Excited state density distributions of H, C, C 2 , and CH by spatially resolved opticalemission in a diamond depositing dc-arcjet reactorJ. Luque, W. Juchmann, E. A. Brinkman, and J. B. Jeffries

Citation: Journal of Vacuum Science & Technology A 16, 397 (1998); doi: 10.1116/1.581037 View online: http://dx.doi.org/10.1116/1.581037 View Table of Contents: http://scitation.aip.org/content/avs/journal/jvsta/16/2?ver=pdfcov Published by the AVS: Science & Technology of Materials, Interfaces, and Processing Articles you may be interested in Measurement and modeling of Ar H 2 C H 4 arc jet discharge chemical vapor deposition reactors II: Modeling ofthe spatial dependence of expanded plasma parameters and species number densities J. Appl. Phys. 102, 063310 (2007); 10.1063/1.2783891 Laser-induced fluorescence of cyclohexadienyl (c- C 6 H 7 ) radical in the gas phase J. Chem. Phys. 121, 6861 (2004); 10.1063/1.1791634 Dynamics of the C + C 2 H 2 reaction from differential and integral cross-section measurements in crossed-beamexperiments J. Chem. Phys. 116, 5603 (2002); 10.1063/1.1456508 Spatial density distributions of C 2 , C 3 , and CH radicals by laser-induced fluorescence in a diamond depositingdc-arcjet J. Appl. Phys. 82, 2072 (1997); 10.1063/1.366017 Laser-induced fluorescence of the CH 2 CFO radical J. Chem. Phys. 106, 6302 (1997); 10.1063/1.473641

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Excited state density distributions of H, C, C 2, and CH by spatially resolvedoptical emission in a diamond depositing dc-arcjet reactor

J. Luque, W. Juchmann,a) E. A. Brinkman,b) and J. B. Jeffriesc)

Molecular Physics Laboratory, SRI International, Menlo Park, California 94025

~Received 30 September 1997; accepted 12 December 1997!

Spatially resolved optical emission spectroscopy is used to investigate excited species in a dc-arcjetdiamond depositing reactor. Temperature measurements indicate a cold plasma with electrons,excited states, and gas in nonthermal equilibrium. The H, C, C2, and CH excited state numberdensities decrease exponentially with the distance from the nozzle and have a pronounced increasein the shock structure above the substrate. The H emission increases throughout the boundary layerto the substrate surface, whereas emission from other species has a maximum in the boundary layerand then decreases again towards the substrate. The reconstructed radial distribution of excited stateconcentrations are Gaussian, with the C and C2 distributions broader than the H and CH ones. Theoptical emission is calibrated with either Rayleigh scattering or laser-induced fluorescence to furnishabsolute number densities. We find all the excited species to be present in concentrations two ormore orders of magnitude smaller than the corresponding ground states measured in the samereactor and conditions. We find that C2(d-a) emission intensity correlates well with laser-inducedfluorescence measurements of C2(a) concentration in the arcjet plume. Ground state concentrationsof the other species do not vary as their emission intensity except near the substrate, where thevariations of CH(A-X), CH(B-X), and C2(d-a) emission intensities are good monitors of thecorresponding concentration changes. ©1998 American Vacuum Society.@S0734-2101~98!06102-8#

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I. INTRODUCTION

Low-pressure dc-arcjet reactors are attractive sourcechemically reactive gas flows for spray coating and chemvapor deposition~CVD!. Arcjet reactors have demonstratediamond growth with rates approaching 1 mm/h,1 at least tentimes faster than in other reactors.2 This rapid growth rate isa consequence of the large fraction of dissociation ofhydrogen feedstock gases in the reactive gas flow fromarcjet discharge.3

Gas mixtures containing argon, hydrogen, and methare commonly used to produce diamond films in plasmaactors. The chemistry in most diamond CVD is dominaby charge neutral reactions of ground state radicals andoms formed in the discharge, and there are models predicC atoms and CH3 radicals4,5 as well as C2 and C2H2

6,7 as thedominate precursors to diamond growth. In order to charterize the reactive environment for diamond CVD, expements to determine the ground state concentration of H,8–10

C,11 C2,12,13C3,

13 CH,13–17CH3,11,14,15,18–20and C2H2

20 havebeen undertaken using nonintrusive optical diagnostics teniques in a wide variety of diamond producing reactors.though this research has increased our understanding ofmond CVD,21 the methodology is of limited use for real-timindustrial process control, as such careful, quantitative, labased measurements require expensive, high maintenequipment with highly trained technicians. Optical emiss

a!Permanent address: Physikalisch Chemisches Institut, Universita¨t Heidel-berg, Germany

b!Permanent address: IBM, San Jose, Californiac!Electronic mail: Jeffries@mplvax.sri.com

397 J. Vac. Sci. Technol. A 16 „2…, Mar/Apr 1998 0734-2101/98/

tribution subject to AVS license or copyright; see http://scitation.aip.org/ter

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spectroscopy~OES! is another nonintrusive method, witquite simple data collection and straightforward automatiUnfortunately optical emission arises only from atoms amolecules in electronically excited states, and interpretaof the optical emission signal requires an understandingthe link between excited and ground state concentrationsspite of these limitations, OES is widely used for real-timmonitoring in plasma processing.

The diamond film quality varies dramatically with depsition method and conditions and a large body of reseahas been undertaken to develop a simple relationshiptween OES from a species, the ground concentration ofspecies, and the quality of deposited diamond film. KleiDouwelet al.22 found a correlation between C2 emission andthe diamond film quality for material grown in a oxyacetlene flame. In a microwave plasma reactor, Langet al.23

found the diamond film quality to correspond to H atoactinometry24 measurements. Gruenet al.25 found OES sig-nals from C2 emission in a microwave plasma correlate wthe growth rate, but not the emission from either H or CH.a hot filament reactor, Cuiet al.26 observed emission from Hand CH1 relate to high quality diamond, and CH emissionindicate the presence of amorphous carbon films.

In CVD dc-arcjet reactors, the diamond film grows-otemperature controlled substrates from hydrogen arplumes with a trace (,1%) of hydrocarbon. Although, optical emission from the reactive plumes of dc arcjets has bstudied, all of the published work focuses on temperatdetermination from the rotational and vibrational distribtions of the excited molecules. Raiche and Jeffries27 reportemission from CH(A-X), CH(B-X), CH(C-X), C3(A-X),

39716 „2…/397/12/$10.00 ©1998 American Vacuum Society

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and C2(d-a) in a dc arcjet~1 kw, 220 Torr!, and do not findthermalization between excited and ground states of2.Reeve and Weimer28 observe CH(A-X) and C2(d-a) emis-sion, and find quite different vibrational and rotational teperatures in CH(A) and C2(d). The OES study by Cubertafon et al.29 reports a rotational temperature of CH(B) near2700 K along the plume of their arcjet~3–5 kW,;50 Torr!which is nearly three times less than their C2 vibrationaltemperature of 7500 K. They also find quite different vibrtional and rotational temperatures from the excited C2(d).Brinkmanet al.30 find nearly the same C2(d) rotational andvibrational temperatures as Cubertafon in their arcjet~1.6kW, ;25 Torr!. Analysis of the spatial distributions of themission intensities led them to suggest that the excC2(d) was formed by chemical reactions and CH(A) byelectron impact.

In this work, we present spectroscopic observations fra dc-arcjet reactor during diamond CVD using the sameerating conditions30 where diamond film grows at 50mm/hon a water cooled molybdenum substrate. The diamondis well faceted with primarily~111! morphology, and theRaman spectrum of the film shows no trace of graphite ctent. We have characterized the arcjet plume in previlaser-based and probe measurements. Using quantitlaser-induced fluorescence~LIF!, we determined the numbedensities and spatial distributions of CH, C2, C3

radicals13,31,32 and H atoms in the ground state.10 The gastemperature13,30distribution was previously determined fromLIF measurements of rotational distributions of ground stmolecules. The flow velocity10 was measured from the Doppler shift of LIF from NO seeded into the flow. Langmuprobe was used to determine the electron temperatureion density.33 We report here the quantitative, spatially rsolved optical emission of H, C, C2, and CH. From thesemeasurements, we determine excited state concentracorrelate the excited state concentration distribution withrespective ground state distribution and discuss the chemroles and excitation mechanisms.

II. EXPERIMENTAL METHOD

The CVD reactor, diamond deposition, and details ablaser measurements have been describedviously.10,13,30,33,34An arc ~1.6 kW, 12 A, 140 V! is struck ina mixture of H2/Ar ~0.9:1 at 6.9 slm total flow and six atmospheres pressure!; the effluent from this arc expands througa converging/diverging nozzle into a low-pressure reac~typically 25 Torr!. Methane~;0.5% of the H2 flow! is in-jected in the flow in the diverging section of the nozzle. Texpanding gas forms a luminous plume approximately 1in diameter which impinges on a water cooled molybdensubstrate 38.2 mm from the nozzle. Diamond grows at ne1 mm/min with a well faceted~111! morphology with a Ra-man spectrum free from graphitic features.10

The optical emission from the arcjet plume is collectwith a lensf /6, spatially filtered with a 1 mmaperture, andfocused with another lens identical to the first one intomonochromator selected to fit the requirements of the m

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surement. For rotationally resolved scans, a Heath mochromator is used~f /7, 0.35 m focal length, 250 or 500 nmblaze gratings!. Laser-based measurements require a detion bandpass with equal response for any rotational levethe selected vibrational band; here we construct a trapezobandpass with 30 nm full width at half maximum~FWHM!from a Bausch–Lomb high intensity monochromator~f /6,0.2 m focal length, 500 nm blaze grating! using a narrowfront slit and a wide back slit. The signal is detected by1P28 photomultiplier, preamplified (310), and averagedwith a boxcar integrator~Stanford Research Systems SR250!. During the calibration procedures of the emission snal, the voltage in the photomultiplier power supply and bocar settings were kept identical to those used for the optemission measurements. A SC Technology Plasma Chetry Monitor 401, consisting of a spectrograph with a gateintensified, photodiode array of 512 elements, is used asoptical multichannel analyzer to obtain emission spectramultaneously in the range from 200 to 1000 nm with a 4 nmbandwidth. The relative spectral response of this instrumis calibrated using standard lamps~Optronics Laboratories!,tungsten in the visible and deuterium in the ultraviolet. Ttwo different lamps provide an overlapping region from 3to 350 nm where we find good (,5%) agreement betweethe two independent calibration measurements.

The absolute intensity of the optical emission is calibraby both Rayleigh scattering and laser-induced fluoresceof a known gas concentration and composition. A XeCl ecimer laser~Lambda Physik EMG 103! pumping a dye laser~Lambda FL 2002! is the source of vertically polarized laselight to excite CH(B-X) or provide a Rayleigh scatterinsource. The 14 ns laser pulses have a spectral bandwid0.2060.02 cm21 at 430 nm, measured with a monitor etaloSome measurements around 315 nm, were made with aquency doubled PDL-1 dye laser~bandwidth ;1 cm21,pulse length;7 ns!, pumped by a Quanta Ray GCR-Nd:yttrium–aluminum–garnet~YAG! laser. A high preci-sion energy meter~Rj-7200, Laser Precision Corp.! monitorsthe laser pulse energies from 10 nJ to 1 mJ.

III. QUANTITATIVE OPTICAL EMISSION

The optical emission signal of a given electronic trantion between an excited stateu and the ground stateg duringa time intervaltg , is equal to

SOES5Aug•nexc•Vfl•V

4p•e•h•tg , ~1!

where Aug is the Einstein emission coefficient of the oserved vibrational band (s21!, nexc is the steady state numbedensity of excited species (cm23), and Vfl is the observedvolume. The remaining factors are given by the optics aelectronics in the detection of the fluorescence; whereV isthe solid angle,e is the transmission efficiency of the opticand h the photoelectric conversion. The emission from ttotal production of electronically excited species,nnascent, isreduced by collisional quenching and predissociation;steady state concentration of excited species

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nexc5nnascentF, where F5A/(A1Q1P) is the quantumyield, Q the quenching rate (s21), andP the predissociationrate (s21). We note thenexc is the excited state number desity which is measured in absorption.

One of the main problems related to OES absolute msurements is the limited spatial resolution of optical emsion. When a single lens or a fiber optic are utilized to collthe emission from the reactor, the volumeVfl is defined bythe lensf number or the fiber optic acceptance angle, andboth cases gives poor results. Using optical spatial filters,obtain a line of sight measurement of the emission. Howeonly when the spatial distribution of emitters is homogneous and the size of the plasma is known~d, in cm!, thenumber density in the line of sight volume is

nexc51

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nexc~x!dx5Nexc

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whereNexc is the number of emitters,Vfl5Afld, Afl5pr 2 isthe collection cross section given by the spatial filter,d is theplasma length. The plasma size and emitter distributionusually unknown, and we can only obtain integrated coludensities (emitters/cm2). This is the same problem that occurs for absorption measurements, and it is solved for geetry with cylindrical symmetry through Abel’s inversionThe arcjet plume is cylindrically symmetric and the spatdistribution of the different species can be reconstrucfrom the set of measurements taken along the perpendicaxes to the line of sight. There are many proposed methfor the computation of Abel’s inversion. In this work, whave followed the method proposed by Buieet al.,35 whichfits the data to a polynomial with even powers. The paraeters are the input to an analytically derived form of the Ainversion. We will find below that all the species haGaussian radial distributions in the arcjet plume. The pnumber densities are fit by Eq.~2! with the parameterdequal to the FWHM of the reconstructed Gaussian distrition.

The instrumental factors~V,e,h! in Eq. ~1! can be deter-mined by other optical measurements which includesame set of parameters. For example, Rayleigh scatterina gas with the same optical collection given by36

SRay5n•

EL

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]V DV•e•h•

V

AL, ~3!

wheren is the number density of the gas,n is the frequencyof the scattered photon (cm21), (ds/dV) is the averagedcross section,EL is the laser energy (J), V is the collectionvolume, andAL is the laser cross section, set by apertuapproximately equal toAfl. From the plot of Rayleigh scattering signal versus the product of laser energy and presswe determine the experimental factorVehV/AL .

The optical emission can also be calibrated by comparito the signal from a known excited state number density.can be used if the ground state number density of one ofplasma species is known as well. With low laser specirradiance to insure linear excitation and full time integrati

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of the fluorescence signal, the relationship between thetected LIF signalSLIF and the molecular number densityn0

is given by31,34

SLIF5n0• f B•

B

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f B , the Boltzmann factor, is the fraction of molecules in tprobed quantum state and is calculated from the temperadetermined by LIF excitation scans.B is the absorption co-efficient for the rotational transition excited (cm2 J21 s21),EL is the laser energy (J!, G is the lineshape overlap integraDn is the laser bandwidth (cm21), the ratio teff /t0 is thefluorescence quantum yield withteff as the effective lifetimeincluding collisional quenching, andt0 is the radiative life-time. Ffl is the fraction of the fluorescence collected in tspectral bandwidth of the detector.

The LIF signal is produced only in the laser probed vume and can be related to the OES volume. AssumingLIF measurement excites a rotational line in the same etronic transition observed in optical emission

SLIF

SOES5

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nexc•

teff

tg•

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at a given laser energyEL , and with integration timetg longenough to integrate the whole laser-induced fluorescencenal or the Rayleigh signal, we can estimate the steady snumber density of the corresponding excited state (nexc).

IV. RESULTS AND DISCUSSION

The wavelength resolved optical emission spectra frthe arcjet plume varies dramatically as the feedstock gachanged. When the feedstock is pure argon, we see stemission features from the Ar and weak lines from Ar1.With a mixture of argon and hydrogen, we see a few ofstrongest Ar lines, but the dominant emission is from tBalmer series of atomic hydrogen~Fig. 1!; we are not able todetect the vacuum ultraviolet Lymana to compare its emis-sion intensity. Adding just 0.5% methane to the flow agaalters the emission from the plasma plume, we find signcant atomic emission from H atoms in the Balmer seriesatoms, and very weak Ar I lines. There is strong emissfrom CH(A-X), CH(B-X), CH(C-X), and C2 (d-a) bands.The remaining structure in the spectra is assigned to mecules as well. Emission from two other C2 electronic sys-tems is assigned: the C2(D-X) Mulliken bands at 232 nmand the C2(C-A) Deslandres-D’Azambuja bands near 3nm.

The molecular emission becomes more dominant dostream from the expansion nozzle; Fig. 2 shows the spectat z520 mm which is roughly halfway between the nozzand the substrate. The optical emission spectrum also va

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with radial position in the plume; the upper panel showsspectrum from the center of the plume which is dominaby CH emission with only a small underlying broadbavisible background. Figure 2 lower panel is taken at a radof 5.5 mm where the total emission intensity scale has bmultiplied by 20. Here we see the dominant structured emsion is from the C2 Swan bands (d-a). In addition, thebroadband visible background contains most of the emisintensity. The C3 radical ground state has its maximum itensity at large radius in the cylindrically symmetric plume32

similarly at large radius near the edge of the plume, we idtify C3 emission as the 405 nm feature of the C3(A-X) ~000!-~000! band, and we infer C3 as the source of the less strutured background emission between 330 and 500 nmaddition to C3 emission, the visible background likely includes contributions from other hydrocarbon fragment lC2H

37 or carbon clusters C4 and C5 by analogy to observations in neon matrices.38 This speculation is further reinforced byab initio calculations;38,39 of both radicals whichfind electronic bands in the visible region, near 500 nHowever, C4 and C5 have not been spectroscopically iden

FIG. 1. Upper panel: Optical emission spectrum~4 nm FWHM!, taken nearthe nozzle in a dc arcjet with 25 Torr reactor pressure, and 55% Ar andH2 feedstock at 1.6 kW. Lower panel: Electron temperature from atohydrogen Balmer series.

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fied in gas phase yet. In addition, we observe light froOH(A-X) and NH(A-X) at 308 and 336 nm, respectivelythese molecules are present in the plume either from imprities in the feedstock gases or minor leaks in the vacuusystem. The only ion observed is emission assignedCH1(A-X) as it can be seen in Fig. 3. Details of the moimportant species and transitions identified can be foundthe Table I.

A. Temperatures

The energy distribution in the plasma is an importacharacterization parameter. We determine excited state tperatures from the rotational~or vibrational! distribution ofmolecular optical emission, the ground state~gas! tempera-ture from LIF measurements of the ground state rotationdistribution, and electron temperature from the atomic hdrogen excited state distribution. Atomic hydrogen emissilines are a good measure of the electron temperature welectron impact is the excitation mechanism and the excition energies are all in the tail of the electron energy distbution. Assuming the various atomic hydrogen excited sta

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FIG. 2. Optical emission spectra~4 nm FWHM!, taken 20 mm downstreamfrom the arcjet nozzle with the standard conditions. Upper panel. Centeplasma plume. Lower panel. At a radius of 5.5 mm from the center.

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have similar excitation cross sections and collisional quening rates, the atomic hydrogen emission intensity from elevel is proportional to the number density of electronsthat energy. The lower panel in Fig. 1 shows the Boltzmaplot of the atomic hydrogen Balmer series. The relationsbetween the line intensitiesI i and temperatureT is

lnS I i

giAi jD52

Ei

kT1C, ~7!

wheregi is the degeneracy of the statei , Ai j the emissioncoefficient, andEi the energy.40 When we calculate an emission temperature for the Ha , Hb , Hg , and Hd with a feed-

FIG. 3. Optical emission spectrum from the plasma plume on the centewith z520 mm~0.1 mm FWHM! showing emission from CH(B), CH1(A),C2(C), and atomic C and H in the lower panel. Upper panel shows simtion of CH(B) with a rotational temperature of 2500 K, and vibrational2100 K.

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stock mixture of only Ar and H we obtain a temperature1.2560.25 eV near the nozzle~Fig. 1, bottom!, in goodagreement with earlier Langmuir probe measurementselectron temperature.33 Although some slight systematic deviations from a linear Boltzmann plot are observed in Fig.these are minor and can be attributed to either quencheffects or nonequilibrium features of the plasma.41 The addi-tion of methane lowers the temperature to;1 eV(;11 600 K).

We examine the rotational distribution in the exciteCH(B) and CH(C) and compare the results to our previoresults30 for excited CH(A) and C2(d). The emission is analyzed by spectral simulation with LIFBASE,42 including bothpredissociation and collisional quenching. These correctiare important to determine the nascent population distritions, especially in the case of the CH(C). From time re-solved LIF, we measure the quenching of the CH(B)31 to be1 ms21 Torr21, and found no rotational dependence of thcollisional quenching rate. There is no data for the CH(C)state, but there is evidence of its quenching with H2 that isfaster than the quenching of the CHA andB states,43,44 andwe estimate a quenching rate of;2 ms21 Torr21. Predisso-ciation is strong in CH~B, v850, N8.15!, CH~B v851,N8.6!,45 and for all levels of CH(C),46,47 varying with ro-tational and vibrational quantum numbers.

Emission from CH(B) is prominent in the wavelengthdispersed optical emission in the region 384–410 nm shoin the lower panel of Fig. 3. This emission is collectedmm downstream of the nozzle from the center of the plumThe upper panel is a simulation of the CH(B) ~0,0! and~1,1!bands with a rotational temperature of 2500 K. We find texcited CH~B, v850! state is well fit by rotational temperatures between 2300 and 2700 K. These temperatures arestantially lower to the ones measured30 in CH(A) and C2(d),and in good agreement with measurements of CH(B) of Cu-bertafonet al.29 in a similar reactor. In addition, the rotational distributions of CH(B) produced by electron impacon CH4 and C2H2 near the appearance potential (;14 eV)

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TABLE I. Summary of the identified species, electronic transitions, and their dominant band or line posAlso, a comparison of the ground and excited states number densities in the middle of the arcjet plummm from the nozzle.

Species Transition

Linepositions

~nm!

Emissioncoefficient

(s21)

Excited statenumber density

(cm23)

Ground statenumber density

(cm23)

H 3n22n 656 4.43107 ~Ref. 40! 107 331016 ~Ref. 10!4n22n 486 8.43106 107

C 1P0-1D 193 2.43108 ~Ref. 40! 53106 not measured1P0-1S 247 3.43107

CH A-X(2D-2P) Dv50 431 1.83106 ~Ref. 47! 1.23109

B-X(2S2-2P) Dv521,0 387 33106 ~Ref. 47! 33108 3.531012 ~Ref. 13C-X(2S1-2P) Dv50 314 13107 ~Ref. 64! 63107

CH1 A-X(1P-1S1) Dv51,0 396, 423 2.53106 ~Ref. 65! ;33107 not measuredC2 d-a(3Pg-3Pu) Dv51,0,21 465, 480, 515 13107 ~Ref. 13! 23108 331010 ~Ref. 13!

D-X(1Su1-1Sg

1) Dv50 231 5.53107 ~Ref. 66! ;53105

C-A(1Pg-1Pu) Dv51,0,21 360, 385, 410 3.23107 ~Ref. 66! ;23106

C3 A-X(1Pu-1Sg1) 405 53106 ~Ref. 13! ,108 ;331012 ~Ref. 1

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have been reported in the literature, with temperaturesv850 of ;2600 and;2300 K, respectively,48,49reinforcingthe hypothesis that CH(A) and CH(B) are products of electron impact dissociation.

Figure 4 compares the wavelength resolved emissionCH(C) with our simulation using a rotational and vibrationtemperature of 5500 K. All of the CH electronic states hadifferent rotational temperatures, 5500 K for CH(C), 2500 Kfor CH(B), and 3500 K for CH(A). Figure 5 shows the LIFexcitation spectrum of CH(C-X) taken in the same positioin the plume which compares well with the simulation atemperature of 2200 K in good agreement with previoground state LIF measurements13,30,31with the same reactoconditions. These earlier experiments found the LIF rotional distribution of ground state CH to be a good measof the gas temperature. Thus, we find the dc-arcjet plumenonequilibrium plasma with different thermal distributionfor the electrons, molecular excited states, and the bulk

B. Excited state number densities

The number densities are proportional to the ratiotween band areas and emission coefficients in spectrallyrected scans like the ones in Fig. 2. The optical detectiocalibrated to determine quantitative excited state numdensities from the optical emission. We use Rayleigh stering to calibrate the optical emission signal collection. Tscattering was produced with a laser wavelength of 388in the same spectral region where the CH(B-X) emissionoccurs. The calibration of the emission signal is perform20 mm downstream from the nozzle, with the plasma jet

FIG. 4. Optical emission from the plasma plume on the centerline witz520 mm ~0.2 nm FWHM!, comparing emission from CH(C) in the uppertrace with a simulation at 5500 K in the lower trace. Note the experimespectrum also shows emission from OH (A2X) near 308 nm, and its simulation is set toT54000 K.

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and the chamber filled with argon to a pressure betweenand 100 Torr. The number density of CHX is known fromearlier measurements,31 and LIF onR1(10) CH(B-X) ~0,0!was used as a secondary calibration standard. We foundmethods in agreement within 15%, but the LIF calibrationless reliable because it is an indirect measurement, whrequires calibration as well. For the excited state numdensity measurements reported here, the errors are dnated by the mismatch of the calibrated detection voluand the actual emission volume, and we expect overall 2550% uncertainty.

Once the ratio between optical emission and calibratsignal is obtained, the number density of CH(B) is correctedby the radial profile to account for line of sight integrationthe emission signal. Table I shows the number densitiesexcited state species after normalizing to the CHB value, theemission coefficients, and ground state number denswhenever they are available. The excited state number dsities estimated are in the 105– 109 mol/cm3 range, and areall several orders of magnitude less than the respecground state number density. Those values are reasonaba system where the chemistry is dominated by ground sspecies.

The highest ratio of excited to ground state concentratis found for C2(d)/C2(a);0.01. Even higher ratios, withpopulation inversion between C2(d) and C2(a) have beenmeasured by absorption spectroscopy in an arc plasmaing the deposition of amorphous hydrogenated carbcoatings.67 Excited C2(d) appears readily in these systembut it is not accompanied by a large amount of C2 groundstate; for example, Gruenet al.,25 observe bright emissionduring hydrogen free diamond growth in a microwa

l

FIG. 5. Laser-induced fluorescence spectrum exciting CH(C)2CH(X) inthe plasma plume on the centerline withz520 mm in the lower trace~0.012nm FWHM!. The lower trace is a simulation spectrum at 2200 K.

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plasma reactor and they infer C2 is an important reactant fodiamond growth. In the dc arcjet, a strong chemilumincence does not correlate with a large amount of C2, and thetotal number density of this radical is too small to supportobserved diamond growth rate.

1. Spatial distributions

Radial distributions of the excited state concentrationsH, C, CH(A), CH(B), CH(C), C2(d), and C2(D) stateshave been obtained by the Abel transform, and measments of CH(A) and C2(d) at z520 mm from the nozzle areshown in the upper panel of Fig. 6. We find the recovedistributions to have a Gaussian-like shape, and the C2 dis-tribution is wider than for CH(A) ~7 mm vs 5 mm FWHM!,which is consistent with observed differences between trespective ground states. Nonetheless, the excited stateobserved in a region of the plume significantly narrower thfor the ground states,13 where we find the radial distributionwith a FWHM greater than 10 mm~Fig. 6, lower panel!. Wefind two distinct radial distributions with excited H, CH(A),CH(B), and CH(C) have narrow distributions, and CC2(d), and C2(D) have wide distributions.

Figure 7 is a contour map of the cylindrically symmetrexcited state distribution for CH(B); the top and center othe figure is the nozzle exit and the substrate is at 38.2 m

FIG. 6. Upper panel: Radial distribution of excited state number densitz520 mm in the freestream of the plasma plume. Note the C2(d) structureis wider than that for CH(B). Lower panel: Radial distribution from Ref. 13of ground states from LIF measurements in the same arcjet conditions

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Along the centerline in the plume, we see the number dendecreases noticeably, before rising again just above thestrate. However, the radial distribution does not changetween the nozzle exit and the shock structure just abovesubstrate. Figure 8 shows the distribution of excited C2(d),where the vertical gradient is not so large, and againradial distribution does not change between the nozzlethe substrate. Emissions from H, C, CH(A), and CH(C) alsohave maxima on the centerline of the plume. However,emission from C3 and larger hydrocarbons does not peakthe centerline as seen in the radial variation of the broadbvisible background in Fig. 2.

There is a large variation of the optical emission intensas a function of distance from the nozzle. The upper paneFig. 9 plots the excited state number density along the cterline of the plume versus distance from the nozzleatomic carbon (1P), CH(A), atomic hydrogen (n53),C2(D), and C2(d); CH(B), and CH(C) are omitted becausethey have a similar behavior to CH(A). The lower panel ofFig. 9 contrasts the excited state concentrations on theterline of the arcjet plume with the ground state concentions measured earlier by laser-induced fluorescence.13,52

Note the excited state number densities are several ordemagnitude smaller than the respective ground states. Batomic hydrogen and CH radical ground state concentratare nearly constant with distance from the nozzle while th

tFIG. 7. Contour plot of the spatially resolved concentrations of CH(B) be-tween the nozzle and the substrate; note the increased emission iboundary layer above the substrate. Number densities are in unit108 molecules/cm3.

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excited state concentrations decline rapidly. WhereasC2(d) and C2(a) state concentrations have quite similvariation with distance from the nozzle.

The excited state number density for all of the specdecreases with distance from the nozzle until the shheated boundary layer just above the substrate surface.plume velocity is greater than the sound speed, therefoshock is created when this supersonic plume impinges onsubstrate. The shock, called a normal shock because thevelocity is normal to the substrate, creates a pressuretemperature rise in the boundary layer. The excited snumber density for all the species except atomic hydrorises and shows a peak between the shock and the subsExcited atomic hydrogen also rises in the shock heaboundary layer; however, instead of peaking in the boundlayer and decreasing near the surface, the excited H atcontinue to increase with a maximum at the surface.

In the freestream, the region of the plume flow beforeshock, the excited state number density exponentiallycreases, as evident from the linear semilogarithmic plotFig. 9; all of the excited state concentrations decreasemore than a factor of 100 except the factor of 8 for tdecrease of C2(d). The variation in excited state numbedensity is much more dramatic than the decline of less thafactor of 2 observed for the ground state CH31 and atomichydrogen.52 The data in Fig. 9 show that each of the differeexcited species has a different exponential decay with

FIG. 8. Contour plot of the spatially resolved concentrations for C2(d).Number densities are in units of 108 molecules/cm3.

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tance, or in the semilogarithmic plots a different slopeb:

nexc~d!5nexc~0!•e2b•d. ~8!

We can use the rapid decrease in optical emission with dtance from the nozzle and the variation of theb to unravelexcitation mechanism of the optical emission.

The radiating species are excited in the plume and emtheir optical emission without moving very far from positionof excitation. The distance from the nozzle in Fig. 9 is related to time via the plume velocity. For the conditions reported here, we have measured10 the plume velocity to be;2.5 km/s; therefore, the transit time between the exit of tnozzle and the boundary layer above the substrate;15ms. This time is very long compared to the excited stalifetimes; we measured collisionally shortened effective lifetimes of CH(A,B) and C2(d) to be 30–45 ns. Therefore,even at the supersonic plume velocity, the excited speciesproduced and deactivated within a distance of only 0.1 mThere are four excitation mechanisms which might produexcited atoms and molecules in the arcjet plume: radiatitransfer from the discharge inside the nozzle, thermal ex

FIG. 9. Centerline number density of CH(A), C2(d), C2(D), C, and 3nhydrogen atoms as a function of distance from the nozzle with a substrat38.2 mm in the upper panel contrasted with LIF measurements of CH(X),C2(a), and ground state hydrogen atoms from Refs. 13 and 52 in the lowpanel.

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405 Luque et al. : Excited state density distributions of H, C, C 2, and CH 405

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tation, electron impact, and chemiluminescent reactions.can quickly eliminate radiative transfer and thermal exction as important sources of optical emission from the arplume.

Radiative transfer from optical emission in the discharegion inside the nozzle can produce an exponential decaexcited state population with distance from the nozzle onlthe lower-state densities in the optical transition are laenough for the plume to be optically thick. Previous quantative LIF measurements13 show that CH(X) and C2(a) havenumber densities of 1012 and 1010 cm23, respectively. Thus,the CH and C2 transitions can not be optically thick. Grounstate atomic hydrogen has a density of greater t1016 cm23 and the plume is optically thick for Lyman transitions which terminate on the ground state. However,find the number density of H(n53) to be in the range o106– 109 cm23 and Balmer transitions are optically thin ithe arcjet plume. Atomic carbon is similarly optically thiTherefore, the H, C, CH, and C2 excitation mechanisms inthe arcjet plume are not radiative transfer from the dischainside the nozzle.

Thermal excitation is not important in the plume eitheThe temperature is nearly constant between the nozzlethe boundary layer;30,31 therefore, thermal excitation woulnot produce the exponential decline in excited state poption with distance from the nozzle. In addition, thermal eqlibrium calculations with temperature of 2200 K predictratio of 1027– 1025 for CH ~A or B! or C2~d! and the respective ground states, much smaller than the ratio1022– 1023 observed.

Chemiluminescent chemical reactions are an imporexcitation mechanism in many reacting flows; for exampchemiluminescent reactions are the primary production pway for the formation of excited CH(A), CH(B), and C2(d)in flames. However, the number density and the spatialtribution of most of the excited species in the arcjet pluare inconsistent with a chemiluminescent reaction mecnism.

Most of the combustion reactions which produce emissfrom CH require oxygen containing reactants.50 In the arcjetplume, oxygen is only present as an impurity; thus, thchemiluminescent reactions are unlikely to producebright emission from CH(A), CH(B), and CH(C) observedfrom the arcjet plume. The possible chemiluminescent retion excitation mechanisms are also constrained by the ladecrease in optical emission intensity with distance fromnozzle. Fast chemical reaction rate coefficients1011 cm3/s, and the plume feedstock consists of only hydgen, argon, and less than 1% hydrocarbon. Therefore,chemical composition of the freestream is in nearly frozand we do not expect large gradients in concentrations athe centerline of the freestream of the plume.5,51 Our mea-surements of the ground state concentrations of the reaintermediates H,52 CH, C2, and C3

13 find only modest con-centration variations between the nozzle and the boundlayer ~Fig. 9, lower panel!; H, CH, and C2 decrease less thaa factor of 2 and C3 increases approximately a factor of

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tribution subject to AVS license or copyright; see http://scitation.aip.org/ter

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Except for C2(d), all of the excited state concentrationsFig. 9 decrease at least a factor of 100 between the noexit and the boundary layer. Thus, chemiluminescent retion can be the dominant excitation pathway only for the2swan band (d-a) emission. The most likely reaction to explain the chemiluminescence of C2, as suggested byBrinkman30 and Wakisaka,53 is the formation of C2(d) bythree body recombination:

C1C1M→C2~d!1M.

This is consistent with the predictions,5,51 that in the arcjetplume with its large molefraction of atomic hydrogeatomic carbon is the most abundant carbon species.

Electron impact is an important excitation mechanismmuch of the optical emission in the plume. The electrnumber density is the only plasma parameter with a signcant variation along the vertical axis, wit;1012 electron/cm3 at 12 mm downstream from the explane of the nozzle which decreases by an order of matude at 32 mm downstream.33 Measurements and models oelectron densities in dc arcjets show the electron numdensity is much higher inside the nozzle than in the plum41

Thus, the electron density declines rapidly with distanfrom the nozzle exit similar to the decrease in optical emsion, and the high electron density in the nozzle region ctributes to enhance the dissociation of methane.

Electron impact dissociation of methane can have excCH products when the electron energy is greater thanappearance potential of approximately 14 eV

e2~;14 eV!1CH4→CH~A, B, C or X!1H21H1e2.

At higher electron energies, excited H, C, and CH1 speciesas products are possible.49,54–57Hydrocarbon fragments caalso be dissociated or excited by direct electron impact.58 Forexample, the CH radical can be directly excited by low eergy electrons

e2~;3 – 4 eV!1CH→CH~A,B,C!1e2.

The most abundant two-carbon hydrocarbon in the arplume was measured and predicted to be C2H2.

59 Its electronimpact dissociation has been studied48,56,57,60and the elec-tronically exited fragments detected, in addition to the onobserved from methane, are the C2(d), C2(C), andC2(D).56,60We find emission from all of these radicals in thdc-arcjet plume. Collisions of metastable argon atoms cocontribute to the excitation mechanism. However, argmetastables are very rapidly deactivated by molecuhydrogen,61 and we estimate a lifetime in the plume of lethan 0.5ms. Even at the fast directed plume flow of 2.5 kmthe argon metastables are collisionally deactivated innozzle or in the first few mm of the freestream plume.

Assuming the number density of electrons in the pludecreases with distance with a constant electron temperawe should observe the same gradient in the excited semission for all the species produced by electronic impaHowever, we find a different slopeb for each excited species, and Fig. 10 shows the correlation ofb with the excita-tion energy. We see a remarkable linear correlation betw

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b and the excitation energy, with only C2(d) falling off thisline. We find a similar correlation between the appearanpotential for electron impact dissociation to produce excitCH(A), CH(B), and CH(C) from methane, excited C2(D)from C2H2, and excited H from H2. Thus, we could explainthe spatial distribution of optical emission for all the speciexcept C2(d) with an electron impact excitation mechanisif the high energy tail of the distribution depletes with distance from the nozzle in addition to the drop in electrodensity. Such a decrement is consistent with the Langmprobe observation33 that the high energy component to thelectron distribution was greatly reduced by the additionhydrocarbon molecules into the plume.

FIG. 10. Variation of the exponential factorb vs excitation energy of thecorresponding radical or atom.

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2. Effect of methane addition

The amount of methane in the gas mixture is one ofmost critical parameters controlling the growth rate and quity of the deposited diamond films. Methane addition areduces the electron temperature and number density inplume of the dc-arcjet plasma. We found feedstock mixtuof Ar and H2 without added methane had bimodal electrenergy distributions characterized by temperatures;2 and;8 eV, respectively,33 when methane is added, the high eergy component disappears. This observation is commoother plasma reactors with H2 and CH4 mixtures.62 The ad-dition of methane, a polyatomic collision partner with malow-energy vibrational modes and overtones, provides ecient relaxation of the high energy electrons in the plasplume.63 Thus, as seen in Fig. 11, the addition of methasignificantly reduces the H atom optical emission, consistwith an electron impact excitation mechanism.

Figure 11 shows excited state densities deduced fromoptical emission near the nozzle, in the arcjet plume, andthe shock heated boundary layer as a function of methaddition. Near the nozzle, the addition of methane producstrong decrease in the H atom concentration, and the risemission from carbon containing species from electronicpact dissociation of hydrocarbons; above 1% of methanedition, this increase slows. In the arcjet plume, the atomhydrogen emission decreases with methane addition;emission increases for the C species up to 0.5% of admethane, but beyond this value, emission from all thespecies except C2(d) decreases. The C2(d) behavior is con-sistent with the hypothesis of a chemiluminescent producmechanism from atomic carbon recombination. The risefall of the other species is related to the depletion of elect

FIG. 11. Variation of excited state number density vs methane addition near the nozzle (z50), in the freestream of the plume (z520 mm!, and in the shockheated boundary layer (z557.5 mm!.

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energy and number density, similar to the reduction in emsion with distance seen in Fig. 9 for constant methane ation. Finally, in the shock heated boundary layer, wheretemperature and pressure are higher than in the other regthere are more paths for the radical production. ExcitationH, C, and CH(C) by electron impact is still likely, butCH(A), CH(B), and C2(d) are proportional to the methanflow and more likely to be produced by chemiluminescereactions. At this point, we do not know which reactions aresponsible for CH(A) and CH(B) production, nor why theCH(C) is not chemically produced.

V. SUMMARY AND CONCLUSIONS

In the arcjet plume, the predominant production mecnism of electronically excited H*, C* , CH(A), CH(B),CH(C), CH1(A), C2(C), and C2(D) is electronic impactexcitation, whereas C2(d) is the product of chemiluminescent reactions. The excited state populations are severaders of magnitude lower than the ground state, with pconcentrations near the nozzle, where the electron denshigher. The spatial variation of excited state number denis quite different than the spatial distribution of the groustate atoms and radicals. The number density of excstates is sufficiently low that excited state chemistry islikely to play any important role in the overall chemistrydiamond CVD.

ACKNOWLEDGMENTS

This work is supported by ARPA via contract with thNaval Research Laboratory, the Army Research Office,the Air Force Office of Research. W. Juchmann is sponsoby Universitat Heidelberg via Landesgraduiertenfo¨rderung.We thank Professor Mark Cappelli of Stanford Universfor the loan of an arcjet and his assistance in the desigthe diamond CVD reactor.

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