This content has been downloaded from IOPscience. Please scroll down to see the full text.

Download details:

IP Address: 93.180.53.211

This content was downloaded on 03/02/2014 at 08:12

Please note that terms and conditions apply.

Optical emission measurements of electron energy distributions in low-pressure argon

inductively coupled plasmas

View the table of contents for this issue, or go to the journal homepage for more

2010 Plasma Sources Sci. Technol. 19 065001

(http://iopscience.iop.org/0963-0252/19/6/065001)

Home Search Collections Journals About Contact us My IOPscience

IOP PUBLISHING PLASMA SOURCES SCIENCE AND TECHNOLOGY

Plasma Sources Sci. Technol. 19 (2010) 065001 (15pp) doi:10.1088/0963-0252/19/6/065001

Optical emission measurements ofelectron energy distributions inlow-pressure argon inductively coupledplasmasJohn B Boffard1, R O Jung1, Chun C Lin1 and A E Wendt2

1 Department of Physics, University of Wisconsin-Madison, WI 53706, USA2 Department of Electrical and Computer Engineering, University of Wisconsin-Madison,WI 53706, USA

E-mail: jboffard@wisc.edu

Received 11 June 2010, in final form 10 August 2010Published 6 October 2010Online at stacks.iop.org/PSST/19/065001

AbstractOptical modeling of emissions from low-temperature plasmas provides a non-invasivetechnique to measure the electron energy distribution function (EEDF) of the plasma. Whilemany models assume the EEDF has a Maxwell–Boltzmann distribution, the EEDFs ofnumerous plasma systems deviate significantly from the Maxwellian form. In this paper, wepresent an optical emission model for the Ar(3p54p → 3p54s) emission array which is capableof capturing details of non-Maxwellian distributions. Our model combines previouslymeasured electron-impact excitation cross sections with Ar(3p54s) number densitymeasurements and emission spectra. The model also includes corrections for radiationtrapping of the Ar(3p54p → 3p54s) emission lines. Results obtained with this opticaltechnique are compared with corresponding Langmuir probe measurements of the EEDF forAr and Ar/N2 inductively coupled plasma systems operating under a wide variety of sourceconditions (1–25 mTorr, 20–1000 W, %N2 admixture). Both the optical emission method andprobe measurements indicate the EEDF shapes are Maxwellian for low electron energies, butwith depleted high energy tails.

(Some figures in this article are in colour only in the electronic version)

1. Introduction

One of the most fundamental quantities in a low-temperatureplasma is the electron energy distribution function (EEDF).Experimental characterization of the EEDF is central toassessing the plasma state and is of considerable interest inoptimizing the design of low-temperature plasma systemsand as a benchmark in the development of predictivemodels and simulations. In thermodynamic equilibrium,the EEDF follows a Maxwell–Boltzmann (Maxwellian)distribution form, characterized by two parameters, theelectron temperature, Te, and the electron density, ne. Plasmasemployed in applications, however, typically are stronglynon-equilibrium in the velocity and energy distributions oftheir neutral and charged constituents [1–5]. Nevertheless,

some portion of the EEDF is often Maxwellian, and the practiceof specifying an electron temperature is widespread despitethe possibility of significant errors in computed reaction ratesbased on this simplification. For low-pressure plasmas, themost common method to measure the EEDF involves use of‘Langmuir’ or electric probes inserted directly into the plasma.However, Langmuir probes are limited in their ability to fullycharacterize the important features of the EEDF in many low-temperature plasma systems [2, 6].

Optical diagnostics utilizing plasma radiation offer anon-invasive alternative to Langmuir probe measurementsof EEDFs. Optical emission spectroscopy (OES) has beenemployed as a non-intrusive diagnostic tool to characterizeelectron temperature [7–13] and chemical composition[8, 14–17] in low-temperature plasmas. Relying only on the

0963-0252/10/065001+15$30.00 1 © 2010 IOP Publishing Ltd Printed in the UK & the USA

Plasma Sources Sci. Technol. 19 (2010) 065001 J B Boffard et al

spectrum of visible emissions from the plasma, OES is, forexample, widely used as a real-time ‘end-point’ monitor todetect changes that signal completion of a plasma etching.

Gas-phase reactions in low-temperature processingplasmas are driven primarily by electron impact reactions,and produce a mixture of chemically reactive species, theconcentrations of which are critically important to processoutcomes. Reaction rates that determine the species mixare sensitive to the details of the EEDF energy dependence[18–21], motivating the development of an optical EEDFdiagnostic. In this paper, we examine the prospect of OESas a tool for capturing details of non-Maxwellian EEDFs.

In section 3.1 we present a simple emission model forthe Ar(3p54p → 3p54s) transition array. The model predictsthe intensities of the Ar(3p54p → 3p54s) plasma emissionsby combining an assumed EEDF with known electron-impactexcitation cross sections and measurements of the Ar(3p54s)number densities. These number densities are derived fromexperimental measurements (section 2) either directly fromoptical absorption measurements or from radiation-trappinginduced changes to 3p54p → 3p54s branching fractions[22]. One determines the EEDF by minimizing the differencebetween predicted spectra and measured spectra as a functionof parameters that describe the model EEDF (i.e. the electrontemperature). In section 4 we compare the results of this opticaltechnique with Langmuir probe measurements of the EEDFmade on an inductively coupled plasma (ICP) under a widevariety of operating conditions.

Low-pressure ICPs have been extensively studied andhave wide technological application for materials processing,lighting, space propulsion and ion sources [6]. Argon hasbeen selected as a test system for this study, due to itsimportance in many low-temperature plasma applications,simple gas-phase chemistry, extensive technical literature onargon plasma characterization and availability of electron-impact cross section data.

1.1. EEDF description

While the statistically most probable distribution of electronenergies for a population in thermodynamic equilibrium is theMaxwell–Boltzmann (or Maxwellian) distribution, fe-Max(E):

fe-Max(E) = 2√π

T −3/2e

√E e−E/Te (1)

where the EEDF fe(E) is normalized such that∫ ∞

o

fe(E) dE = 1, (2)

non-equilibrium electron populations are common among low-temperature, weakly ionized plasmas and have significantimplications for reaction rates of gas-phase processes resultingfrom electron-impact collisions. Note that in this paperwe follow the convention that electron temperatures, Te,are measured in units of electron volts. The concept ofelectron temperature arises naturally from the Maxwell–Boltzmann distribution, and may also be extended to assist in

characterization of non-Maxwellian distributions, giving riseto the following definitions. Consistent with the definitionof Te for Maxwellian distributions, an ‘effective electrontemperature’, Teff , is defined as 2/3 of the average electronenergy, and can be applied to non-Maxwellian distributionswith arbitrary dependence on electron energy.

Several non-Maxwellian EEDF forms make use ofthe notion of temperature and are good representations ofmeasured EEDFs under certain discharge conditions. In thecase of the ‘bi-Maxwellian,’ the EEDF is divided into tworegions according to electron energy, with the low energyor ‘bulk’ electron population and higher energy ‘tail’ of thedistribution characterized by different respective temperatures[23, 24]. Another widely used functional form is the two-parameter (x, Tx) function [25–27]

fe-x(E) = c′1 T −3/2

x

√E e−c′

2(E/Tx)x

, (3)

where

c′1 = x

(2

3

)3/2 [�(5/2x)]3/2

[�(3/2x)]5/2, (4)

c′2 =

(2

3

)x [�(5/2x)

�(3/2x)

]x

, (5)

with �(ψ) being a Gamma function of ψ . The Maxwell–Boltzmann distribution is a sub-category of this form thatcorresponds to the case of x = 1 with c′

1 = 2π−1/2 and c′2 = 1.

Likewise, a Druyvesteyn distribution corresponds to the caseof x = 2 with c′

1 = 0.5652 and c′2 = 0.2432. Note that Tx

corresponds to an effective temperature Tx = (2/3)〈E〉, where〈E〉 is the average electron energy, 〈E〉 = ∫ ∞

0 E fe(E) dE.Sample curves for EEDFs and electron energy probabilityfunctions (EEPFs) described by equation (3) with the samevalue of Tx = 3 eV for different x-values (1.0, 1.2 and 2.0)are shown in figure 1. The EEPF, fp(E) = E−1/2 fe(E),has a linear dependence on electron energy for a Maxwelliandistribution.

Several groups have reported simulations [28, 29] andLangmuir probe measurements [1, 6, 24, 30] of EEDFs inICPs. For similar Ar pressures (1–25 mTorr) and RF powers(∼102 W) as examined in this work, the EEDF has generallybeen found to be Maxwellian in the lower energy range of theEEDF, due to a sufficiently high electron–electron collisionfrequency to ‘Maxwellianize’ the distribution. Deviation froma Maxwellian is observed in the higher energy range in theform of a ‘depletion of the tail,’ i.e. fewer electrons thanwould be predicted by the Te determined from the lower energyelectrons. This depletion is attributed to electron losses to thewalls at lower pressures [28], and energy loss through inelasticcollisions at higher pressures. Deviations from a MaxwellianEEDF can also occur in the lower energy range for low plasmadensities (i.e. very low pressures or power levels) due to areduced Coulomb collision rate [2].

Langmuir probes are well suited for measurements ofEEDFs in the low electron energy range, but the accuracydiminishes at higher energies. This is due to (i) a decreasingsignal-to-noise ratio at higher energies and (ii) a larger ioncontribution to the recorded probe current. Nonetheless, while

2

Plasma Sources Sci. Technol. 19 (2010) 065001 J B Boffard et al

0 5 10 15 20 25 300.0

5.0x109

1.0x1010

1.5x1010

2.0x1010

EE

DF

(cm

-3eV

-1)

Electron Energy (eV)

0 5 10 15 20 25 30103

104

105

106

107

108

109

1010

1011

EE

PF

(cm

-3eV

-3/2)

Electron Energy (eV)

Figure 1. Sample EEDFs (left) and EEPFs (right) for three distributions with the same average electron energy (Teff = 3 eV) and the sameelectron density (ne = 1011 cm−3): x = 1.0 Maxwell–Boltzmann (——), x = 2.0 Druyvesteyn (– – –) and x = 1.2 (· · · · · ·).

13.48 eV13.33 eV13.30 eV13.28 eV13.27 eV13.17 eV13.15 eV13.09 eV13.08 eV12.91 eV

11.83 eV11.72 eV11.62 eV11.55 eV

2p10 (J=1)

1s2 (J=1)1s3 (J=0)1s4 (J=1)1s5 (J=2)

750.

39nm

667.

73nm

826.

45nm

772.

42nm

727.

29nm

696.

54nm

852.

14nm

794.

82nm

747.

12nm

714.

70nm

935.

42nm

866.

79nm

810.

37nm

772.

38nm

1148

.8nm

1047

.0nm

965.

78nm

912.

30nm

857.

81nm

751.

47nm

840.

82nm

738.

40nm

706.

72nm

922.

45nm

800.

62nm

763.

51nm

978.

45nm

842.

47nm

801.

48nm

811.

53nm

2p1 (J=0)2p2 (J=1)

2p3 (J=2)2p4 (J=1)

2p5 (J=0)2p6 (J=2)

2p7 (J=1)2p8 (J=2)

2p9 (J=3)

Figure 2. Partial energy level diagram for argon. Energies of the 3p54s and 3p54p levels relative to the 3p6 ground state are given on the left.

the EEDF above the threshold for electron-impact inelasticcollisions (>11.5 eV for Ar) is only a small fraction of the totalelectron population, it plays a dominant role in both dischargereactions and excitation kinetics of many excited Ar levels.

1.2. Ar emission spectra

The ground state of argon has an electron configuration1s22s22p63s23p6, abbreviated as 3p6 with total angularmomentum J = 0. Plasma emissions are dominated bytransitions between the first two excited configurations, whichare displayed in figure 2. The first excited configuration3p54s contains four levels designated in Paschen’s notationas 1s2, 1s3, 1s4 and 1s5 with J = 1,0,1,2, respectively.While the Paschen notation labels the individual levels withina configuration, it is the value of J that is most relevant to theexcitation and radiation processes.

Optical transitions from the J = 2 1s5 and J = 0 1s3

levels into the J = 0 ground state are dipole forbidden,making these levels metastable. The J = 1 resonance levels(1s2 and 1s4) do decay optically into the ground state with

radiative lifetimes for isolated atoms of 1.96 ns and 8.4 ns,respectively [31]. At sufficiently high number densities,however, resonance radiation trapping/blockade caused byreabsorption of the resonance photons by nearby atoms in theground state leads to repopulation of the 1s2 and 1s4 levels,lengthening their effective lifetimes significantly. As a result ofthese long effective lifetimes, plasmas may contain substantialpopulations of atoms in both the metastable and resonancelevels.

The next configuration 3p54p consists of ten levels labeledas 2p1, 2p2,. . . ,2p10 in Paschen’s notation and have J -valuesranging between 0 and 3. Transitions from the 2px levelsinto the 1sy levels are the only dipole-allowed radiative decaychannels of the 2px levels. Wavelengths for all of these lines(667–1149 nm) are included in figure 2.

2. Experimental method

2.1. Plasma source

Measurements were made on the inductively coupled Arplasma system illustrated in figure 3. A 30 cm diameter,

3

Plasma Sources Sci. Technol. 19 (2010) 065001 J B Boffard et al

MCH

PMT CGF

RM

700 800 900 1000 11000

2000

4000

6000

8000 2.5 mTorr, 600 W ICP

Em

issi

onR

ate

(arb

.uni

ts)

Wavelength (nm)

10 cm

VCAT

EC-DLWM

PD

SP

PM

PDA

XAL

LP

Figure 3. ICP and diagnostic equipment: AT: 2.5 turn rf-antenna (35 cm diameter), VC: 50 cm diameter vacuum chamber, LP: Langmuirprobe. For gas temperature measurements: EC-DL: 800–812 nm tunable, external-cavity diode laser, WM: wavelength meter, PD:photodiode. For white light absorption spectroscopy: XAL: 150 W Xe arc lamp, PM: pre-monochromator, SP: 0.5 m Ebert spectrometer,PDA: thermo-electrically cooled, 1024 pixel photodiode array. For optical emission spectroscopy: RM: rotatable mirror, MCH: 0.5 mmonochromator, CGF: colored glass filter, PMT: optical detector (PMT for 300–850 nm, Ge detector for 850–1200 nm). Sample 2p → 1semission spectra recorded for a 2.5 mTorr, 600 W ICP is illustrated in the inset plot.

2.5 turn flat spiral antenna was connected to a 13.56 MHzRF power supply via a pi-matching network. Measurementswere made at selected power levels (forward minus reflected)between 20 and 1000 W. The external antenna was separatedfrom the plasma volume by a ceramic vacuum window.Measurements (optical and probe) were made in a planeequidistant (7.5 cm) from the RF window and a groundedbottom electrode. Mass flow controllers (for Ar and N2) wereused in conjunction with a throttle valve to set the chamberpressure to values in the range 1–25 mTorr. Typical flow rateswere between 2 and 9 sccm.

2.2. Number densities

To account for neutral depletion of ground state atoms inthe center of the plasma due to neutral gas heating, the gastemperature in the center of the plasma was obtained bymeasuring Doppler widths of 3p54s–3p54p transitions via laserabsorption spectroscopy [32–35]. Measurements were madeusing a narrow-band, tunable diode laser assembly [36] onthree Ar lines in the 800–815 nm wavelength range: 800.617,801.472 and 810.372 nm. For each wavelength, the laserintensity was measured with a photodiode after the beamtraversed the plasma as the frequency of the laser was slowlyswept over a 15 GHz range around the atomic transition byramping the laser diode current. Temperatures extractedfrom the three line width measurements were consistentwithin ±10%.

Number densities of the atoms in each of the four levels ofthe Ar(3p54s) group (1s2, 1s3, 1s4, 1s5) are determined by whitelight, optical absorption spectroscopy (OAS) as described indetail in [22, 37]. A Hamamatsu L2175, 150 W super-quiet

Xe arc lamp is used as the white light source. Light fromthe lamp is passed through the plasma chamber fitted withglass viewports, collimated by a lens and reimaged on theentrance slits of a 10 cm pre-monochromator, which is used fororder-sorting and to decrease the scattered light entering themain spectrometer (a 0.5 m Ebert spectrometer equipped witha 316 grooves mm−1 Echelle grating). Spectra are recordedwith a 1024 pixel photodiode array (25 µm × 2.5 mm pixels),chilled to −5 ◦C to reduce noise, and read out to an opticalmultichannel analyzer (OMA). As a redundancy cross check,measurements were made on seven lines to obtain numberdensities for the four Ar(3p54s) levels, the densities from thevarious measurements were consistent within experimentaluncertainties. To account for radial variations in the numberdensities, the densities in the center of the plasma volumeare estimated to be 40% greater than the average numberdensities obtained from the line-of-sight, integrated columndensity measurements [22, 32, 38].

2.3. Optical emission spectroscopy

Optical emissions from the center of the plasma volumewere focused onto the entrance slits of a 0.5 m scanningmonochromator after passing through a colored glass filter.Emission spectra were recorded over the 300–1800 nmwavelength range using a combination of photomultiplier tubes(PMTs) and infrared detectors with a typical resolution of0.14 nm [22], although only the 2px → 1sy emissions inthe 665–1150 nm wavelength range are used in the analysispresented here. A quartz-tungsten–halogen standard lamp wasused for radiometric calibration. The area of each λij emissionpeak was converted into a relative photon emission rate, �ij .

4

Plasma Sources Sci. Technol. 19 (2010) 065001 J B Boffard et al

Total uncertainties including the calibration of the wavelength-dependent system response are estimated to be ±5%.

2.4. Langmuir probe

In our experiments, recorded current–voltage characteristics ofthe probe are analyzed using the Druyvesteyn method [2, 39]to obtain the EEDF from the second derivative of the probecurrent I as a function of bias voltage,

fe(V ) = 2m

e2 A

√2eV

m

d2I

dV 2, (6)

where A is the area of the probe tip, m is the mass of theelectron, e is the fundamental electronic charge and V is equalto the plasma potential minus the applied bias voltage. Thephysical design of the probe is described in detail in [40].

Peak-to-peak floating potential fluctuations in the plasmawere recorded to be on the order of 10–18 V in the argonICP discharge, dominated by fluctuations at the dischargefrequency, 13.56 MHz, but also with contributions withdecreasing amplitude from the 2nd (−6 dB), 3rd and 4thharmonics. An external passive RF filter [40] produces a highimpedance between the probe tip and ground at 13.56 MHzand its 2nd and 3rd harmonics, and is used to suppress RFfluctuations in the voltage drop between the probe and plasmaat 13.56 MHz and its 2nd and 3rd harmonics, so that the voltagedifference between the probe and plasma remains fixed whileprobe current is recorded for each probe bias voltage [41].

Noise suppression and differentiation of the probeI–V curves is accomplished using a FFT Gaussian-basedconvolution [40]. This analysis further uses an adaptivemethod, addressing a tradeoff between noise suppression inthe tail and preserving energy resolution in the low energyportion of the EEDF [2, 42]. The adaptive method utilizes anarrower Gaussian ‘window’ at low electron energies wherethe signal is both strong and rapidly changing with energy andan increasingly wider window at increasingly higher energieswhere the signal-to-noise ratio is lower but the EEDF changesmore gradually with energy. Further processing of the EEDFaddresses the gap � between the bias voltages correspondingto the peak of ∂2I/∂V 2 and the adjacent zero crossing, where� can be considered a measure of peak suppression due tosmoothing, as well as other aspects of probe system design [2].To compensate for the residual suppression of the peak, whichwill otherwise lead to an underestimate of the EEDF at thelowest electron energies (typically below 2 eV) and therefore asignificant underestimate of the plasma density, the measuredEEDF in the 5–12 eV range is fit to the generalized form ofequation (3), typically yielding an x-value in the 1–1.2 range.A weighted average of this fit function and the measurementsis used to determine the corrected EEDF in the 0–5 eV range,with the relative weights being a function of energy, i.e. theweighting of the extrapolated fit decreasing smoothly to zerobetween 2 and 5 eV.

After processing, the noise levels in the extracted EEPFcurves are approximately 3 orders of magnitude less than thepeak value, except at the lowest plasma densities where thenoise level was closer to 1% of the peak (see section 4.3 for

sample data). The Maxwellian electron temperature, Tprobe

e ,was extracted from the slope of the linear region of theEEPF curve; the ‘effective temperature’, Teff was found bynumerically integrating the EEDF. A non-linear least squareroutine was used to fit the EEDF curve to equation (3) to extractvalues for the x and T

probex parameters.

3. Model framework

3.1. Emission model

We adopt a modified, zero-dimensional, corona model todescribe the Ar plasma emissions. The model assumes the2px levels are populated by electron-impact excitation fromthe ground state and from the long-lived 1sy levels, withradiative decays as the only loss mechanism for the excited 2plevels. The radiative decay rates are corrected for radiationtrapping/reabsorption, which also functions as a modifiedpopulating mechanism of the 2px levels. The model is zerodimensional in the sense that no spatial variations in the numberdensities are explicitly included; in our particular application,we apply the model to the emissions from the center of theplasma volume. The model, however, can be generalized todescribe emissions originating from any volume element of theplasma after proper consideration of radiation-trapping effectswhich are spatially dependent.

Consider excitation of Ar by electrons of energy E froman initial level-l into one of the 2px levels (i) with an apparentexcitation cross section Q

appl→i (E). The apparent cross section

is the sum of the direct excitation section from level-l to level-iand the sum of the cascade contributions from excitation intohigher levels that radiatively decay into level-i. Subsequentlythe atom can decay into one of the levels (j ) of the 1sy manifold.The i → j optical emission cross section Ql

ij (E) of theemission from level-i into a lower level-j is related to theapparent cross section into i by the branching fraction �ij ofthe transitions,

Qlij (E) = Q

appl→i (E)�ij . (7)

The l-superscript in the emission cross section indicates thatthe i → j emission is caused by electron-impact excitation outof level-l which may be either the ground state or one of thefour 1sy levels. The i → j emission rate coefficient (due toexcitation from level-l) is obtained by finding the convolutionof the energy dependent optical emission cross section withthe plasma’s electron energy distribution function fe(E),

klij =

√2

me

∫ ∞

0Ql

ij (E) fe(E)√

E dE. (8)

In a plasma the 1sy levels (j ) are sufficiently wellpopulated that part of the i → j emission may be reabsorbedby the 1sy atoms in level-j regenerating 2px atoms in level-i. Repetition of this emission–reabsorption factor resultsin a redistribution of the emission intensities among thedecay channels from a given 2px level, thus yielding a new

5

Plasma Sources Sci. Technol. 19 (2010) 065001 J B Boffard et al

effective branching fraction �effij [22]. Accordingly, we define

a reabsorption factor

Rij = �effij /�ij . (9)

This factor can be obtained by replacing the canonical photontransition rate Aij for the i → j transition with an effectiveone that is weighted by the probability that the emitted photonescapes the plasma volume. This yields

Rij = g(κλijρ)

∑l Ail∑

l g(κλilρ)Ail

, (10)

where g is the photon escape factor which is a function ofthe reabsorption coefficient κλij

and the characteristic scalelength of the source ρ (i.e. the radius of the plasma chamber).The reabsorption coefficient κλij

, in turn, is proportional tothe number density of atoms in level-i. A more completedescription the reabsorption factor and its applicability tomodeling plasma emissions can be found in our earlierpaper [22].

Summing the contributions from various excitationchannels and accounting for reabsorption, the i → j photonemission rate, �ij , is equal to

�ij = K ne Rij

[∑l

nl klij

], (11)

where ne is the electron number density, nl represents thenumber density of atoms at the center of the plasma volumein the initial level-l (ground state, 1s2, 1s3, 1s4 and 1s5) andK is an overall normalization factor that absorbs everythingnot explicitly relevant to the discussion (such as variousgeometrical and solid angle factors). Note that in addition tothe explicit nl factor in the sum, the number densities of atomsin the 1s levels are also included in the reabsorption correctionfactor Rij . Similarly, the ‘electron temperature’ dependenceis implicitly contained in the kl

ij excitation rate coefficients.In this paper, we are mainly interested in extracting

information on the EEDF. To remove the dependence on bothK and ne, we calculate the line ratios, �ij/�i ′j ′ using thei ′ → j ′ transition as a normalization standard. For thispurpose, we use the 2p1 → 1s2 transition at 750.39 nm sinceit is generally dominated by ground state excitation and has aminimal radiation-trapping correction.

The required optical emission cross sections for excitationfrom the ground state of Ar are obtained from our extensiveexperimental measurements [43]. Experimentally measuredapparent and optical emission cross sections for 2p levelsexhibit a pressure dependence arising from the cascadecontribution of these levels from high-lying resonance levels[44]. Radiation trapping of the vuv ground state transitions ofthese resonance levels at ‘high’ target gas pressures leads to anenhancement of the radiative cascade transitions terminatingon 2p levels. Due to the much longer reabsorption pathlength in our plasma (≈25 cm) versus the electron beamexperiments (≈1.4 cm), all of source pressures in this workcorrespond to the ‘high’-pressure limit of cross section workwith nearly complete reabsorption. Nevertheless, while these

pressure effects are very striking at high electron energieswhere the apparent cross section into 2p levels is dominatedby the cascade contribution from resonance levels [44], forlow-temperature plasmas only low energy electrons contributesubstantially to the integral in equation (8), where the cascadecontribution from resonance levels, and thus the pressuredependence, is much less [43]. In their OES studies offluorocarbon/rare gas plasmas Schabel et al also found whenAr is the main carrier gas the Ar excitation cross sections arein their high-pressure limit [45].

We have also measured the apparent cross sections forexcitation out of both 1s3 and 1s5 metastable levels into the 2px

levels from which we obtain the 2px → 1sy optical emissioncross sections Q

1s3ij (E) and Q

1s5ij (E) [46–48]. Cross sections

for the 1s3 → 2px and 1s5 → 2px excitation correspondingto optical dipole allowed transitions (�J = 0,±1 and J =0 → J = 0) have much larger cross sections than theoptically forbidden ones, and have been found to scale with theoscillator strength (fli) of the corresponding optical transitionl → i even at low electron energies [46, 48]. Accordingto standard collision theory (Born–Bethe approximation) thisscaling relation is expected to hold only at high energies. Theclose tracking of the 1sy → 2px excitation cross sections withthe corresponding optical oscillator strengths at low energiesas observed in [46] can be traced to the particular functionalform of the generalized oscillator strengths for the 1sy → 2px

series of all the rare gases [48, 49]. This relationship providesa means to obtain the 1s2 → 2px and 1s4 → 2px cross sectionswhich have not been measured [48].

We emphasize that in calculating the excitation rates, onemust use the apparent excitation cross sections rather thanthe direct excitation cross sections since the former includeradiative cascade from the higher-lying levels. For electronexcitation into the 2px levels from the ground state, cascadesare responsible for a large part of the population, typically40% [44].

3.2. Sample model results

To illustrate how the 2px → 1sy emissions can be used tomeasure the EEDF, we will examine in detail two sample cases:one with a high electron temperature (5 eV) and one with alower electron temperature (2.5 eV). These cases correspondclosely to our measurements for 600 W Ar plasmas withpressures of 2.5 mTorr and 15 mTorr, respectively. Using theprobe-derived EEDF and measurements of the ground stateand 1s number densities, we compute separately the percentagecontributions to the 2px → 1sy emission lines from electronexcitation into 2px out of (i) the ground level, (ii) the twometastable levels and (iii) the two resonance levels, with valueslisted in table 1. These percentage contributions are differentfor different upper level (2px) but are unaffected by the choiceof lower level. For pressures over ∼5 mTorr (as exemplifiedby the 15 mTorr values in table 1), excitation out of the groundlevel is not the dominating mechanism except for emissionsfrom a few select levels such as the 2p1 and 2p5 levels. Incontrast, excitation out of the metastable and/or the resonancelevels often is mainly responsible for the observed radiation.

6

Plasma Sources Sci. Technol. 19 (2010) 065001 J B Boffard et al

Table 1. Fractional contributions to emission intensity due to excitation out of the ground (Grd), metastable (Met) and resonance (Res)levels obtained from emission model. The ground state, metastable and resonance atom densities are from table 2. The EEDF is of thegeneralized form with x = 1.2. The fractional contributions depend only on the upper level of the transitions but are the same for all the 1sy

lower levels with a given 2px .

Fractional contribution Fractional contribution2.5 mTorr, Tx=1.2 = 5.4 eV 15 mTorr, Tx=1.2 = 2.7 eV

Transition Grd Met Res Grd Met Res

2p1 → 1sy 0.937 0.043 0.020 0.621 0.134 0.2452p2 → 1sy 0.722 0.237 0.041 0.326 0.299 0.3752p3 → 1sy 0.829 0.088 0.083 0.302 0.115 0.5832p4 → 1sy 0.679 0.292 0.029 0.328 0.394 0.2772p5 → 1sy 0.908 0.034 0.058 0.426 0.077 0.4962p6 → 1sy 0.523 0.456 0.021 0.231 0.591 0.1782p7 → 1sy 0.684 0.256 0.059 0.229 0.359 0.4122p8 → 1sy 0.670 0.266 0.064 0.237 0.329 0.4332p9 → 1sy 0.452 0.547 0.001 0.217 0.765 0.0182p10 → 1sy 0.527 0.460 0.013 0.244 0.650 0.106

Differences between levels populated primarily byexcitation from the ground state and those from metastablelevels have been previously used in optical plasma diagnostics[50–52]. In particular, the 2p1 and 2p5 J = 0 levels do notconform to the optical dipole selection rules with respect to the1s3 and 1s5 metastable levels (with J = 0 and 2, respectively),and as a result have some of the smallest cross sections forexcitation from the metastable levels [46, 47]. Assumingthese levels are then dominated by ground state excitation,emissions from these levels may act as an indicator of highenergy (>13 eV) electrons [53–56]. This is reflected in the2.5 mTorr values in table 1, where both the 2p1 and 2p5 levelsare populated primarily through excitation out of the groundstate. However, this is no longer completely true when theplasma contains an appreciable fraction of 1s2 and 1s4 atoms(both J = 1) as excitation from these resonance levels into 2p1

and 2p5 is favored by the optical selection rules. At 15 mTorr,absorption of the resonance radiation causes a drastic increaseof the 1s2 and 1s4 atom densities with gas pressure (table 2) sothat excitation from the ground state and the resonance statesbecome more comparable.

Because of the very large difference in electron energythreshold between excitation out of the ground (13 eV) andof the metastable/resonance levels (2 eV), the excitation ratesfrom the different initial states sample different segments ofEEDF. This can be seen by examining the energy dependenceof the integrand in equation (8) for excitation out of the groundstate and the corresponding expression for excitation out of themetastable/resonance level as illustrated in figure 4(a) for the2p9 → 1s5 emission and in figure 4(b) for the 2p1 → 1s2.Due to contributions from the lower energy threshold andlarger excitation cross sections, the metastable contributionfor excitation into the 2p9 level is approximately 8000 timeslarger than the ground state contribution for this level, but thisdifference is partially offset by the small fraction of atomsin the metastable levels (nm/ng ≈ 3 × 10−4). Thus, for amore equal comparison, the metastable level contribution infigure 4(a) has been multiplied by a factor of nm/ng. Similarlythe metastable/resonance contributions for the 2p1 level in infigure 4(b) have been multiplied by factors of (nm/ng) and

0 5 10 15 20 25 300.0

2.0x10-12

4.0x10-12

6.0x10-12

8.0x10-12

1.0x10-11

1.2x10-11

1.4x10-11

weighted metastable level

ground state

(a) 811.53 nm 2p →9 1s5

`Exc

itatio

nR

ate'

(cm

2eV

-1s-1

)

0 5 10 15 20 25 300.0

1.0x10-12

2.0x10-12

3.0x10-12

weightedresonance level

(b) 750.39 nm 2p →1 1s2

weightedmetastable level ground state

`Exc

itatio

nR

ate'

(cm

2eV

-1s-1

)

Electron energy (eV)

Figure 4. Excitation rates for (a) 2p9 level and (b) 2p1 level forconditions corresponding to a 15 mTorr, 600 W ICP(Tx=1.2 = 2.8 eV, nm/ng = 3 × 10−4, nr/ng = 1 × 10−4).

(nr/ng), respectively. Only those electrons within the range13–25 eV are relevant for exciting the ground state atoms intothe 2px level whereas excitation out of the 1sy levels entailselectrons of energy as low as 2 eV all the way through 15 eV.Excitation from the 1sy levels constitutes a significant or even amajor portion of the observed radiation as is evident in table 1.

Because the various 2px levels are populated by excitationout of the ground, metastable and resonance levels withdifferent weighting, it is possible to extract the relative ratio oflow-to-high energy electrons in the plasma by examining theemissions from a number of 2px → 1sy emission lines. Foran EEDF characterized by a Maxwell–Boltzmann distribution,this low-to-high electron ratio uniquely determines the electrontemperature. The sensitivity of the derived OES electron

7

Plasma Sources Sci. Technol. 19 (2010) 065001 J B Boffard et al

0

2

4

6

8

10

12

14

2.5 mTorr

15 mTorr

Red

uced

χ2

T OES

e (eV)

Figure 5. Temperature dependence of goodness of fit measure χ 2

(divided by the number of degrees of freedom) for 2.5 mTorr and15 mTorr 600 W Ar plasma analysis. Dashed vertical linescorrespond to best-fit values of T OES

e .

2.0 2.5 3.0 3.5 4.0 4.5 5.01.0

1.2

1.4

1.6

1.8

2.0

T OES

x (eV)

x

Figure 6. Contour plot of χ2-values for OES analysis of 15 mTorr,600 W Ar ICP, with darker shades of gray correspond to smallervalues of χ 2 and thus a better quality fit. Data points representbest-fit (T OES

x , x) values for 50 synthetic data sets in Monte Carlosimulation.

temperature can be seen by examining figure 5 which plotsthe χ2 difference between the model and experimental lineratios as a function of the electron temperature used in themodel calculation. The minimum χ2 value, corresponding tothe best fit, is well localized in the neighborhood of 2.8 eVfor the 15 mTorr curve. The minimum in the 2.5 mTorr curveis much shallower, indicating a larger relative uncertainty inthe extracted electron temperature. This reduced sensitivity isdue in part to the greater overall domination of the excitationrates from the ground state for all levels, which reduces thedifferences between lines from levels dominated by low energyelectrons/metastable excitation (e.g. 2p6 or 2p9) and linesfrom levels dominated by high energy electrons/ground stateexcitation (e.g. 2p1 or 2p5).

Moving beyond the assumption of a Maxwell–Boltzmanndistribution, it would appear possible, in principle, to extractthe full EEDF shape (i.e. both Tx and x using equation (3))from the observed OES measurements. In practice, however,there is not enough information in the 2px → 1sy emissions tosimultaneously constrain the values of both Tx and x. This isillustrated in χ2 contour plot of figure 6 for the 15 mTorr case.

All of the trial EEDFs described by the pair of parameters(Tx, x) running along the line from Tx = 2.4 eV, x = 1 toTx = 3.6 eV, x = 2 have roughly the same ratio of low-to-high electrons, leading to approximately equal quality fitsto the observed OES line ratios. We have also investigatedthis point by conducting a Monte Carlo simulation of thedata analysis. Fifty synthetic data sets were generated fromthe observed emission and number density measurements byshifting each quantity (OES intensities and number densities)by amounts within the range of the estimated uncertainties.The best-fit (Tx, x) values generated using the 50 syntheticdata sets are included in figure 6 as points. As would beexpected based on the shape of the χ2 surface, the extractedvalues tend to fall along the line from (Tx = 2.4 eV, x = 1) to(3.6 eV, 2). Moreover, the values tend to cluster loosely around(Tx = 2.7 eV, x = 1.2). Assuming the standard deviations oftheir respective distributions reflect their fitted uncertainties,this leads to a ±0.3 eV uncertainty in Tx and ±0.14 uncertaintyin x. By fixing the value of x at 1.2, however, the correlationdegeneracy is removed and the uncertainty in the value ofTx=1.2 can be substantially reduced to ±0.1 eV.

4. Results

4.1. Plasma conditions

To perform a robust test of the emission model, we havemeasured the optical emission intensity of the 2px → 1sy

lines for an Ar ICP as a function of three main controlparameters of the plasma: (1) pressure, (2) power and (3)gas composition. In each case we also measured the numberdensities of argon atoms in the four 1sy levels with whitelight absorption spectroscopy and extracted the ground statedensity from the measured source pressure after accountingfor neutral depletion due to gas heating and electron pressure[11, 57]. The ‘electron temperature’ was extracted from theOES results assuming both a simple Maxwell–Boltzmann formfor the EEDF (designated as T OES

e ) and using the generalizedform of EEDF given by equation (3) with a fixed valueof x = 1.2 (designated as T OES

x=1.2). The fixed choice ofx = 1.2, based on the Langmuir probe fits, was requiredto remove the correlation degeneracy between x and Tx (seefor example figure 6). Values of T

probee and T

probex=1.2 were

extracted from Langmuir probe measurements as describedin section 2.4. A more detailed analysis of the EEDF shapeand departures from a Maxwellian EEDF will be addressed insection 4.3.

4.1.1. Source pressure. As revealed by a simple globalmodel analysis, an increase in the operating pressure leadsto a decrease in the electron temperature and an increase inthe plasma density (ne) [25, 59]. These general trends are wellreflected in our optical and probe measurements for a 600 WICP for argon pressures between 1.0 and 25 mTorr summarizedin table 2. The gas temperature was also found to increasefrom 600 to 850 K as the pressure was increased. Whitelight absorption measurements of the metastable and resonancelevel densities reveal that the metastable atom density reaches

8

Plasma Sources Sci. Technol. 19 (2010) 065001 J B Boffard et al

Table 2. Measured number densities and electron temperatures as a function of Ar source pressure, at fixed power of 600 W. Values for thepeak number densities (in the center of the plasma) for the ground level (derived from laser absorption measurements of the gas temperature)and 1sy levels (OAS measurements) have an estimated uncertainty of ±10%. Number densities of the 1s2 level were found to be very nearlyequal to those of the 1s4 level, and are omitted. Number densities for the 1s4 and 1s5 levels derived from the variation in observed2px → 1sy branching fractions [22, 58] are listed under optical emission measurements. The estimated uncertainties in the T OES

e and T OESx=1.2

values are ±5% to ±10% based upon Monte Carlo simulations of the extracted temperatures; uncertainties in the corresponding probevalues are also estimated to be approximately ±10%.

Source pressure (mTorr) 1.0 2.5 5.0 10 15 20 25

Optical absorption/laser measurementsn(gr) (1013 cm−3) 1.3 3.1 5.9 11 18 22 27n(1s5) (108 cm−3) 315 445 520 590 585 540 490n(1s3) (108 cm−3) 28 56 59 67 62 60 74n(1s4) (108 cm−3) 7 25 56 146 190 210 215

Optical emission measurementsn(1s5) (108 cm−3) 307 357 458 589 595 561 519n(1s4) (108 cm−3) 2 16 56 138 175 203 187T OES

e (eV) 8.1 5.5 3.6 2.9 2.4 2.2 2.1T OES

x=1.2 (eV) 6.5 5.4 3.8 3.2 2.7 2.5 2.4

Probe measurementsT

probee (eV) 6.0 4.8 4.1 3.4 3.0 2.9 2.8

Tprobex=1.2 (eV) 5.5 4.5 3.9 3.2 2.8 2.7 2.6

ne (1010 cm−3) 4.7 8.3 13 26 40 54 72

Table 3. Data as a function of power, 15 mTorr Ar. See table 2 for additional details.

Power (W) 20 50 100 200 400 600 800 1000

Optical absorption/laser measurementsn(gr) (1013 cm−3) 27 24 20 18.6 17.7 15.5 12.8 11.6n(1s5) (108 cm−3) 321 430 466 553 536 575 514 522n(1s3) (108 cm−3) 45 50 67 81 78 76 64 63n(1s4) (108 cm−3) 22 64 112 167 178 186 182 175

Optical emission measurementsn(1s5) (108 cm−3) 384 494 555 602 693 657 642 590n(1s4) (108 cm−3) 32 62 113 160 256 241 243 214T OES

e (eV) 2.5 2.4 2.2 2.4 2.2 2.3 2.5 2.5T OES

x=1.2 (eV) 2.9 2.7 2.6 2.8 2.6 2.7 2.8 2.9

Probe measurementsT

probee (eV) — 3.9 3.6 3.3 3.2 3.0 3.1 3.1

Tprobex=1.2 (eV) — 3.5 3.3 3.1 3.0 2.8 2.8 2.8

ne (1010 cm−3) — 0.94 2.8 9.1 24.4 39.4 50.9 60.8

a maximum at 10–15 mTorr, decreasing at higher pressure.The decrease in metastable densities at higher pressures is dueto increasing electron-impact excitation/ionization loss ratescaused by the increase in electron density. The densitiesof the 1s4/1s2 atoms, whose effective lifetime is lengthenedthrough reabsorption of resonance radiation (i.e. transitionsfrom 1s4/1s2 into the ground state), are seen to increase withthe gas pressure over the entire range in table 2.

There is generally poor agreement between the probe- andOES-derived values for the electron temperature when bothare fit to the simple Maxwell–Boltzmann distribution. Thesituation is considerably better when both sets of data are fit tothe generalized form with the fixed value of x = 1.2. Indeed,at pressures above 5 mTorr, the two values of Tx=1.2 agree tobetter than 8%. The agreement at 1 and 2.5 mTorr is worse,at ±20%; however, both derived temperatures have higherexperimental uncertainties at lower pressures. For the OESmethod, as was illustrated in figure 5, the extracted temperature

has greater uncertainty when ground state excitation is thedominate mechanism for populating all of the 2px levels.For the probe analysis, the difficulty is a result of the lowerplasma density and resulting poorer signal-to-noise ratio inthe resulting IV curve.

4.1.2. RF power. At a fixed pressure, the primary effectof increasing RF power levels is to increase the plasmadensity [25, 59]. In contrast, the electron temperature isexpected to remain fairly constant as a function of power.Nonetheless, Godyak et al, did observe some changes in theshape of the EEDF with discharge power, although the electrontemperature changed little [6]. In the work, measurementswere made as a function of power for values from 20 to1000 W at two Ar pressures, 15 mTorr (table 3) and 2.5 mTorr(table 4), corresponding to a low and high electron temperaturerepectively. While the measured electron densities do increase

9

Plasma Sources Sci. Technol. 19 (2010) 065001 J B Boffard et al

substantially with power, the number densities in the four1s metastable/resonance levels remain fairly constant. Theground state density, however, decreases by approximately50% between 20 and 1000 W due to the rising gas temperaturewith increasing power (increasing from 450 K at 20 W to 930 Kat 1000 W). Since the photon emission rate scales with electrondensity, emission intensities are significantly increased athigher power.

As with the pressure data, there is generally betteragreement between the probe- and OES-derived values for the‘electron temperature’ when using the x = 1.2 generalizedform for the EEDF than a simple Maxwell–Boltzmanndistribution, with the two methods agreeing to better than±15% for the RF powers greater than 100 W in table 3.Both the probe and OES techniques suffer from reducedsignal rates at the lowest power levels (<100 W), and havegreater variations in the extracted values of Tx=1.2 (±20–30%). Indeed, poor signal to noise prevented any meaningfulextraction of probe parameters from the 20 W probe data. Onthe other hand, for the 2.5 mTorr data in table 4 the probe-and OES-derived Maxwellian temperatures are slightly moreconsistent than the generalized EEDF form.

Table 4. Data as a function of power, 2.5 mTorr Ar. See table 2 foradditional details.

Power (W) 100 200 400 600 800 1000

Optical absorption/laser measurementsn(gr) (1013 cm−3) 3.7 3.4 3.1 2.7 2.3 2.1n(1s5) (108 cm−3) 357 344 410 412 381 424n(1s3) (108 cm−3) 48 49 59 50 42 48n(1s4) (108 cm−3) 3 10 15 17 14 13

Optical emission measurementsn(1s5) (108 cm−3) 313 365 366 414 340 314n(1s4) (108 cm−3) 1 2 4 22 10 4T OES

e (eV) 5.4 5.1 5.0 5.3 5.2 5.5T OES

x=1.2 (eV) 5.7 5.4 5.3 5.6 5.5 5.8

Probe measurementsT

probee (eV) 4.8 5.4 5.9 5.8 5.6 5.5

Tprobex=1.2 (eV) 4.4 4.9 5.2 5.1 5.0 5.1

ne (1010 cm−3) 0.8 2.2 5.4 8.2 10.8 14.2

Table 5. Ar/N2 data (600 W, 15 mTorr total pressure). See table 2 for additional details.

% N2 gas 0 6.7 14 25 33 50 67 86

Optical absorption/laser measurementsn(gr) (1013 cm−3) 18 17.2 16.1 14.5 13.0 9.9 6.7 2.9n(1s5) (108 cm−3) 585 472 362 225 155 94 50 20n(1s3) (108 cm−3) 62 56 48 32 21 13 7 3n(1s4) (108 cm−3) 192 139 87 41 28 14 5 2

Optical emission measurementsn(1s5) (108 cm−3) 626 475 306 185 150 72 34 4n(1s4) (108 cm−3) 208 138 73 37 21 9 6 1T OES

e (eV) 2.4 2.5 2.4 2.3 2.4 2.5 2.3 2.3T OES

x=1.2 (eV) 2.7 2.8 2.8 2.6 2.7 2.8 2.6 2.6

Probe measurementsT

probee (eV) 3.0 3.2 3.3 3.2 3.1 3.0 2.9 2.7

Tprobex=1.2 (eV) 2.8 2.9 3.1 3.0 2.9 2.8 3.0 2.6

ne (1010 cm−3) 39 19.5 13.3 10.0 8.4 6.6 5.2 4.8

4.1.3. Gas composition. As a third control parameter,we varied the gas composition of the plasma at a fixedpower and pressure by adding N2 to the feed gas. Resultsfor Ar–N2 mixtures of eight compositions at 600 W and atotal pressure of 15 mTorr are shown in table 5. Collisionsbetween nitrogen molecules and Ar(3p54s) atoms quenchthe metastable atoms [60], leading to significantly reducedmetastable/resonance densities with increasing N2 gas fraction.Measurements revealed that in addition to the decrease inmetastable density, the plasma density also decreased withincreasing N2 admixture. On the other hand, both the gastemperature and electron temperatures were fairly independentof the N2/Ar ratio.

Since excitation out of metastable atoms plays a centralrole in the ability of the emission model to extract the EEDF,one may expect the performance of the model to sufferas one increases the N2 admixture which quenches the Armetastables. Nonetheless, the agreement between probe-and OES-derived ‘electron temperatures’ is generally quitegood for all the sampled Ar/N2 mixtures. The two setsof Maxwellian temperatures agree within ±25%, and thegeneralized Tx=1.2 values agree to better than ±15% for allN2/Ar ratios.

4.2. Radiation-trapping correction: measurement of3p54s densities

Information about the EEDF is extracted by examiningratios of lines from different upper levels. As describedin [22, 58], information about the metastable and resonancelevel number densities can be extracted by examining lineratios from lines with a common upper state. In the presentcontext, a comparison of the metastable densities derivedfrom this OES-branching fraction (OES-BF) analysis and the‘direct’ measurements via white light absorption spectroscopyprovides a test of the radiation trapping correction used inthe emission model. The number densities for the 1s5 and1s4 levels extracted from the OES-BF analysis are included intables 2–5 under the optical emission measurements, and arealso plotted in figure 7 as a function of the densities measuredby the OAS technique. Except at the very lowest densities,

10

Plasma Sources Sci. Technol. 19 (2010) 065001 J B Boffard et al

0 100 200 300 400 500 600 7000

100

200

300

400

500

600

700

1sx n

umbe

r de

nsit

y (1

08 cm

-3)

OE

S b

ranc

hing

fra

ctio

ns

1sx number density (10

8 cm

-3)

white light absorption

Figure 7. Comparison of extracted 1s4 (open points) and 1s5 (solidpoints) number densities obtained from OAS measurements andOES-BF analysis under a wide variety of plasma operationconditions: power (circles), pressure (squares) and Ar/N2 mix(triangles).

there is better than ±10% agreement between the two methods.While this work used the OAS number densities, in practiceit would be possible to omit the OAS measurements of thenumber densities and use the OES-BF method to extract therequired metastable and resonance level densities.

4.3. EEDF shape analysis

When the emission model is used with an assumed Maxwell–Boltzmann form for the EEDF, the extracted electrontemperature was found to differ systematically from the samevalue derived from Langmuir probe measurements for thedifferent sets of plasma conditions as illustrated in figure 8.While some of the disagreement can be related to uncertaintiesin the experimental measurements and cross sections usedin the model, departures of the EEDF from the assumedMaxwellian form are a much larger source of deviations. Theprobe-derived electron temperature is a measure of the electronenergy distribution mainly at low energies. For a 600 W,15 mTorr plasma this corresponds to the 0–15 eV energy range.In contrast, the OES-derived electron temperature samples therelative number of electrons in the low (2–15 eV) and high(>13 eV) ranges via their contributions to the excitation ratesfrom the 1s levels and ground state, respectively. As a result,the optical method is far more sensitive to the distribution ofhigh energy electrons than probe measurements where noisein the probe-derived EEDF dominates.

The approximation of plasma EEDFs by a simpleMaxwell–Boltzmann form is a computational simplificationnot rigorously supported for argon ICP discharges. Indeed,studies of argon ICPs have produced EEDFs that deviatesignificantly from the Maxwellian form [6, 28]. Similardepartures from the Maxwellian form of the EEDF can also beobserved in our Langmuir probe measurements of the EEPF

Figure 8. Comparison of extracted electron temperatures, Te,values obtained from OES analysis and probe assumingMaxwell–Boltzmann form for the EEDF. Symbols for each set ofplasma conditions: variable Ar pressure (�), variable RF power (◦)and variable Ar/N2 mixing ratio (�).

at 2.5 and 15 mTorr in figure 9. Also shown are two (best fit)analytical forms of the EEDF: a Maxwellian (which appearsas a straight line in the EEPF versus electron energy plot)and the two-parameter (x, Tx) function (equation (3)). Forboth pressures the EEDF was best fit by the generalized formswith x-values of x = 1.2, indicative of the observed decreasein high energy electrons relative to Maxwellian distributions.This depletion of high energy electrons seriously reduces thenumber of electrons with E > 13 eV required for electron-impact excitation into the 2p levels from the ground state.Probe traces for other pressures and plasma conditions displaysimilar depletions of high energy electrons, with EEDFs thatcan be well approximated using equation (3), having x- valuesin the range 1.1–1.3, with an average of 1.24. It should be notedthat the fitted Tx (or Tx=1.2) values for these cases are essentiallyequal to the ‘effective electron temperature’ Teff , obtained fromnumerically integrating the measured EEDF. In contrast, theMaxwellian Te values are systematically greater than the Teff

values. The depletion in the higher range of electron energyhas been attributed to wall losses of energetic electrons notconfined in the plasma electrostatically.

Due to the difficulties in simultaneously extracting valuesfor both x and Tx from OES measurements using our 2p → 1semission model (see figure 6), we also analyzed both the probeand OES data using an EEDF described by equation (3) withx fixed at 1.2. As illustrated in figure 10 there is generallyvery good agreement between the two methods. Indeed, thedifferences between the T

probex=1.2 and T OES

x=1.2 values are generally

much smaller than the corresponding Maxwellian Tprobe

e /T OESe

comparison. Behringer and Fantz have used a related methodto measure non-Maxwellian EEDF forms in an Ar/He/N2

plasma [61]. In their method, the value of x was adjusted

11

Plasma Sources Sci. Technol. 19 (2010) 065001 J B Boffard et al

0 5 10 15 20 25106

107

108

109

1010

(a) 2.5 mTorr

EE

PF

(cm

-3eV

-3/2)

0 5 10 15 20107

108

109

1010

1011

(b) 15 mTorr

EE

PF

(cm

-3eV

-3/2)

Electron Energy (eV)

Figure 9. Electron energy probability function (EEDF ×E−1/2) for600 W ICPs at a pressure of (a) 2.5 mTorr and (b) 15 mTorr. Solidlines are fits to generalized x-form EEDF (Tx = 4.5 eV and 2.8 eV,for 2.5 mTorr and 15 mTorr, respectively, both with x = 1.2), dashedlines are Maxwellian fits (Te = 4.8 eV and 3.0 eV, respectively).Vertical gray lines demarcate the range of threshold energies forexcitation into the ten Ar(3p54p) levels from the ground state.

to bring the ‘electron temperatures’ values derived for eachgas separately into a common alignment.

5. Concluding remarks

For optical diagnostics of argon plasmas we have introducedan emission model which takes into account the production ofradiating atoms through electron-impact excitation out of theground state as well as the metastable and resonance levelsusing cross sections based on experimental measurements.When metastable and resonance atoms are present insignificant quantities, the 2px → 1sy radiation may bereabsorbed causing a change in the branching fractions ofthe 2px levels from those derived from the known Einsteincoefficients. The effect of reabsorption is also included in theradiation model. Our analysis shows that electron excitationout of the ground state is generally not the dominate mechanismfor the 2px → 1sy emission except for a few cases.

While the emission model could be used to extract electrontemperatures using a simple Maxwellian form for the EEDF,the results were found to differ significantly from similarprobe-derived measurements of the electron temperature.Much better agreement was found between the two methodswhen we used a generalized form for the EEDF with x = 1.2.

2 3 4 5 6 72

3

4

5

6

7

TO

ES

x=1.

2(e

V)

Tprobe

x=1.2 (eV)

Figure 10. Comparison of extracted ‘electron temperatures,’ Tx=1.2,for non-Maxwellian EEDF, obtained from OES analysis and fromLangmuir probe measurements. Symbols are same as figure 8: Arpressure (�), power (◦) and Ar/N2 mix (�).

While the Langmuir probe-derived EEDF could be fit to thegeneralized form of equation (3) with both x and Tx as freeparameters, degeneracies in the ratio of high-to-low energyelectrons prevented a similar fitting of OES measurementsto extract well-defined values of x using Ar(2px → 1sy)emissions alone owing to the similar energy thresholds for theexcited 2px levels. Nevertheless, at least for the 15 mTorr,600 W plasma case considered in section 3.2, the pair of(Tx , x) values obtained from the OES analysis, (2.7 ± 0.3,1.21 ± 0.14), agree quite well with the probe values, (2.8 eV,1.2). This agreement, however, is somewhat fortuitous, assimilar attempts to simultaneously fit x and Tx values forthe data sets taken at other pressures produced best-fit x-values ranging from 0.8 to 2.0, whereas the x-values obtainedfrom the Langmuir probe analysis were consistently in the1.1–1.3 range.

The apparent cross correlation between x and Tx can beremoved by expanding the analysis to include other emissionlines that sample different regions of the EEDF. One approachis to use emissions from other atoms. The TRG-OES methodof Donnelly et al uses a mixture of rare gas atoms thathave a wide range of thresholds for ground state excitation(9.5 eV, 13 eV, 11 eV and 9.5 eV for Ne, Ar, Kr and Xe,respectively) [7, 50]. By comparing electron temperaturesobtained from the each of the gases individually or in variouscombinations, it is possible to ascertain some measure of howthe ‘tail’ temperature deviates from the ‘bulk’ (low energy)temperature [9, 50] and by combining the two energy regionsobtain a non-Maxwellian EEDF shape [8]. A second approach,incorporates more argon emission lines to our existing modelsuch as those in the 3p55p → 3p54s (3px → 1sy in Paschen’snotation) transition array in the 395–470 nm wavelength range[62]. Experimental cross sections for excitation into these

12

Plasma Sources Sci. Technol. 19 (2010) 065001 J B Boffard et al

Figure 11. Contour plot of χ 2-values for expanded OES analysis of15 mTorr, 600 W Ar ICP (including emissions from both 3p54p and3p55p levels). Squares represent best-fit (T OES

x , x) values for50 synthetic data sets in Monte Carlo simulation.

levels are available for excitation from the ground state [43]and metastable levels [63]. The difference in ground stateexcitation thresholds is not that large (14.5 eV for the 3px-levelsversus 13 eV for the 2px-levels), but is generally sufficient tobetter determine both x and Tx as illustrated in figure 11.Compared with the similar analysis using only 2px-levels(figure 6), the average of the Monte Carlo runs of the 15 mTorrdata in figure 11 provides much tighter constraints to the pairof (Tx , x) values (2.85 ± 0.07 eV, 1.24 ± 0.04). The emissionmodel to produce these results, however, is considerably morecomplicated due to the need to include other effects thatcompete with the production/emission mechanisms for the 2px

levels considered in this paper [62]. In particular, due to thelonger radiative lifetimes of the 3px levels [31, 64], electron-induced de-excitation of excited levels becomes non-negligible[51, 65, 66]. Nevertheless, the added experimental work ofmeasuring the 3px → 1sy emissions and added modelingcomplexity provides a more robust method of extracting theshape of non-Maxwellian EEDFs [62].

This work also demonstrates that an all optical emissionmethod for measuring the EEDF is possible. With theexception of the ground state number density (which requiresan accurate estimate of the gas temperature), the required1sy number densities can be determined using the OES-BFtechnique which exploits the radiation-trapping induceddeviations in the observed 2px → 1sy branching fractions fromthose based on Einstein coefficients as outlined in section 4.2[22, 58]. Using these number densities in conjunction with theemission model and the observed 2px → 1sy (and possibly3px → 1sy) intensities, it is possible to measure the shape(i.e. Tx=1.2 or Tx and x) of the EEDF. Finally, using lineratios involving high lying 4p5 and 5p5 levels it is possible toextract the electron density [51, 66, 65]. With the restriction ofassuming a Maxwellian EEDF, such all optical methods havealready been introduced using collisional–radiative modelsof Ar 2px → 1sy emissions [67, 68]. As demonstrated in

this work, the inclusion of non-Maxwellian EEDFs shouldsubstantially improve the accuracy of these methods.

Acknowledgments

This work was supported by the NSF under grant CBET0714600.

References

[1] Godyak V A 2006 Nonequilibrium EEDF in gas dischargeplasmas IEEE Trans. Plasma Sci. 34 755–66

[2] Godyak V A, Piejak R B and Alexandrovich B M 1992Measurements of electron energy distribution in lowpressure RF discharges Plasma Sources Sci. Technol.1 36–58

[3] Avtaeva S V and Skornyakov A V 2009 Effect of nonlocalelectron kinetics on the characteristics of a dielectricbarrier discharge in xenon Plasma Phys. Rep. 35 593–602

[4] Iza F, Lee J K and Kong M G 2007 Electron kinetics inradio-frequency atmospheric-pressure microplasmasPhys. Rev. Lett. 99 075004

[5] Choi J, Iza F, Lee J K and Ryu C-M 2007 Electron and ionkinetics in a DC microplasma at atmospheric pressureIEEE Trans. Plasma Sci. 35 1274–8

[6] Godyak V A, Piejak R B and Alexandrovich B M 2002Electron enery distribution function measurements andplasma parameters in inductively coupled argon plasmaPlasma Sources Sci. Technol. 11 525–43

[7] Malyshev M V and Donnelly V M 1997 Determination ofelectron temperatures in plasmas by multiple rare gasoptical emission, and implications for advancedactinometry J. Vac. Sci. Technol. A 15 550

[8] Donnelly V M and Schabel M J 2002 Spatially resolvedelectron temperatures, species concentrations, and electronenergy distributions in inductively coupled chlorineplasmas, measured by trace-rare gases optical emissionspectroscopy J. Appl. Phys. 91 6288

[9] Fuller N C M, Donnelly V M and Herman I P 2002 Electrontemperatures of inductively coupled Cl2–Ar plasmasJ. Vac. Sci. Technol. A 20 170–3

[10] Zhu X-M, Chen W-C, Li J and Pu Y-K 2009 Determining theelectron temperature and the electron density by a simplecollisional–radiative model of argon and xenon inlow-pressure discharges J. Phys. D: Appl. Phys. 42 025203

[11] Crintea D L, Czarnetzki U, Iordanova S, Koleva I andLuggenholscher D 2009 Plasma diagnostics by opticalemission spectroscopy on argon and comparison withThomson scattering J. Phys. D: Appl. Phys. 42 045208

[12] Gans T, Schulz-von der Gathen V and Dobele H F 2004Spectroscopic measurements of phase resolved electronenergy distribution functions in RF-excited dischargesEurophys. Lett. 66 232–8

[13] Schulze J, Schungel E, Donko Z, Luggenholscher D andCzarnetzki U 2010 Phase resolved optical emissionspectroscopy: a non-intrusive diagnostic to study electrondynamics in capacitive radio frequency discharges J. Phys.D: Appl. Phys. 43 124016

[14] Malyshev M V and Donnelly V M 2000 Diagnostics ofinductively coupled chlorine plasmas: Measurement ofCl2 and Cl number densities J. Appl. Phys. 88 6207–15

[15] Shannon S, Holloway J P and Brake M L 1999 Spatiallyresolved fluorine actinometry J. Vac. Sci. Technol. A17 2703–8

[16] Bruckl T and Zull H 2005 Actinometry of inductivelycoupled Cl2/N2 plasma for dry etching of GaAs J. Appl.Phys. 98 023307

13

Plasma Sources Sci. Technol. 19 (2010) 065001 J B Boffard et al

[17] Czerwiec T, Greer F and Graves D B 2005 Nitrogendissociation in a low pressure cylindrical ICP dischargestudied by actinometry and mass spectrometry J. Phys. D:Appl. Phys. 38 4278–89

[18] Sugai H, Ghanashev I, Hosokawa M, Mizuno K,Nakamura K, Toyoda H, and Yamauchi K 2001 Electronenergy distribution functions and the influence onfluorocarbon plasma chemistry Plasma Sources Sci.Technol. 10 378–85

[19] Lu Z C, Foster J E, Snodgrass T G, Booske J H andWendt A E 1999 Measurements of electron energydistribution function in an argon/copper plasma for ionizedphysical vapor deposition J. Vac. Sci. Technol. A 17 840–4

[20] Hassouni K, Scott C D, Farhat S, Gicquel A and Capitelli M1997 Non-Maxwellian effect on species and energytransport in moderate pressure H2 plasmas Surf. Coat.Technol. 97 391–403

[21] Andrew Y, Lu Z, Snodgrass T, Teitzel G and Wendt A E 2000Interactions between plasmas in ionized physical vapordeposition discharges J. Vac. Sci. Technol. A 18 2137–42

[22] Boffard J B, Jung R O, Lin C C and Wendt A E 2009Measurement of metastable and resonance level densitiesin rare gas plasmas by optical emission spectroscopyPlasma Sources Sci. Technol. 18 035017

[23] Godyak V A, Piejak R B and Alexandrovich B M 1993 Probediagnostics of non-Maxwellian plasmas J. Appl. Phys.73 3657

[24] Seo S-H, Kim S S, Hong J-I, Chang C S and Chang H-Y2000 Evolution of the electron energy distribution functionin a planar inductive argon discharge Appl. Phys. Lett.76 149–51

[25] Gudmundsson J T 2001 On the effect of the electron energydistribution on the plasma parameters of an argondischarge: a global (volume-averaged) model studyPlasma Sources Sci. Technol. 10 76–81

[26] Amemiya H 1997 Sheath formation criterion and ion flux fornon-Maxwellian plasma J. Phys. Soc. Japan 66 1335–8

[27] Druyvesteyn M J and Penning F M 1940 The mechanism ofelectrical discharges in gases of low pressure Rev. Mod.Phys. 12 87–174

[28] Meige A and Boswell R W 2006 Electron energy distributionfunctions in low-pressure inductively coupled boundedplasmas Phys. Plasmas 13 092104

[29] Kolobov V I, Beale D F, Mahoney L J and Wendt A E 1994Non-local electron kinetics in an inductively coupled radiofrequency discharge Appl. Phys. Lett. 65 537

[30] Mahoney L J, Wendt A E, Barrios E, Richards C J andLeon Shohet J 1994 Electron-density and energydistributions in a planar inductively coupled dischargeJ. Appl. Phys. 76 2041–7

[31] Ralchenko Yu, Kramida A E, Reader J and NIST ASD Team2010 NIST Atomic Spectra Database (version 3.1.5),[Online]. Available: http://www.nist.gov/asd3 NationalInstitute of Standards and Technology, Gaithersburg, MD

[32] Hebner G A 1996 Spatially resolved, excited state densitiesand neutral and ion temperatures in inductively coupledargon plasmas J. Appl. Phys. 80 2624–36

[33] Beverini N, Cicconi G, Genovesi G L and Piano E 19974s3P2 metastable level density and temperaturemeasurement in a low-density argon plasma PlasmaSources Sci. Technol. 6 185–8

[34] O’Connell D, Gans T, Crintea D L, Czarnetzki U andSadeghi N 2008 Neutral gas depletion mechanisms indense low-temperature argon plasmas J. Phys. D: Appl.Phys. 41 035208

[35] Clarenbach B, Lorenz B, Kramer M and Sadeghi N 2003Time-dependent gas density and temperaturemeasurements in pulsed helicon discharges in argonPlasma Sources Sci. Technol. 12 345–57

[36] MacAdam K B, Steinbach A and Wieman C 1992 Anarrow-band tunable diode laser system with gratingfeedback, and a saturated absorption spectrometer for Csand Rb Am. J. Phys. 60 1098–111

[37] Andrew Y, Abraham I, Booske J H, Lu Z C and Wendt A E2000 Absolute densities of long lived species in an ionizedphysical vapor deposition copper-argon plasma J. Appl.Phys. 88 3208

[38] Kiehlbauch M W and Graves D B 2002 Modeling argoninductively coupled plasmas: the electron energydistribution function and metastable kinetics J. Appl. Phys.91 3539–46

[39] Druyvesteyn M J 1930 Der Niedervoltbogen Z. Phys. 64 781[40] Wendt A E 2001 Passive external radio frequency filter for

Langmuir probes Rev. Sci. Instrum. 72 2926–30[41] Godyak V A 1990 Probe measurements of the space

potential in a radio frequency discharge J. Appl. Phys.68 3157–62

[42] Magnus F and Gudmundsson J T 2008 Digital smotthing ofthe Langmuir probe I–V characteristic Rev. Sci. Instrum.79 073503

[43] Boffard J B, Chiaro B, Weber T and Lin C C 2007Electron-impact excitation of argon: optical emissioncross sections in the range 300–2500 nm. At. Data Nucl.Data Tables 93 831–63

[44] Chilton J E, Boffard J B, Schappe R S and Lin C C 1998Measurement of electron-impact excitation into the 3p54plevels of argon using Fourier-transform spectroscopy Phys.Rev. A 57 267–77

[45] Schabel M J, Donnelly V M, Kornbilt A and Tai W W 2002Determination of electron temperature, atomic flourineconcentration, and gas temperature in inductively coupledflurocarbon/rare gas plasmas using optical emissionspectroscopy J. Vac. Sci. Technol. A 20 555–63

[46] Boffard J B, Piech G A, Gehrke M F, Anderson L W andLin C C 1999 Measurement of electron-impact excitationcross sections out of metastable levels of argon andcomparison with ground-state excitation Phys. Rev. A59 2749–63

[47] Piech G A, Boffard J B, Gehrke M F, Anderson L W andLin C C 1998 Measurement of cross sections for electronexcitation out of the metastable levels of argon Phys. Rev.Lett. 81 309–12

[48] Boffard J B, Jung R O, Anderson L W and Lin C C 2006Electron-impact excitation of rare-gas atoms from theground level and metastable levels Adv. At. Mol. Opt.Phys. 54 319–421

[49] Jung R O, Boffard J B, Anderson L W and Lin C C 2009Excitation into 5p57p levels from the ground level and theJ = 2 metastable level of Xe Phys. Rev. A 80 062708

[50] Donnelly V M 2004 Plasma electron temperatures andelectron energy distributions measured by trace rare gasesoptical emission spectroscopy J. Phys. D: Appl. Phys.37 R217–36

[51] Boffard J B, Lin C C and DeJoseph C A 2004 Application ofexcitation cross sections to optical plasma diagnoticsJ. Phys. D: Appl. Phys. 37 R143–61

[52] Miyoshi Y, Lj Petrovic Z and Makabe T 2002 Opticalcomputerized tomography of the E-H transition oninductively coupled plasmas in Ar and Ar–CF4 mixturesJ. Phys. D: Appl. Phys. 35 454

[53] Moshkalyov S A, Steen P G, Gomez S and Graham W G1999 Role of low-energy electrons in Ar emission fromlow-pressure radio frequency discharge plasma Appl.Phys. Lett. 75 328

[54] Lin C C 2004 Measurements of electron-impact excitationcross sections out of the ground and metastable levels ofrare gases and applications to low-temperature plasmasContrib. Plasma Phys. 44 405–12

14

Plasma Sources Sci. Technol. 19 (2010) 065001 J B Boffard et al

[55] Booth J P, Cunge G and Sadeghi N 1997 The transition fromsymmetric to asymmetric discharges in pulsed 13.56 MHzcapacitively coupled plasmas J. Appl. Phys. 82 552–60

[56] Petrovic Z Lj, Bzenic S, Jovanovic J and Djurovic S 1995 Onspatial distribution of optical emission in radio frequencydischarges J. Phys. D: Appl. Phys. 28 2287–93

[57] Shimada M, Tynan G R and Cattolica R 2008 Neutraldepletion in inductively coupled plasmas usinghybrid-type direct simulation Monte Carlo J. Appl. Phys.103 033304

[58] Schulze M, Yanguas-Gil A, von Keudell A and Awakowicz P2008 A robust method to measure metastable and resonantstate densities from emission spectra in argon andargon-diluted low pressure plasmas J. Phys. D: Appl. Phys.41 065206

[59] Lieberman M A and Lichtenberg A J 1994 Principles ofPlasma Discharges and Materials Processing (New York:Wiley)

[60] Velazco J E, Kolts J H and Setser D W 1978 Rate constantsand quenching mechanisms for the metastable states ofargon, krypton, and xenon J. Chem. Phys. 69 4357

[61] Behringer K and Fantz U 1994 Spectroscopic diagnosticsof glow discharge plasmas with non-Maxwellian

electron energy distributions J. Phys. D: Appl. Phys.27 2128

[62] Boffard J B, Jung R O, Lin C C and Wendt A E 2010 inpreparation

[63] Jung R O, Boffard J B, Anderson L W and Lin C C 2007Excitation into 3p55p levels from the metastable levels ofAr Phys. Rev. A 75 052707

[64] Zatsarinny O and Bartschat K 2006 B-spline calculations ofoscillator strengths in neutral argon J. Phys. B: At. Mol.Opt. Phys. 39 2145

[65] Zhu X-M and Pu Y-K 2007 A simple collional-radiativemodel for low-pressure argon discharges J. Phys. D: Appl.Phys. 40 2533–8

[66] Zhu X-M and Pu Y-K 2007 A simple collisional–radiativemodel for low-pressure argon-oxygen mixture dischargesJ. Phys. D: Appl. Phys. 40 5202–5

[67] Iordanova S and Koleva I 2007 Optical emission specroscopydiagnostics of inductively-driven plasmas in argon gas atlow pressures Spectrochim. Acta B 62 344–56

[68] Zhu X-M and Pu Y-K 2010 A simple collisional–radiativemodel for low-temperature argon discharges with pressureranging from 1 Pa to atmospheric pressure: kinetics ofPaschen 1s and 2p levels J. Phys. D: Appl. Phys. 43 015204

15