Spatially resolved, excited state densities and neutral and ion temperatures in
`inductively coupled argon plasmas
`G. A. Hebner
`
`Citation: Journal of Applied Physics 80, 2624 (1996); doi: 10.1063/1.363178
`View online: http://dx.doi.org/10.1063/1.363178
`View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/80/5?ver=pdfcov
`Published by the AIP Publishing
`
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`GILLETTE 1211
`
`

`

`Spatially resolved, excited state densities and neutral and ion temperatures
`in inductively coupled argon plasmas
`G. A. Hebnera)
`Sandia National Laboratories, Albuquerque, New Mexico 87185-1423
`共Received 12 February 1996; accepted for publication 30 May 1996兲
`Spatially resolved, line integrated, excited state densities, and neutral and ion temperatures have
`been measured in inductively coupled argon plasmas. Absorption spectroscopy was used to measure
`the line integrated density and temperature of the argon 1s5, 1s4, 1s3, and 1s2 energy levels.
`Laser-induced fluorescence was used to confirm the neutral temperatures and to measure argon
`metastable ion temperatures. For rf powers between 50 and 300 W and pressures of 4–50 mTorr, the
`line integrated density of the 1s5 energy level varied between 1⫻1016 and 2⫻1016 m⫺2. The
`densities of the 1s4, 1s3, and 1s2 levels were approximately 4–10 times smaller. In the center of the
`plasma, the ion and neutral temperatures were identical, between 550 and 1000 K for plasma powers
`between 30 and 240 W and pressures between 4 and 50 mTorr. The neutral temperature had a
`maximum in the center of the discharge and decreased towards the edge of the discharge. However,
`the ion temperature increased to between 3000 and 4000 K at the edge of the discharge. Ion drift
`velocity in the radial direction was between 1⫻105 and 2⫻105 cm/s at the edge of the plasma. No
`significant changes in the spatial density distribution or temperature were observed when either a rf
`bias was applied to the lower electrode or when the stainless-steel lower electrode was covered with
`a bare silicon wafer. The addition of nitrogen to the argon discharge resulted in the density of the
`1s5 state decreasing by a factor of 2 and the density of the 1s4 state decreasing by a factor of 10.
`Implications of these measurements on the radial electric fields, radiation trapping, and the energy
`transport in the plasma are discussed. 关S0021-8979共96兲02817-4兴
`
`I. INTRODUCTION
`
`As integrated circuit dimensions decrease and feature as-
`pect ratios increase, plasma etching becomes more challeng-
`ing and control of the ion energy and angle striking the wafer
`surface becomes more critical. The current generation of
`high-density plasma processing reactors has been developed
`to address the increasingly stringent industrial requirements
`for a uniform, high-density source of ion and chemically
`reactive neutral species over large diameters 共d⭓200 mm兲
`with controllable ion energy at the wafer surface and with
`reduced contamination.1 The inductively coupled plasma
`共ICP兲 source is one tool that has been developed to satisfy
`current requirements. In theory, ICP sources can provide in-
`dependent control of the ion energy at the surface of the
`wafer, and the bulk plasma parameters such as ion density.
`The bulk plasma parameters are set by the power and geom-
`etry of the inductive antenna while the ion energy is con-
`trolled by the bias voltage on the wafer chuck. In practice,
`there can be a significant overlap of control between the
`antenna power and wafer bias. An improved understanding
`of the relevant plasma physics and bias sheath characteristics
`will aid in improving these tools to meet current and future
`production requirements.
`While radio-frequency inductively coupled discharges
`are not new, they have only recently been used for semicon-
`ductor plasma processing. As a result, recent work has fo-
`cused on both measurements of
`fundamental plasma
`parameters1–16 and the development of codes17–25 to improve
`our understanding of the important physics of ICP sources.
`
`a兲Electronic mail: gahebne@sandia.gov
`
`In order to understand the fundamental plasma physics
`mechanisms and to provide data to benchmark codes, many
`experiments have focused on inductive discharges in argon.
`Argon has the advantage of a relatively complete set of cross
`sections, and a minimum of discharge chemistry. Recent ex-
`periments in argon ICP systems include characterization of
`the rf circuit and rf power deposition,2,10,11 measurements of
`the electron density, electron energy distribution, tempera-
`ture and plasma potential using Langmuir probes and micro-
`wave interferometry,2,3–7 spatially resolved electromagnetic
`fields,8,9 and optical emission.15,16 In particular, probe mea-
`surements have shown that the electron density is maximum
`in the center of the discharge.2 However, the optical emission
`has been shown to peak in a ring-shaped region that corre-
`sponds to the regions of maximum electric field and electron
`heating.8,9,15 Measured azimuthal electric fields had a ring
`shape with a maximum electric field of approximately 4–8
`V/cm centered between the center of the coil and the edge.9
`Code results confirm the location and magnitude of the elec-
`tric field, and also indicate that the location of the maximum
`electric fields corresponds to the region of greatest power
`deposition and excitation.19–24
`Ion energy measurements can be used to provide insight
`into sheath and presheath characteristics such as potential
`drop and energy transfer mechanisms such as charge ex-
`change and elastic collisions.12–14 For example, argon-ion
`energy measurements at the grounded wafer surface indi-
`cated that the peak ion energy in an ICP system is approxi-
`mately equal to the plasma potential and that the ion energy
`distribution is less than 3 eV wide.13 Analysis of the ion
`
`J. Appl. Phys. 80 (5), 1 September 1996
`0021-8979/96/80(5)/2624/13/$10.00
`2624
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`angular distributions shows that the transverse argon ion en-
`ergy at the wafer surface is on the order of 3500–5000 K.13
`In addition to analysis of the ion energy at the surface, laser-
`induced fluorescence 共LIF兲 is a sensitive, noninvasive, spa-
`tially localized probe of the ion energy distribution function
`共IEDF兲 in the bulk of the plasma.26–29 However, due to the
`thin sheath length in high electron density plasmas, LIF can
`not be used to probe the ion energy distributions at the wafer
`surface. Thus, LIF measurements of the bulk plasma IEDF
`are complimentary to electrostatic measurements of the ion
`energy distributions obtained through pinholes in the lower
`electrode surface; LIF provides the IEDF before the sheath
`and electrostatic probes provide the IEDF after the sheath.
`Ion and neutral temperatures can also be determined by
`analyzing the line shape of the plasma optical emission using
`a scanning Fabry–Pe´rot interferometer.16,30,31 Since the mea-
`surement is performed along a line of sight in the plasma, it
`is difficult to obtain good spatial resolution and to identify
`Doppler shifts due to species drift.
`The objective of this work is to examine the details of
`the excited state and ion interactions in argon ICP systems.
`To this end, two different but complementary experimental
`techniques were employed. First, absorption spectroscopy
`was utilized to measure the spatially resolved density and
`temperature of the argon 1s5, 1s4, 1s3 and 1s2 共Pashen no-
`tation兲 energy levels. Second, spatially resolved LIF was
`used to confirm the argon neutral temperatures and measure
`the metastable argon ion temperature. Separately, these two
`measurement techniques provide information on fundamen-
`tal discharge parameters such as species density, species
`temperature,
`transverse ion energy, radial electric fields,
`electron collisional induced mixing, and radiation trapping.
`When examined together, these experiments provide infor-
`mation on the energy exchange between neutral and ion spe-
`cies, charge exchange and an experimental cross check of the
`unexpectedly high neutral temperatures. For example, the
`metastable argon energy levels 共1s5 and 1s3兲, and the reso-
`nance levels 共1s4 and 1s2 levels, radiatively coupled to the
`ground state but radiation trapped兲 can be important to the
`discharge physics since they comprise a reservoir of signifi-
`cant energy and density within the plasma. The relative
`population density in these energy levels provides an indica-
`tion of the importance of electron collisional quenching and
`radiation trapping. Since LIF measurements provide infor-
`mation on the ion energy distributions before they are modi-
`fied in the sheath, they can be used, together with measure-
`ments of the ion energy at the surface,12–14 to provide insight
`into the energy transfer mechanisms between the charged
`and uncharged plasma species, to gain information about the
`effects of collisions in the presheath region on the ion energy
`distribution, and to benchmark sheath and presheath codes.
`Due to the many processes involved, the accurate pre-
`diction of the excited state densities, temperatures, and ion
`energies can be a stringent test of discharge codes. To facili-
`tate code comparisons, this article includes a characterization
`of the voltage and current in the inductive coil and the bias
`electrode.
`
`FIG. 1. Schematic of the rf circuit used to power the inductive coil and bias
`the lower electrode. In most cases the lower electrode was grounded and the
`bias circuit was disconnected.
`
`II. rf CHARACTERIZATION
`The experiments were performed in a Gaseous Electron-
`ics Conference 共GEC兲 rf reference reactor that has been
`modified to include an inductively coupled plasma source.2,32
`Design and construction details of this system have been
`previously discussed.2 Briefly, the inductive coil was a five-
`turn, 11-cm-diam, planar coil constructed from 1/8-in.-diam,
`oxygen-free high-conductivity 共OFHC兲 copper tubing. The
`coil was separated from the plasma by a 1-cm-thick quartz
`window. Distance from the window to the lower electrode
`was 3.8 cm. The lower electrode can be grounded, or biased
`with rf or dc voltage. Due to the design of the ICP source,
`the clear view between the ICP antenna and the lower elec-
`trode was approximately 13 cm in the radial dimension and
`3.1 cm in the axial dimension. Both the inductive coil and
`the lower electrode were water cooled.
`A schematic of one of the circuits used to supply rf
`power 共13.56 MHz兲 to the inductive coil and bias power to
`the lower electrode is shown in Fig. 1. One of the experi-
`mental parameters that was investigated in this study was the
`influence of lower electrode bias. In some cases, the lower
`electrode was grounded by connecting it to the metal vacuum
`chamber. When the lower electrode was grounded, the rf
`supply 共ENI ACG-5兲 was connected directly to the inductive
`coil matching network and the match box 共ENI Matchwork
`5兲 shown in Fig. 1 was not used. The inductive coil circuit
`consisted of two vacuum variable tuning capacitors, direc-
`tional wattmeter 共Bird 4411兲, and calibrated Vdot and Idot
`probes. The details of the inductive system and calibration of
`the voltage and current probes have been discussed
`previously.2
`When the lower electrode was biased with rf power, out-
`put from the rf power supply and impedance matching circuit
`was connected to the inductive coil matching network and
`the lower electrode bias circuit. A fraction of the output
`power from the rf source and matching network was supplied
`to the lower electrode bias circuit using a series variable
`capacitor. The matching network after the rf supply was
`found to be necessary to keep the load impedance at the rf
`generator near 50 ⍀ as the lower electrode bias power was
`varied 共by changing the series coupling capacitance兲. A cus-
`tom low-pass filter was used to isolate the drive system from
`the harmonics generated by the plasma.33–35 The cable length
`between the coupling capacitor and the low-pass filter was
`
`G. A. Hebner
`J. Appl. Phys., Vol. 80, No. 5, 1 September 1996
`2625
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`

`

`FIG. 2. Power into the plasma, coil voltage, and coil current as functions of
`total input power 共forward power–reflected power兲. The argon pressure was
`10 mTorr and the lower stainless-steel electrode was grounded.
`
`FIG. 3. Power into the plasma, coil voltage, and coil current as functions of
`argon pressure. The total input power was 200 W and the lower stainless-
`steel electrode was grounded.
`
`adjusted to match the impedance of the lower electrode bias
`circuit. Reflected power in the bias circuits was typically
`10%–30% of the forward power. Voltage and current at the
`lower electrode were measured by using calibrated Vdot and
`Idot probes and an equivalent circuit model to derive the
`voltage and current at the electrode, similar to the procedure
`used for parallel-plate rf discharge studies.32–35
`Voltage and current for the inductive coil are shown in
`Figs. 2 and 3 as a function of power and pressure respec-
`tively. For the data in Fig. 2, the argon pressure was constant
`at 10 mTorr and for the data in Fig. 3, the total input power
`was 200 W. In both cases, the lower electrode was grounded.
`Total input power was the difference between the forward
`and reflected rf power as measured by the wattmeter. In all
`cases, the reflected power was less than 2 W. Plasma power
`is the difference between the total input power minus the
`power deposited into the coil, calculated from I2R/2. For a
`typical coil resistance of 0.5 ⍀, approximately 80% of the
`total input power was deposited into the plasma. The re-
`ported voltages and currents are zero to peak values.
`The rf characteristics of the lower electrode bias circuit
`are shown in Fig. 4 as functions of the bias power. For these
`measurements, the total input power into the inductive coil
`was maintained at 200 W and the pressure was 10 mTorr.
`Two electrode materials were used, the native stainless steel
`and a 6-in.-diam silicon wafer placed on top of the stainless-
`steel electrode 共6.5 in. diameter兲. The wafer was bare silicon,
`without photoresist or patterning and no attempt was made to
`remove the native oxide. The intent of the experiment was to
`investigate the effect of different surface materials on the
`argon discharge parameters. As the bias power was in-
`
`creased, the rf voltage, current, and impedance increased,
`independent of surface material; however, the dc self-bias
`and phase were different for the two materials. This is likely
`the result of the different secondary electron generation prop-
`erties of silicon and stainless steel.
`
`III. EXPERIMENTAL CONFIGURATION
`A. Absorption measurements
`A schematic of the experimental configuration used to
`make the two-dimensional absorption measurements is
`shown in Fig. 5. Output from an argon-ion-laser-pumped
`ring titanium 共Ti兲–sapphire laser 共Coherent 899-21兲 was am-
`plitude stabilized 共Coherent Noise Eater兲 and collimated us-
`ing a 6-in.-diam telescope. Collimation was optimized by
`using a shear plate. The collimated light was passed through
`the entire discharge volume and then imaged onto a charge-
`coupled-device 共CCD兲 camera 共Hamamatsu C3140, 512
`⫻480 pixels兲 using a second telescope. Spectral bandpass
`filters 共⌬␭⫽10 nm兲 and neutral density filters 共OD⫽2.5–3.5兲
`were placed in front of the CCD camera to attenuate the
`laser, discharge emission, and room lights. Spatial resolution
`in this configuration was less than 0.5 mm. A fraction of the
`laser output was directed to a wavemeter 共Burleigh兲 and e´ta-
`lon 共7.5 GHz free spectral range兲 to monitor the absolute
`laser frequency.
`To measure the line integrated density, the output wave-
`length of the Ti–sapphire laser was scanned across the ab-
`sorption lineshape. Typically, the laser was scanned a total of
`6 GHz in 51 discrete steps. The laser was tuned to 801.4,
`810.4, 794.8, and 826.6 nm to probe the 1s5(1s5– 2p8),
`
`G. A. Hebner
`J. Appl. Phys., Vol. 80, No. 5, 1 September 1996
`2626
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`

`

`FIG. 6. Example of the 801.4 nm (1s5– 2p8) absorption line shape as
`scanned by the Ti–sapphire laser and the fit. Total input power was 200 W
`at 10 mTorr argon. Optimized fit parameters were line-integrated density of
`1.97⫻1016 m⫺2, Doppler width of 1.149 GHz 共751 K,兲 and frequency offset
`of 48 MHz.
`
`2D CCD image of the transmitted laser light was stored. In
`addition, the background plasma emission was recorded and
`subtracted from each laser image before processing. To re-
`duce the data to manageable quantities, the pixels of the
`CCD camera data were averaged. Typically, pixels in an
`8⫻16 array were averaged. The averaged data was then fit to
`a Voigt absorption line shape36 using a computer program.
`The unknowns in the Voigt line-shape fit were line integrated
`density, Doppler width, and center frequency. To optimize
`the line-shape fit, the center frequency determined by the
`line-shape fitting program was allowed to vary within the
`uncertainty of the absolute center frequency of the probed
`transition. The uncertainty in the absolute center frequency
`共⫾75 MHz兲 was related to the frequency uncertainty in the
`wavemeter and the e´talon. Neutral temperatures 共K兲 were
`determined from the Doppler width. If the energy distribu-
`tion function is well fit by a Gaussian profile, then tempera-
`ture is a good parameter to describe the distribution function.
`As confirmed by the LIF measurements 共discussed below兲,
`the neutral temperature data were well fit by a Gaussian line
`shape.
`An example of the raw transmission data and optimum
`fit are shown in Fig. 6 for an absorption measurement on the
`801.4 nm argon transition (1s5– 2p8). For these discharge
`conditions 共200 W, 10 mTorr兲, the absorption on line center
`was greater than 99% and the line shape was significantly
`different than a pure Gaussian or Lorentzian. For the data in
`Fig. 6, the optimum fit parameters returned by the computer
`algorithm were integrated density of 1.97⫻1016 m⫺2, Dop-
`pler width of 1.149 GHz 共751 K兲, and a small center fre-
`quency offset of 48 MHz. In all cases, the absolute frequency
`offset provided by the computer fitting program was less
`than 50 MHz. The uncertainty in the line integrated density
`共⫾10%兲 and the temperature 共⫾10%兲 is based upon several
`measurements of the 1s5 energy level under nominally iden-
`tical operating conditions over the course of several months
`and upon a sensitivity analysis of the line-shape fitting pro-
`gram.
`
`FIG. 4. rf voltage, current, bias voltage, phase, and rf impedance 共magni-
`tude兲 as functions of lower electrode bias power for two electrode materials,
`stainless steel and silicon. The inductive coil total input power was 200 W
`and the pressure was 10 mTorr.
`
`1s4(1s4– 2p7), 1s3(1s3– 2p4), and 1s2(1s2– 2p2) energy
`levels of neutral argon, respectively. The 1s5 and 1s3 energy
`levels are metastable levels while the 1s4 and 1s2 levels are
`radiatively coupled to ground. At each laser wavelength, the
`
`FIG. 5. Schematic of the absorption experiment.
`
`G. A. Hebner
`J. Appl. Phys., Vol. 80, No. 5, 1 September 1996
`2627
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`

`

`FIG. 8. Example of the normalized laser-induced argon ion fluorescence,
`and Gaussian line-shape fit. The plasma conditions were 249 W plasma
`power and 10 mTorr.
`
`Neutral and ion temperatures were inferred by scanning
`the laser across the transition lineshapes and monitoring the
`fluorescence. The neutral
`temperatures were measured
`by exciting the 2p6– 4d5(4p[3/2] – 4d[1/2]0) transition at
`805.3
`nm and monitoring
`fluorescence
`of
`the
`4d5– 2p10(4d[1/2]0– 4p[1/2]) transition at 687.1 nm. Ion
`temperatures were determined by exciting the 3d 4F7/2
`0 metastable ion transition at 811.2 nm and moni-
`– 4p 4P5/2
`
`toring the fluorescence of the 4p 4P5/20 – 3d 4D7/2 transition
`at 440.1 nm. The resulting line shape was fit to a Gaussian
`line shape. An example of the LIF data from the laser-
`excited metastable ion state and the Gaussian line-shape fit
`are shown in Fig. 8. A Gaussian line shape was found to be
`an excellent fit for the neutral transition and the ion transi-
`tions within the center of the discharge 共r⫽⫾4 cm兲. As a
`result, the distribution was characterized by converting the
`Doppler width to temperature 共K兲. Several ion data points at
`r⫽⫺5 cm showed a line shape that was beginning to diverge
`from a Gaussian 共discussed below兲. Based upon the repro-
`ducibility of the data from day to day under nominally iden-
`tical operating conditions, the uncertainty in the LIF tem-
`perature measurements is estimated to be ⫾80 K.
`Neutral and ion drift velocities at various radial locations
`were obtained by fixing the probe laser parallel to the lower
`electrode 共r⫽0 cm, z⫽1.6 cm兲 and scanning the monochro-
`mator radially. In this orientation, we were measuring the
`velocity vector in the direction of the laser beam. The Dop-
`pler shift was determined from the frequency difference be-
`tween the center frequency of the measured LIF line shape
`and the drift-free center frequency as determined by the
`wavemeter/e´talon system and the LIF monitoring system that
`was fixed in the center of the plasma. In all cases, the Dop-
`pler shift indicated the ions were moving away from the
`center of the plasma 共r⫽0 cm兲.
`It should be noted that these measurements provide the
`temperature of the probed ion and neutral excited energy
`levels. The excited state temperature should be equal to the
`ground-state temperature provided that the lifetime of the
`state is short and the energy levels are well coupled to other
`short-lived states. Recent work has shown that metastable
`ion temperatures should be equal to the ground-state ion
`
`FIG. 7. Schematic of the experimental configuration.
`
`B. Laser-induced fluorescence measurements
`A schematic of the LIF experimental configuration is
`shown in Fig. 7. In this case, the output from the Ti–sapphire
`ring laser was amplitude stabilized, chopped, and loosely
`focused 共f ⫽500 mm兲 through the discharge. Fluorescence
`from the laser-excited neutral and ion states was detected at a
`right angle to the excitation beam by two detector systems, a
`spectral bandpass filtered photomultiplier tube 共PMT兲 and a
`monochromator/PMT system. Output from the PMTs was
`recorded using two lock-in amplifiers. The monochromator
`was mounted on a translation stage to facilitate measure-
`ments of the LIF at various radial positions. The point in the
`plasma imaged by the bandpass-filtered PMT system was
`fixed in the center of the plasma 共r⫽0, z⫽1.6 cm above the
`lower electrode兲. The fixed PMT served as an independent
`check on the wavemeter/e´talon absolute laser frequency
`monitoring system and as an additional absolute center fre-
`quency reference for the determination of the radial drift ve-
`locity. Alignment of the two fluorescence detection systems
`was accomplished by back lighting the monochromator with
`a laser, directing the beam through the center of the dis-
`charge 共r⫽0 cm, z⫽1.6 cm兲, and aligning the lens and band-
`pass filtered PMT along the line defined by the laser beam.
`In most cases, the excitation laser was parallel to the lower
`electrode. In this case, the transverse ion energy parallel to
`the lower electrode is determined. For one experiment, the
`excitation laser was directed through the quartz window of
`the inductive source, at a small angle 共10°兲 from the normal
`to the lower electrode. When the probe laser is perpendicular
`to the lower electrode, the IEDF perpendicular to the lower
`electrode is determined. Together, measurements in the two
`orientations provide an indication of the anisotropy of the
`IEDF. For
`these experiments,
`the lower electrode was
`grounded.
`
`G. A. Hebner
`J. Appl. Phys., Vol. 80, No. 5, 1 September 1996
`2628
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`134.84.3.58 On: Sun, 13 Apr 2014 16:27:48
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`

`

`FIG. 9. Surface plots of 共a兲 the line-integrated density of the 1s5 level and
`共b兲 the translational temperature. Discharge conditions were 200 W, 10
`mTorr, and bottom electrode grounded. The axial dimension is measured
`from the lower, grounded electrode.
`
`temperature.37 As is discussed below, the absorption mea-
`surements suggest that the neutral metastable levels and ex-
`cited states are well mixed by electrons to levels that are
`strongly coupled to ground. Thus, the neutral and ion meta-
`stable state temperatures reported in the work should be
`close to the neutral and ion ground-state temperatures.
`
`IV. NEUTRAL ARGON DENSITY AND TEMPERATURE
`A. Characteristics of the 1s5 metastable level
`An example of a surface plot of the line integrated den-
`sity and temperature as functions of spatial
`location are
`shown in Fig. 9 for the 1s5 energy level. The argon meta-
`stable 1s5 state is the lowest-energy excited state in argon
`and thus should be expected to have the highest density of
`the states investigated. Discharge conditions were 10 mTorr
`of argon and 200 W total input power. Radial position ex-
`tends from r⫽⫾6 cm while the axial position is measured
`from the bottom electrode. For these conditions, the line in-
`tegrated density had a broad maximum at r⫽0 cm that was
`centered axially between the lower electrode and the quartz
`window. Neutral temperature, as derived from the Doppler
`width, was 750 K and peaked in the center of the discharge.
`Due to the line-of-sight measurement, the temperature is an
`effective temperature, weighted by the density distribution.
`
`FIG. 10. Contour plots of the line-integrated, 1s5 state density as a function
`of total input power. The pressure was 10 mTorr and the lower electrode
`was grounded. The units of the numbered 共solid line兲 contours are 1⫻1016
`m⫺2.
`
`In addition, the mean free path at these pressures is a few cm.
`Thus,
`the temperature derived from the Doppler width
`should represent the peak temperature in the cell and the
`temperature distribution should be relatively uniform. As
`discussed below, the radially dependent temperatures deter-
`mined by absorption were confirmed using LIF.
`Contour plots of the line-integrated, 1s5 state density as
`function of total input power are shown in Fig. 10. The pres-
`sure was 10 mTorr. The labeled contours 共solid lines兲 are in
`units of 1016 m⫺2, while the spacing of the unlabeled con-
`tours 共dashed lines兲 is 0.25⫻1016 m⫺2. The axial position
`was measured from the lower electrode. As the rf power was
`increased, the density through the center of the discharge
`decreased slightly; however, the density through the plasma
`at the edges increased as noted by the change in location of
`the 1⫻1016 m⫺2 contour line. The net result was that the line
`integrated density became more uniform as the rf power into
`the plasma was increased.
`Contour plots of the line integrated density of the 1s5
`level as a function of argon pressure are shown in Fig. 11.
`
`G. A. Hebner
`J. Appl. Phys., Vol. 80, No. 5, 1 September 1996
`2629
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`

`FIG. 12. Line-integrated density of the 1s5 energy level 共circles兲, Gaussian
`fit 共solid line兲, and volume density 共dashed line兲 as a function of radius.
`Discharge conditions were total input power of 200 W, pressure of 10
`mTorr, and z⫽1.6 cm.
`
`was a factor of 5–10 below the peak electron density.2 The
`observation that the 1s5 density was maximum at r⫽⫾4 cm
`is in qualitative agreement with previous measurements that
`showed the optical emission15 and electric-field strength8,9
`peak off axis. In addition, recent code predictions in this
`geometry indicate that the maximum electric field and power
`deposition peak off axis at r⫽⫾3 cm;23 however, caution
`must be exercised when fitting the line integrated density
`beyond the range of available data. If the real density is not
`well fit by a flattopped Gaussian at large radius, then the
`radial dependence of the volume density cannot be decon-
`volved from the existing data. One possible method to re-
`solve this ambiguity is to measure the spatial profile of the
`excited states using LIF.39 Due to the uncertainties in the
`spatial distribution of the excited states outside the measure-
`ment volume, and due to the fact that for model comparison
`the line-integrated density is straightforward to calculate,
`line-integrated density is reported in this work.
`As shown in the surface plot, the neutral temperature
`was maximum in the center of the discharge. The tempera-
`ture of the population in the 1s5 energy level is shown in Fig.
`13 as a function of radius for various total input powers 共a兲
`and pressures 共b兲. The pressure was 10 mTorr for the varia-
`tion in rf power and 200 W for the variation in pressure. In
`all cases, the lower electrode was grounded. As both the
`pressure and power were increased, the peak temperature
`increased, and the difference between the temperature at r⫽0
`cm and r⫽⫾6 cm increased. For the 300 W and 50 mTorr
`cases, the temperature difference was approximately 200 K.
`The spatial profile of the neutral argon temperature was con-
`firmed using LIF measurements. For a total input power of
`200 W at 10 mTorr, the peak temperature determined by LIF
`was 900 K. The radial profile of the neutral temperature, as
`measured by LIF, was peaked in the center of the discharge
`and decreased approximately 200 K from the center to the
`edges of the plasma. In addition, examination of the neutral
`argon Doppler shift indicates that the radial drift velocity of
`the argon neutrals at r⫽⫾4 cm was less than 5⫻103 cm/s. A
`temperature difference of this magnitude can have a signifi-
`cant impact on the discharge kinetics. For example, the tem-
`perature gradient can drive particulates 共if present兲. In addi-
`
`FIG. 11. Contour plots of the line-integrated, 1s5 state density as a function
`of pressure. The total input power was 200 W and the lower electrode was
`grounded. The units of the numbered 共solid line兲 contours are 1⫻1016 m⫺2.
`
`The total input power was fixed at 200 W. The labeled con-
`tours 共solid lines兲 are in units of 1016 m⫺2, while the spacing
`of the unlabeled contours 共dashed lines兲 is 0.25⫻1016 m⫺2.
`The density through the center of the discharge had a maxi-
`mum as the pressure was increased from 4 to 50 mTorr. As
`the pressure was increased from 4 to 20 mTorr, the density
`through the center of the discharge increased approximately
`30%, while the density decreased 20% from 20 to 50 mTorr.
`The density through the edge of the discharge, as followed
`by the 1⫻1016 m⫺2 contour line, had a maximum at approxi-
`mately 10 mTorr. A general trend appears to be that the
`spatial distribution of the line integrated density of the 1s5
`level becomes more uniform at higher pressures, primarily
`due to the decrease in the density at the center. This is in
`contrast to the power dependent density which became more
`uniform due to the density at r⫽⫾6 cm increasing.
`A radial slice of line-integrated, 1s5 state density was
`transformed to provide volume density.38 Line-
`Abel
`integrated density, a fit to the line-integrated density, and the
`calculated volume density are