter a1.2 cm thick. A 450 l/s turbomolecular pump backed bytwo-stage rotary pump is used to evacuate the plasma chber. The inflow rate and pressure of the working gasregulated by a combination of a gate valve and MKS maflow controllers. The pressure is measured by an MKS Batron capacitance manometer. The operating pressure of agas feedstock is typically maintained in the rangep0

520– 200 mTorr. The global plasma parameters, such aselectron/ion number densities, plasma potential and effecelectron temperature have been estimated by meanstime-resolved rf-compensated single Langmuir probe tenique. The electron energy distribution function has beenculated using the Dryuvestein routine employing the secderivative of the Langmuir probe current-voltagcharacteristics.5 A number of holes in four rectangular sid

FIG. 1. Schematic diagram of the discharge chamber.

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4937J. Appl. Phys., Vol. 92, No. 9, 1 November 2002 Ostrikov et al.

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ports and in the bottom plate of the chamber allow oneinsert the Langmuir probe into the plasma and move itradial and axial directions. The optical emission from tICP discharge has been collected using a light recemounted on different port holes and transmitted via thetical fiber to a SpectroPro-750 spectrometer~Acton ResearchCorporation! with the resolution of 0.023 nm. The OES oexcited neutral and/or ionized argon atoms have been intigated in the wavelength range 350–850 nm. Further deof the Langmuir probe and optical emission intensity msurements can be found elsewhere.12,15 Due to the limitedspace of the article, the experimental results are presentethe computation sections to enable a direct comparison.

III. MODEL DESCRIPTION

A. Basic assumptions

Theoretically, the plasma chamber is modeled by conering a metal cylinder of the inner radiusR and lengthL,with a dielectric disk of widthd and permittivityed atop. Thecomponents of the electromagnetic field are calculatedsuming that the chamber is uniformly filled by the plasmwith the electron/ion number density equal to the spatiaaveraged plasma densityn̄.

The main results of this article are relevant to the prsure range 20–100 mTorr, where the contribution of nonlocollisionless heating is usually smaller than that of cosional heating.32 Our model of the rf power deposition is thusolely based on the assumption of the prevailing ohmic~col-lisional! heating.

To simulate the real environments of some of the plasprocessing experiments14 the study is carried out for elevaterf powers absorbed in a plasma columnPin50.6– 1.4 kW.Consequently, the density of electrons is large, andelectron–electron collisions are expected to strongly afthe EEDFs.

B. Electromagnetic fields

The components of the transverse-electric~TE! electro-magnetic field in the chamber fully filled by the uniformplasma with the plasma densityn̄ are

Bzp5A(

n51

` a1nknH

Dn~TE!zn

H~z!J0~knHr !, ~1!

Brp5A(

n51

` a1ngnH

Dn~TE!hn

H~z!J1~knHr !, ~2!

and

Efp 5 i

v

cA(

n51

`a1n

Dn~TE!zn

H~z!J1~knHr !, ~3!

where

znH~z!5sinh@gn

H~L2z!#/cosh~GnHd!cosh~gn

HL !,

hnH~z!5cosh@gn

H~L2z!#/cosh~GnHd!cosh~gn

HL !,

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Dn~TE!5GnH coth~Gn

Hd!1gnH coth~gn

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a1n5@8p/cR2J22~r1n!#E

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wheref is the azimuthal angle,GnH5@(kn

H)22(v/c)2«d#1/2

and gnH5@(kn

H)22(v/c)2«p#1/2 are the inverse rf field penetration lengths into dielectric and plasma, respectivel12

Furthermore, we haveJj (x) is a Bessel function of thej thorder, J1(r1n)50, kn

H5r1n /R, «p512vpe2 /@v(v1 inen)#

is the dielectric constant of the uniform plasma andvpe

5A4pn̄e2/me is the electron Langmuir frequency. Here,nen

is the electron–neutral collision frequency for momentutransfer,A is a constant, andeandme are electron charge anmass, respectively.

The averaged plasma density is computed from the pticle and power balance equations~see the following subsection! and substituted into the electromagnetic fields Eqs.~1!–~3!, which are continuously updated whenn̄ varies.

C. Particle and power balance

Since the column and inductive coils are fairly uniforin azimuthal direction, the problem is two dimensional athe plasma parameters depend onr andz only. It is assumedthat the ion temperatureTi is equal to the temperature of thworking gasTg . The latter was a variable parameter in tcomputations. The plasma is treated within the ambipomodel that assumes the plasma quasineutrality and the eity of electron and ion fluxes. The effect of negative ionsneglected so that the overall charge neutrality conditionbe written asne5ni[n, wherene is the electron numbedensity.

Accordingly, the particle balance equation for the eletrons or ions is

]n/]t1“•~nv!5nn i , ~4!

wherev is the electron or ion fluid velocity, andn i is theionization rate. We recall that in the ambipolar diffusiocontrolled regime5

v'2¹~nTe!/nmin in ,

where n in'Av21vTi2 /l is the ion–neutral collision fre-

quency, mi is the ion mass, andTi!Te . Here, l51/(nNs in) is the ion mean free path, where we have uss in58310215 cm2, vTi5A8Ti /pmi is the average ion thermal velocity, andnN5p0 /Tg is the number density of neutrals, andTe is the electron temperature. We note thatcomputationTe was self-consistently derived from the setelectrodynamic, plasma particle and rf power balance eqtions. On the other hand, in the experiment,Te was measuredthrough the averaged electron energy^E& asTe52/3 ^E&, asrequired by the Dryuvestein’s routine.5

The rf power balance in the discharge is described b33

3

2ne

]Te

]t1“"qe'2neI e1Sext, ~5!

whereI e is the collision integral for the electrons, andqe'2(5/22gu)neTe /(menen)“Te is the heat flux density withgu5(Te /nen)]nen/]Te . The term Sext denotes the Jouleheating of the electrons by the rf field

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4938 J. Appl. Phys., Vol. 92, No. 9, 1 November 2002 Ostrikov et al.

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Sext'nnemeuosc2 ,

where uosc'ueEfp u/@2me

2(v21nen2 )#1/2 is the time-averaged

oscillation velocity of the electrons in the rf field. The equlibrium state corresponds to setting] t50 in Eqs.~4! and~5!.Our approach is valid for fixed rf power absorption in tplasma column, with

Pin5E0

LE0

R

Sext2pr dr dz,

which also yields the constantA in Eqs.~1!–~3!. The rate ofthe electron–neutral collisionsnen that depends onTe hasbeen determined using the elastic scattering rcoefficients.20

Assuming that the excitation and ionization of the netral gas goes mainly via the electron impact processes,infers that the collision integralI e is equal to the averagpower lost by an electron colliding with a neutral. Accoringly,

I e'~3me /mn!Tenen1(j

n jEj1n iEi ,

wheremn is the mass of the neutral,n j is the excitation ratefrom the ground state to levelj with a threshold energyEj ,andEi is the ionization threshold energy. Stepwise ionizatand excitation processes are not accounted in the presimulation.

For argon gas, the rates for ionization and excitationthe states 4s and 4p are34

n i52.3nN31028Te0.68exp~2Ei /Te! s21,

n4s55.0nN31029Te0.74exp~2E4s /Te! s21,

and

n4p51.4nN31028Te0.71exp~2E4p /Te! s21,

where nN is in cm23, Te in eV, Ei515.76 eV, E4s

511.5 eV, andE4p513.2 eV. It is notable that the abovrate coefficients were calculated by assuming the EEDMaxwellian.34

We now consider the boundary conditions for integratEqs. ~4!–~5!. Because of symmetry, the radial gradientsthe electron temperature and density are equal to zero achamber axis (r 50). At the column edge (r 5R) the radialcomponent of the fluid velocity satisfies the well-knowBohm sheath criterionv r(R,z)5ATe(R,z)/mi .

5 Similarly, atthe side wallsz5zs , wherezs50 or L, we havevz(r ,zs)5ATe(r ,zs)/mi . Likewise, the boundary conditions for heflow are33

qer~R,z!5Te~R,z!~21 lnAmi /me!

3n~R,z!ATe~R,z!/mi , ~6!

and

qez~r ,zs!5Te~r ,zs!~21 lnAmi /me!

3n~r ,zs!ATe~r ,zs!/mi , ~7!

whereqer andqez are the radial and axial components of theat flux density, respectively.

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The set of Eqs.~4!–~5! has been solved numerically. Thdetails of the codes and numerical procedures can be foelsewhere.35,36 The profiles of the electron density, temperture and ion velocity are computed from Eqs.~4!–~5!. Theresulting electron density distribution is used to computespatially averaged plasma densityn̄. Thereafter, the latter issubstituted into Eq.~3! to obtain the azimuthal electric fieldEf

p (r ,z). The computation is initialized using profiles ofn, v,and Te estimated from less accurate analytical or computional results. The computation goes through a numbertemporal steps and is terminated when a steady statreached.

IV. NUMERICAL AND EXPERIMENTAL RESULTS

A. Effect of rf power

We now report on the spatial profiles of the electrnumber density and temperature in the LF ICP obtainedmerically using the 2D fluid model and experimentally usithe Langmuir probe technique.

The calculated 2D profiles of the electron number desity and temperature atp0528.5 mTorr andPin5612.4 Ware shown in Fig. 2. One can see that the electron tempture is maximal near chamber top atr'8 cm. The profile ofTe is linked to the spatial distribution ofEf

p ~3!. Since theelectron temperature is somehow elevated near the fu

FIG. 2. Numerical profiles of the plasma density~a! and electron tempera-ture ~b! at p0528.5 mTorr,Pin5612.4 W, andTg5543 K.

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silica window, the maximum of the plasma density is shiftapproximately 3 cm upwards (z'7 cm) from the centralcross section of the chamber center (z0510 cm). We notethat in the classical case of uniform distribution ofTe , overthe entire chamber, one would expect a cosine-like solutifor the plasma density, with the maximum atz5z0 .5

The computed electron number densities and temptures have been compared with the ones measured byLangmuir probe, with the tip positioned atz55.6 cm andr54.0 cm. Figure 3 displays the computed and measuredues ofne andTe as functions of the input rf powerPin . Thecomputation has been carried out under two different bouary conditions for the electron heat flux:

~i! the electron heat flux towards the boundary is goerned by Eqs.~6! and ~7!; and

~ii ! the electron temperature gradient vanishes atboundary (¹Te50). This boundary condition habeen commonly used in simulations alongside wEqs.~6! and ~7!.19,33

From Fig. 3~a! one can see that the plasma density otained using boundary conditions~i! is closer to the experi-mentally measured one. Indeed, for nonvanishing heatboundary conditions~i!, in the rf power range ofPin

FIG. 3. The computed and measured electron density~a! and temperature~b! at axial z55.6 cm, and radialr 54 cm positions in the chamber. Thcircles correspond to the experimental data. Dotted and dashed curvecalculated for the boundary condition for the heat flux~i! and ~ii !, respec-tively. Other parameters are the same as in Fig. 2.

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,800 W the computed plasma density almost fully recovthe experimental data@Fig. 3~a!#. As the power increase(Pin.800 W), the simulation yields plasma densities somwhat higher than the measured ones. The discrepancypossibly be attributed to consistent elevation of the electtemperature at higher power levels@solid lines with circles inFig. 3~b!#, which cannot be reflected by the ambipoladiffusion particle loss model adopted in our simulatio@dashed and dotted curves in Fig. 3~b!#, where a power-independent value ofTe is normally the case.5 It is thusnatural to expect that the particle loss in the dischargequestion transit to other, than the ambipolar-diffusion cotrolled, mode, with higherTe ~and hence, thermal motionpower loss!, and lowerne at fixed rf power levels. Furtheevidence and discussion on the possible particle loss mconversion follows in Sec. IV B.

We emphasize that the best agreement with the expment is achieved by carefully accounting for nonvanishelectron heat fluxes, thus making the boundary conditions~i!more appropriate for modeling inductively coupled plasmat elevated powers. Specifically, application of~ii ! instead of~i! would lead to higher values of the electron number dsity. Physically, the electron heat fluxes are capable ofmoving a part of the rf power, that could have otherwibeen gainfully used for additional electron-ion pairs creatin the plasma bulk.

Variations of rf power apparently affect the distributioof the electromagnetic fields, which is depicted in Fig. 4.Figs. 4~a! and 4~b! the axial and radial profiles of the computed electric fieldEf

p are shown for different values of thinput power. One can see from Fig. 4 that the electric fiincreases near the chamber top and decreases more rapithez direction when the input power rises. This is consistewith the well-known dependence of the rf field penetratilength on the plasma density.32 It is notable that atz.5 cmthe field componentEf

p is much smaller than atz50. Wethus infer that at larger distances from the window the eltron heat flux is a key factor in controlling the electron temperature.

The normalized axial profiles of the Rf electric fieEf

p (z)/Efp (z50) in the plasma@solid, dashed, and dotte

curves in Fig. 4~c!# have also been compared with the evacated chamber case@dash-dotted curve in Fig. 4~c!#. We notethat the skin lengthls is maximal in the evacuated chambcase and can be estimated from Eq.~5! of Ref. 32. In par-ticular, for low-frequency ICP (v/c!3.83/R) operation, theskin length in the evacuated chamber can be approximateR/3.83).32 However, for large-area and higher-density dcharges satisfying (R@c/vpe), ls is inversely proportionalto ne @Eq. ~7! of Ref. 32#, which is consistent with the data iFig. 4~c!. One can also notice that, while the normalizvacuum and plasma fields are quite different, the rf field slength in the established inductive discharge mode doeschange much with power, which is a common featureICPs.

B. Effect of gas pressure

We now turn to the study of the effect of the working gpressure on the plasma parameters and power loss in

are

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4940 J. Appl. Phys., Vol. 92, No. 9, 1 November 2002 Ostrikov et al.

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discharge. The radial profiles~at z56 cm) of the electronnumber density and temperature computed for four differvalues ofp0 are presented in Figs. 5~a! and 5~b!, respec-tively. For the same conditions as in Figs. 5~a! and 5~b! thenormalized axial profiles of plasma density and electron teperature atr 50 are shown in Figs. 5~c! and 5~d!, respec-tively. The plasma density in Fig. 5~c! is normalized to itsvalue atz56 cm, whereas the electron temperature is nmalized to that atz50.

It is clear from Fig. 5 that the working gas pressustrongly affects the plasma density and electron tempera

FIG. 4. Axial ~at r 58 cm) @~a! and~c!# and radial~at z50) ~b! profiles ofthe dimensional@~a! and~b!# and nondimensional~c! electric fieldEf

p for thefollowing values of the power absorbed by the plasmaPin5612.4 W~solidcurve!, 771.7 W~dotted curve!, and 1202.9 W~dashed curve!, respectively.Dash-dotted curve in~c! corresponds to the evacuated chamber case. Oparameters are the same as in Fig. 2.

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We note that the Langmuir probe data suggest that withinpressure range of our interestne is proportional to the gaspressure for a given electron temperature. Hence, an incrof gas pressure results in elevation of the average pladensity in the plasma column and in diminishing of the eletron temperature. It is also seen that the axial uniformitythe electron temperature is better at lower pressures. Furmore, the nonuniform profiles ofTe affect the electron density distribution in the chamber@Figs. 5~a! and 5~c!#. Indeed,the density peak shifts towards the chamber top as thepressure rises. Atp055 mTorr the peak is close to the discharge center (z'10 cm), which is a clear indication of thambipolar-diffusion controlled regime at low discharge presures. However, atp0550 mTorr the maximum of theplasma density is shifted approximately 4 cm towardschamber top. This can indicate a possible gradual onsetdifferent particle loss mode, similar to what has beenported in Sec. IV A for the elevated rf powers.

The gas pressure also controls the rf power deposiprocess by affecting the average power loss per electronpair. To elucidate the role of the electron heat flux in tplasma column we have separated the average power loselectronu into the collisionaluc and heat fluxu f compo-nents, so thatu5uc1u f . Here

uc51

pLR2n̄ E0

RE0

L

n~r ,z!I e~r ,z!2prdr dz

and

u f51

pLR2n̄ E0

RE0

L

“•qe2pr dr dz

51

pLR2n̄ EsqesdS,

whereS is the total surface area of the rf discharge, andqes isthe component of electron flux density perpendicular tosurface.

The dependence ofuc andu f on the working gas pressure are displayed in Fig. 6~a!. The relative contribution ofthe heat transport component in the total power loss per etron u f /u3100% is shown in Fig. 6~b!. One can see that thheat flux contribution to the total power loss varies fro40% at low pressures (p0;10 mTorr) to 17% at 100 mTorrIt should be noted that bothuc andu f decline with pressureas does the contribution of the heat flux to the total powloss per electron. The results of Fig. 6 clearly confirm timportance of the power loss through the heat flux tochamber walls, which also strongly affects the value ofplasma density~Fig. 3!.

C. Effect of the neutral gas temperature

We remark that the discharge in question is powewith relatively high rf powers. Therefore, in the plasma rgions remote from the water-chilled chamber walls, areaselevated neutral gas temperature may appear. To studyeffect of the neutral gas temperature on the plasma proties,Tg was varied in computations. The radial electron desity and temperature profiles calculated atz56 cm, p0

er

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FIG. 5. Radial electron density~a! and temperature~b! profiles atz56 cm; the normalized axial density~c! and temperature~d! profiles atr 50. Solid, dashed,dotted, and dash-dotted curves correspond top055, 10, 20, and 50 mTorr, respectively. Other parameters are the same as in Fig. 2.

ro-

nsimi-f theting

sity,rate

ed

ed

oinlthe

erveearifts

FIG. 6. Power losses into collisionsuc and due to the electron heat fluxu f

~a!, and the percentage of power lost through the electron heat fluxu f /u ~b!.The parameters are the same as in Fig. 2.

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528.5 mTorr, Pin5612.4 W for the gas temperaturesTg

5300, 543, and 700 K relevant to our previous plasma pcessing and materials synthesis experiments15,17,18 are pre-sented in Figs. 7~a! and 7~b!. One can see from Fig. 7 that aincrease of the neutral gas temperature exerts an almostlar effect on the plasma parameters as a decrease oworking gas density. This can best be understood by nothe apparent linkp05nNTg , which means that the fixedpressure conditions require that the neutral gas denwhich enters the expressions for the most of the reactioncoefficients, has to diminish whenTg rises.

D. Distribution of excited species

We now examine the spatial distribution of the excitargon atoms in the 3p55p configuration. The profile of theexcited atom densityn* (r ,z) can be calculated from37

n* ~r ,z!;n~r ,z!n* ~r ,z!, ~8!

wheren* (r ,z)5n0* (r ,z)exp(2U* /Te) is the excitation ratewith U* '14.5 eV being the threshold energy for the excitlevel. Generally,n0* is a slowly varying function ofTe .38

Thus, evaluatingn* (r ,z), one can assume thatn0* does notdepend onr andz.

The normalized profiles of the excited atoms for the twdifferent sets of our experimental conditions are shownFigs. 8~a! and 8~b!. According to Fig. 8, the resulting spatiadistributions of the excited argon species are governed byelectron density and temperature profiles. One can obsthat the radial profiles of the excited atoms are hollow nthe chamber top. Meanwhile, the maximum of the OEI shtowards the chamber axis as the axial positionz increases.

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Likewise, when the gas pressure grows, the ratio ofn* (r50)/nrmax* decreases, wherenrmax* is the maximal density ofthe excited species along the radius.

We note that the radial OEI profiles have been contently related to the integral~along the chamber axis! of theoptical emission collected by the optical probe via the comator positioned in eight portholes in the chamber bottplate. For this purpose, the resulting local density of thecited species Eq.~8! has been integrated alongz direction.Further details of the OES setup and collection of the emsion can be found elsewhere.15 The emission of the 420.07nm argon line is due to the electron transitions from 5p onto4s levels.39,40The radial distribution of emission intensityshown in Fig. 9~a!, which reveals a good consistency of thcomputation and experimental results. Analogously, integing n* (r ,z) in radial direction, the axial distribution of thintensity has been computed. Experimentally, the optprobe in this case was placed in seven available portholethe side observation port of the chamber.

Figure 9~b! presents a comparison of the axial OEI prfiles obtained experimentally and numerically. One cantice a remarkable agreement of the calculated emissiontensities with the experimental data. However, a mindiscrepancy can be seen in the radial profile in the vicinitythe discharge center. We should also note that the experimreveals that the OEI dips~'20% less than the maximavalue! near the chamber axis. The computation results, c

FIG. 7. Radial profiles (z56 cm) of the electron density~a! and tempera-ture ~b! for different temperatures of the neutral gasTg . Solid, dashed, anddotted curves correspond toTg5300, 543, and 700 K, respectively.

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-

-

-

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r-

rectly following the trend, suggest less remarkable diminiing of the OEI near the chamber axis. The deviation ofcomputed OEIs from the experimental data is certaiwithin the accuracy of the model that assumes independeof n0* on r and z. Further discussion on the matter canfound in the following section.

Figure 10 displays the experimental data on variationthe optical emission spectra with the operating pressure.experiment has been carried out in the pressure rang26–80 mTorr~argon gas flow rates were varied from 4 to 8sccm!. The intensity of the selected argon lines is presenin Fig. 11. In the pressure range concerned it is seenthere is a consistent general trend of diminishing of the Owith p0 . For computation of the dependence OEI (p0), the420.07 nm line of neutral argon has been selected. Thispendence has been computed for the same axial positioz59.6 cm) as in Fig. 11 and is shown in Fig. 12. In calcutions, two different assumptions have been made. Theone assumes thatn* (r ,z);nN and corresponds to the dottecurve in Fig. 11. The dashed curve is obtained assumingn* (r ,z) does not depend on the density of neutrals. Infirst case, the agreement between the theory and experim

FIG. 8. Nondimensional profiles of the number density of the excited aratomsnexc in 3p55p configuration atp0529.3 mTorr,Pin5536 W ~a! andp0540 mTorr, Pin5960 W ~b!. In both casesTg5543 K.

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is satisfactory for the gas pressures exceeding 60 mTorr.latter assumption provides much better consistency ofcomputational and experimental data within the entire raof operating pressures.

FIG. 9. The measured~dots! and computed~solid curve! radial @~a!, sameconditions as in Fig. 8~a!# and axial@~b!, same conditions as in Fig. 8~b!#profiles of the optical emission intensity of 420.07 nm atomic argon lin

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heee

V. DISCUSSION

Here, we discuss the main results obtained and limtions of the modeling and experimental approaches. Geally, the modeling and experimental results appear to begood agreement, especially the data for the electron numdensities@Fig. 3~a!#. However, in certain cases discrepancof the order of few tens of percents still remain@e.g., Fig.3~b! for the electron temperature#. It is thus worthwhile todiscuss possible reasons affecting the accuracy of the slation and experiment.

One of the possible reasons is a higher-than-expevalue of the neutral gas temperature in the proximity ofLangmuir probe, causing excessive overheating of the prtip. In this case, emissive properties of the probe surfshould be carefully accounted for.5 Although we did not sys-tematically measure the neutral gas temperature in this sexperiments, our earlier results give an indication that, incourse of materials synthesis and processing in LF ICPstained with 1–2 kW rf powers, the gas temperature inreactor chamber is maintained in the range ofTg

5500– 700 K.15,17,18The above range of the neutral gas teperatures was used in most of the computations in this wHowever, we do not exclude a possibility of somehohigher, than 700 K, temperatures in the area of rf powdeposition. The probe tip position was, in fact, quite closethe above area, which may have resulted in less accuvalues ofTg at the actual measurement position.

To verify the range of the gas temperatures in ourperiments, we make a comparison with the available dfrom the GEC reference cell withR56.5 cm and L53.1 cm.41 At p0510 mTorr, as the total input power raisefrom 50 to 200 W, the temperature of neutrals increased fr500 to 820 K. At fixed rf input of 200 W,Tg51100 K wasachieved atp0530 mTorr. The estimated rf power densitieWrf in Ref. 41 ranged from 0.121 W/cm3 at 50 W to 0.729

ls-

FIG. 10. Wide scan of the opticaemission spectra in a discharge sutained withPin5630 W rf powers fordifferent gas pressures.

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for

4944 J. Appl. Phys., Vol. 92, No. 9, 1 November 2002 Ostrikov et al.

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FIG. 11. OEI of selected argon lines vs pressurePin5630 W. The position of the optical probe isz59.6 cm.

erW

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W/cm3 at 300 W. In our experiments with the much largchamber, variation of the input power from 600 to 1700reflected changes inWrf from 0.037 to 0.105 W/cm3. Thus,comparison of the neutral gas temperatures at similapower densities~although at quite different experimentconditions including gas pressure! does confirm the reasonability of our results onTg in the processing chamber.

The other limitation of the modeling effort in this woris the apparent inaccuracy in the excitation/ionization rcoefficients calculated for Maxwellian EEDFs. Indeed,our experimental measurements of the EEDF suggest~Fig.13!, the latter is not necessary is the case. Figure 13 presthe variation of the EEDF with input power@Fig. 13~a!# andcomparison with the corresponding Maxwellian EEDF plted using the same values of the electron number densitytemperature as in the experiment@Fig. 13~b!#. One can seefrom Fig. 13~a! that the total area under the EEDF increaswith rf power, which obviously confirms proportionality othe electron/ion number densities to the power absorbed

FIG. 12. Nondimensional optical emission intensity of Ar~I! 420.07 nm line~normalized on its value atp0581 mTorr). Other parameters are the samein Fig. 11. The solid, dashed, and dotted curves correspond to the exment, calculations withn* (nN)5const andn* ;nN , respectively.

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rf

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the plasma column.5 However, the power does not noticeabaffect the shape of the curve. The EEDF maximum is slowshifting towards higher values of the electron energy whPin increases. From Fig. 13~b! one can clearly observe thathe measured EEDF is somehow different from the corsponding Maxwellian one. Specifically, the peak of the msured EEDF is higher and corresponds to larger values ofelectron energy. On the other hand, the Maxwellian EEgives a larger number of high-energy electrons, with theergies exceeding 13–14 eV. From Fig. 13 one can noticethe measured EEDF has a shape similar to the Maxwelshape, with the peak shifted toward higher values of theergy, which is peculiar to Dryuvestein-like EEDFs.5 A pos-sible factor that affects a remarkable deviation of the expmentally measured EEDF from a Maxwellian one is stroelectric fields in the rf power deposition area. Also, notadivergence of EEDFs from Maxwellian ones in the skin layof low frequency ICPs can be attributed to the ponderomtive effect.16

sri-

FIG. 13. The measured (r 54 cm,z55.6 cm) EEDFs for different rf powersat p0528.9 mTorr. Curves 1–3 are plotted forPin5612, 919, and 1203 W,respectively. Comparison of the measured~solid curve! EEDF with theMaxwellian ~dashed curve! one (Pin5919 W).

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4945J. Appl. Phys., Vol. 92, No. 9, 1 November 2002 Ostrikov et al.

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It is notable that the electrons with higher energies pan important role in nonelastic electron-impact processThus, the depletion of the electron number density shouldaccompanied by a decrease of the excitation and ionizarates, which inevitably results in a growth of the electrtemperature should the gas pressure remain the same.

Another factor affecting relatively higher values of thmeasured electron temperature is a lower than conventifrequency of the rf generator. At 30 mTorr, the rate of telectron–neutral collisions is much larger the rf frequen(nen@v). Hence, the electrons receive the energy from thfield as if they are in a dc electric field, acquiring somehhigher thermal energy.

Furthermore, the electron–electron collision ratenee

may not necessarily be large enough to ‘‘Maxwellize’’ thEEDF. It can be estimated asnee;neseeATe /me, wherene

is the electron number density,Te is the electron temperature, andsee;2.9310213Te

22 cm238 is the cross section oelectron–electron collisions. Forne*5.031011 cm23 andTe;2 eV, nee*106 s21, which is the value of the same oder of magnitude as the rates of inelastic collisions.33

Meanwhile, the mean free path of electrons becomlarger at lower pressures. Hence, some part of the elecpopulation receiving the energy from the rf electric field nethe chamber top can affect the EEDF non-locally. In this cthe solution of a nonuniform Boltzmann equation is requirto obtain viable values of the plasma parameters. Finally,discrepancy between the experiment and computationcertainly be attributed to the experimental uncertaintiesthe Langmuir probe signal acquisition and measuremtechniques.

We emphasize that the best agreement between theputed and measured values of the plasma density@Fig. 3~a!#has been achieved in case of taking into account the heatonto the chamber walls (¹TeÞ0). For nonvanishing heaflux boundary conditions, atPin,800 W the numerically ob-tained value of the plasma density is almost the same asexperimental one. As the power increases (Pin.800 W) thecalculated plasma density becomes larger than the onetained in experiment. The discrepancy can be attributedthe observed increase ofTe in the subsequent power rang@Fig. 3~b!#. Accordingly, the elevated electron temperatuforces the plasma density to decrease shouldWrf remain thesame.

The electron number density calculated in case ofvanishing heat flux onto the chamber walls (¹Te50) ap-pears to be 20%–30% larger when the one obtained assing ¹TeÞ0. It is consistent with the results of Fig. 6 sugesting that under prevailing experimental conditionselectron heat fluxes consume up to 20%–30% of the tpower. Thus, not accounting for such a significant power lchannel results in higher, than in the experiment, valuesne .

The remarkable agreement between the experimeand numerical~dashed! curves in Fig. 12 suggests that whethe OEI declines with the gas pressure, it is likely thatexcitation raten* (r ,z) indeed does not depend on the desity of neutrals. Thus, we can presume that the increasthe working gas pressure results in pronounced elevatio

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al

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sonre

de

annnt

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ux

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e

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Tg . This tendency is consistent with the available expemental data.42

Finally, knowledge on the neutral gas temperature aheat fluxes in plasma processing discharges is becominmatter of outmost importance for a number of applicatioIn particular, recent results on growth of nanostructursilicon-based films have convincingly demonstrated the ntral gas temperature as a critical factor in managemenhydrogenated silicon nanoparticles ing ~powder-generating!regime.43

VI. CONCLUSIONS

Results on the diagnostics and numerical modelinglow-frequency~;460 kHz! inductively coupled plasmas arpresented in this article. Comparisons are made betweenexperimental and numerical data, particularly for the electdensity and temperature, which show reasonable agreemPossible reasons for any discrepancies are discussed. A sof the influence of the gas pressure and temperatureplasma density and electron temperature shows that ancrease of working gas temperature has the same effectdecrease of gas pressure. The electron heat flux to the wappears to be a factor in the total rf power loss, as is alsoneutral gas pressure. Measurements were made of the spdistribution of the optical emission intensities of the excitargon species in both radial and axial directions. These sgood agreement with the calculated emission intensities.

The fairly accurate agreement between the numerand experimental results confirms the viability of the 2fluid discharge model in simulating the major parameterslow frequency inductively coupled plasmas. The model cfurther be improved by involving both local and nonlockinetic approaches, stepwise excitation and ionization pcesses, complex gas chemistries including radicals, mollar complexes, and negative ions, details of the process~e.g.,substrate bias, power and mass transport in near-subsareas!, as well as the effects of the near-wall sheapresheath areas.

ACKNOWLEDGMENTS

This work was supported in part by the Agency for Sence, Technology, and Research of Singapore~Project No.012 101 00247!, The Flinders Institute for Research in Scence and Technology, and the Science and Technology Cter in Ukraine~Project No. 1112!. Fruitful discussions of theresults of Langmuir probe measurements with other mebers of the PSAC are gratefully acknowledged.

1F. F. Chen, Phys. Plasmas2, 2164~1995!.2H. Sugai, T. H. Ahn, I. Ghanashev, M. Goto, M. Nagatsu, K. NakamuK. Suzuki, and H. Toyoda, Plasma Phys. Controlled Fusion39, A445~1997!.

3H. Sugai, I. Ghanashev, M. Hosokawa, K. Mizuno, K. Nakamura,Toyoda, and K. Yamauchi, Plasma Sources Sci. Technol.10, 378 ~2001!.

4M. A. Lieberman and R. A. Gottscho, inPhysics of Thin Films, edited byM. Francombe and J. Vossen~Academic, New York, 1993!.

5M. A. Lieberman and A. J. Lichtenberg,Principles of Plasma Dischargesand Materials Processing~Wiley, New York, 1994!.

6J. Hopwood, Plasma Sources Sci. Technol.1, 109 ~1992!; J. H. Keller,Plasma Phys. Controlled Fusion39, A437 ~1997!.

ject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

, 14 Jul 2014 03:10:56

S

ys

A

J

ze

.

rry

.

hnol.

nd

ys.

ol.

, J.

ys.

Y.

H.

4946 J. Appl. Phys., Vol. 92, No. 9, 1 November 2002 Ostrikov et al.

[This a

7H. Sugai, K. Nakamura, and K. Suzuki, Jpn. J. Appl. Phys., Part 133,2189 ~1994!.

8K. Suzuki, K. Nakamura, H. Ohkubo, and H. Sugai, Plasma SourcesTechnol.7, 13 ~1998!.

9M. Tuszewski, Phys. Plasmas5, 1198~1998!.10M. Tuszewski, IEEE Trans. Plasma Sci.27, 68 ~1999!.11I. M. El-Fayoumi and I. R. Jones, Plasma Sources Sci. Technol.7, 162

~1998!.12S. Xu, K. N. Ostrikov, W. Luo, and S. Lee, J. Vac. Sci. Technol. A18,

2185 ~2000!.13K. N. Ostrikov, S. Xu, and M. Y. Yu, J. Appl. Phys.88, 2268~2000!.14S. Xu, K. N. Ostrikov, Y. Li, E. L. Tsakadze, and I. R. Jones, Ph

Plasmas8, 2549~2001!.15K. N. Ostrikov, S. Xu, and A. B. M. Shafiul Azam, J. Vac. Sci. Technol.

20, 251 ~2002!.16V. A. Godyak, B. M. Alexandrovich, and V. I. Kolobov, Phys. Rev. E64,

026406~2001!.17E. L. Tsakadze, K. N. Ostrikov, N. Jiang, R. Ahmad, and S. Xu, Int.

Mod. Phys. B16, 1143~2002!.18N. Jiang, S. Xu, K. N. Ostrikov, J. D. Long, J. W. Cai, and Z. L. Tsakad

Int. J. Mod. Phys. B16, 1132~2002!.19H. M. Wu, B. W. Yu, A. Krishnan, M. Li, Y. Yang, J. P. Yan, and D. P

Yuan, IEEE Trans. Plasma Sci.25, 776 ~1997!.20R. A. Stewart, P. Vitello, D. B. Graves, E. F. Jaeger, and L. A. Be

Plasma Sources Sci. Technol.4, 36 ~1995!.21C. M. Ryu and M. Y. Yu, Phys. Scr.57, 601 ~1998!.22M. Y. Yu and L. Stenflo, Nature~London! 384, 224 ~1996!.23N. F. Cramer, J. Phys. D30, 2573 ~1997!; T. A. van der Straaten, N. F

Cramer, I. S. Falconer, and B. W. James,ibid. 31, 191 ~1998!.24S. V. Vladimirov, S. A. Maiorov, and N. F. Cramer, Phys. Rev. E63,

045401~2001!.25M. M. Turner, Phys. Rev. Lett.71, 1844~1993!.26H. M. Wu, Plasma Sources Sci. Technol.9, 347 ~2000!.

rticle is copyrighted as indicated in the article. Reuse of AIP content is sub

131.181.251.131 On: Mon

ci.

.

.

,

,

27U. Kortshagen, C. Busch, and L. D. Tsendin, Plasma Sources Sci. Tec5, 1 ~1996!.

28S. A. Maiorov, S. V. Vladimirov, and N. F. Cramer, Phys. Rev. E63,017401~2001!.

29D. B. Hash, D. Bose, M. V. V. S. Rao, B. A. Cruden, M. Meyyappan, aS. P. Sharma, J. Appl. Phys.90, 2148~2001!.

30J. Henriques, E. Tatarova, F. M. Dias, and C. M. Ferreira, J. Appl. Ph90, 4921~2001!.

31H. Sugai, I. Ghanashev, and M. Nagatsu, Plasma Sources Sci. Techn7,192 ~1998!.

32V. Vahedi, M. A. Lieberman, G. DiPeso, T. D. Rognlien, and D. HewettAppl. Phys.78, 1446~1995!.

33V. E. Golant, A. P. Zhilinskii, and I. E. SakharovFundamentals of PlasmaPhysics~Wiley, New York, 1980!.

34S. Ashida, C. Lee, and M. A. Lieberman, J. Vac. Sci. Technol. A13, 2498~1995!.

35N. A. Azarenkov, I. B. Denysenko, A. V. Gapon, and T. W. Johnston, PhPlasmas8, 1467~2001!.

36I. B. Denysenko, A. V. Gapon, N. A. Azarenkov, K. N. Ostrikov, and M.Yu, Phys. Rev. E65, 046419~2002!.

37I. Peres, M. Fortin, and J. Margot, Phys. Plasmas3, 1754~1996!.38L. M. Biberman, V. S. Vorob’ev, and I. T. Yakubov,Kinetics of Non-

equilibrium Low-Temperature Plasma~Nauka, Moscow, 1982! ~in Rus-sian!.

39D. R. Lide,CRC Handbook on Chemistry and Physics, 78th ed.~ChemicalRubber Corp., New York, 1997!.

40C. M. Ferreira and J. Loureiro, Plasma Sources Sci. Technol.9, 528~2000!.

41G. A. Hebner, J. Appl. Phys.80, 2624~1996!.42V. Lisovsky ~private communication!.43A. Hadjadj, L. Boufendi, S. Huet, S. Schelz, P. Roca i Cabarrocas,

Estrade-Szwarckopf, and B. Rousseau, J. Vac. Sci. Technol. A18, 529~2000!.

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, 14 Jul 2014 03:10:56