Electron energy distribution function and plasma parameters acrossmagnetic filtersA. Aanesland, J. Bredin, P. Chabert, and V. Godyak Citation: Appl. Phys. Lett. 100, 044102 (2012); doi: 10.1063/1.3680088 View online: http://dx.doi.org/10.1063/1.3680088 View Table of Contents: http://apl.aip.org/resource/1/APPLAB/v100/i4 Published by the American Institute of Physics. Related ArticlesLandau damping of a driven plasma wave from laser pulses Phys. Plasmas 19, 012112 (2012) Modeling of asymmetric pulsed phenomena in dielectric-barrier atmospheric-pressure glow discharges Phys. Plasmas 19, 012308 (2012) Effect of guide field on lower-hybrid drift instabilities in current sheet containing energetic particles Phys. Plasmas 19, 012110 (2012) Comparison of entropy production rates in two different types of self-organized flows: Bénard convection andzonal flow Phys. Plasmas 19, 012305 (2012) Influence of plasma loss area on transport of charged particles through a transverse magnetic field Phys. Plasmas 19, 013504 (2012) Additional information on Appl. Phys. Lett.Journal Homepage: http://apl.aip.org/ Journal Information: http://apl.aip.org/about/about_the_journal Top downloads: http://apl.aip.org/features/most_downloaded Information for Authors: http://apl.aip.org/authors

Electron energy distribution function and plasma parameters acrossmagnetic filters

A. Aanesland,1,a) J. Bredin,1 P. Chabert,1 and V. Godyak2

1Laboratoire de Physique des Plasmas, CNRS—Ecole Polytechnique, 91128 Palaiseau Cedex, France2RF Plasma Consulting, Brookline, Massachusetts 02446, USA

(Received 1 December 2011; accepted 10 January 2012; published online 24 January 2012)

The electron energy distribution function (EEDF) is measured across a magnetic filter in

inductively coupled plasmas. The measured EEDFs are found to be Maxwellian in the elastic

energy range with the corresponding electron temperature monotonously decreasing along the

positive gradient of the magnetic field. At the maximum of the magnetic field, the electron

temperature reaches its minimum and remains nearly constant in the area of the negative gradient

of the field, where the plasma density distribution exhibits a local minimum. VC 2012 AmericanInstitute of Physics. [doi:10.1063/1.3680088]

Commonly, in low-temperature plasmas, the electron

temperature Te is governed by the ionization balance (elec-

tron creation and loss processes) and is a function of the gas

kind and the product pL, where p is the gas pressure and L is

the characteristic size of the plasma. The specific mechanism

of electron heating and the value of discharge power have a

minor influence on the electron temperature.1

In some applications, particularly, in negative ion sour-

ces, the reduction of the electron temperature enhances the

formation of negative ions by increasing dissociative attach-

ment and reducing the dissociation of negative ions in colli-

sions with energetic electrons. In negative ion sources, the

electron cooling is usually achieved with magnetic filters (a

localized transverse magnetic field) placed in front of the ion

extracting aperture.2–5 This technique of electron cooling has

been used in negative ion sources for plasma fusion,6 in the

formation of ion-ion plasmas for deep trench etching7,8 and

in space propulsion thrusters.9,10

Although magnetic filters were extensively used, most

of the experiments where electron temperature was measured

were performed at a mixed condition where filtering mecha-

nism was coupled with the plasma expansion (both phenom-

ena resulting in electron cooling).11,12 The measurements,

using Langmuir probes and gridded analysers, suffered from

many limitations of the probe diagnostics associated with

magnetic field, rf plasma potential, and incorrect use of the

probe diagnostics that resulted in inconsistent and mutually

contradictive data.5,13

For thorough understanding of the electron transport and

the related electron kinetics in non-equilibrium plasma

across magnetic barriers, it is important to measure not just

the electron temperature, but the full electron energy distri-

bution function (EEDF). Measuring of the EEDF can provide

the rates of electron elastic collisions defining the electron

transport, as well as the rates of electron inelastic processes

such as ionization, excitation, and electron attachment. How-

ever, due to many difficulties in measuring of the EEDF in

RF plasmas,14,15 and particularly in magnetized RF plas-

mas,16 the evolution of the EEDF and associated plasma

parameters across magnetic fields still remains a controver-

sive and poorly understood issue.

Here, we present the results of the EEDF measurements

across magnetic filters, which are obtained respecting strict

limitations of the probe diagnostics of RF plasma in mag-

netic field.15 The measurements are carried out with tiny

Langmuir probes in an inductively coupled plasma (ICP),

with the Langmuir probe normal to magnetic field lines,

avoiding plasma perturbation caused by a large energy ana-

lyser, and its strong capacitive interaction with plasma RF

potential met in others works. In the present study, the effect

of the magnetic filter is decoupled from other effects such as

plasma expansion and capacitive coupling effects, thus pro-

viding a unique possibility to study the influence of the mag-

netic filter structure on the EEDF and corresponding plasma

parameters inferred through Druyvesteyn procedure.

The experiments are carried out in a purely ICP source

(without capacitive coupling), symmetrically driven at

4 MHz with a ferrite enhanced planar inductor separated

from the plasma by a thin (3 mm) ceramic window.17 The

RF power is fed to the inductor via an impedance matching

network using a low loss transmission-line transformer and

air variable capacitors in symmetrical (push-pull) configura-

tion.17 The symmetrical drive of the ICP inductor practically

eliminates capacitive coupling to the plasma, resulting in

negligible plasma RF potential. The last facilitates the ICP

probe diagnostics, since there is no need for RF compensa-

tion of the probe.

The experimental ICP is schematically illustrated in Fig. 1.

The geometry of the system is rectangular with a cross section

of 8 cm by 10 cm and 12 cm long (respectively, z, y, and x-

direction). The experiments are carried out in Argon gas, with a

pressure between 1 and 100 mTorr, and a RF power of

50–200 W. The neutral gas is injected symmetrically through 8

holes distributed along the x-axis in the middle of the two 8 cm

long walls normal to the y-direction. The source is attached to a

larger pumped vacuum chamber at x¼ 12 cm via a 15 cm long,

10 cm diameter cylindrical tube. This ensures a negligible

plasma expansion in the investigated volume.

The magnetic field B is generated by a set of permanent

neodymium magnets forming a Gaussian magnetic filter.

The magnets can be moved in the x-direction to adjust thea)Electronic mail: ane.aanesland@lpp.polytechnique.fr.

0003-6951/2012/100(4)/044102/3/$30.00 VC 2012 American Institute of Physics100, 044102-1

APPLIED PHYSICS LETTERS 100, 044102 (2012)

filter position relative to the inductor coil, and in the

z-direction to reduce the magnetic field strength. The mag-

netic field lines are shown in Fig. 1 for a magnet position

x¼ 7.5 cm from the window. In this case, the maximum

magnetic field on axis is 245 G.

The EEDF is measured by a small Langmuir probe. The

probe tip, 6 mm long, is made of platinum-iridium wire with

a diameter of 50 lm. The probe shaft is made of a 1.7 mm di-

ameter double bore Quartz tube, which is extended by 4 mm

long capillary Quartz tubes to reduce plasma perturbation in

the probe tip vicinity caused by the 1.7 mm probe shaft. Two

probe tips, perpendicular to each other, are used: one to mea-

sure the probe I/V-characteristic and the other acts as a refer-

ence probe for noise reduction and compensation of the

probe circuit resistance.15 The Langmuir probe I/V acquisi-

tion and data analysis are carried out by the VGPS probe sys-

temVR

of Plasma Sensors. The EEDFs are presented in terms

of the electron energy probability functions (EEPFs) that

according to Druyvesteyn procedure are obtained from the

second derivative of the Langmuir probe characteristics.

Care must be taken when using a Langmuir probe in RF

magnetized plasmas. In the operating conditions of the pres-

ent experiment, the measured RF plasma potential is consid-

erably lower than the electron temperature, so the Langmuir

probe can be used without any RF compensation. The results

of RF plasma potential study will be published elsewhere.

For probe measurement validity in magnetic field, the probe

tip is oriented normally to the magnetic field and the probe

radius (0.025 mm) is chosen to be much less than the elec-

tron Larmor radius (0.1 mm) at the “worst case” (B¼ 245 G

and Te¼ 0.5 eV). Hence, the “classical” non-magnetized

probe theory can be used.15

The EEPFs measured along the x direction at 10 mTorr,

130 W and a magnetic field of 245 G at 7.5 cm are shown in

Fig. 2. The inset shows the case without the magnetic field.

The plasma parameters, the electron temperature, and the

plasma density, found as corresponding integrals of the

measured EEPFs, are shown in Figs. 3(a) and 3(b), respec-

tively, with and without the magnetic field.

Without magnetic field, the measured EEPFs have a two-

temperature structure and are similar to those found in the

literature at similar pL and rf power/plasma densities.14 Away

from the window, where RF heating field is practically absent,

due to electron inelastic collisions and energetic electron

escape to the chamber wall, the EEPF is cooling in the inelas-

tic energy range, e> e* (steeper EEPF slope at the electron

energy e beyond of the excitation energy e*¼ 11.55 eV). The

distribution temperature for these electrons Tef (found from

the slope of the EEPF in this energy range) is 2.2 eV; 1.8 eV

and 1.6 eV, correspondingly, for x¼ 1; 7.5 and 12 cm.

As to slow electrons of the elastic energy range (e< e*),

their distribution temperature Tes� 4.0 eV remains practi-

cally unchanged. The spatial uniformity of Tes is a conse-

quence of non-local electron kinetics when the length of the

electron energy relaxation in the elastic energy range

FIG. 1. Schematic diagram of the rectangular ferrite enhanced ICP source.

The field lines are shown for the transverse magnetic field barrier where the

maximum field on axis is 245 G at 7.5 cm.

FIG. 2. The electron energy probability function for various positions along

the x-axis, with the magnetic field maximum of 245 G at 7.5 cm. The inset

shows the EEPF without the magnetic field.

FIG. 3. The electron temperature (a) and the plasma density (b) along the x

direction. Triangles and circles are obtained without and with the magnetic fil-

ter, respectively. The solid line is the calculated magnetic field strength on axis.

044102-2 Aanesland et al. Appl. Phys. Lett. 100, 044102 (2012)

kes�L, that is not the case for the electrons of the inelastic

energy range, since their electron energy relaxation length is

smaller, kef� kes.1,18

In spite of significant change in the fast electron temper-

ature Tef, the effective electron temperature Te (calculated

from the mean electron energy) changes little along the x

direction. The reason for this is the prevailing number of low

energy electrons with nearly constant temperature Tes.

With the magnets installed, starting at x¼ 2 cm (behind

the skin layer), the measured EEPFs are Maxwellian and ex-

hibit electron cooling along the rising magnetic field. With

limited dynamic resolution of the EEPF measurement (3-4

orders of magnitude) and reduced electron temperature, the

high energy electrons corresponding to inelastic energy

range are non-detectable, since the measured interval of elec-

tron energy is less than the excitation energy. The electron

temperature is falling about linearly towards the maximum

of the magnetic field, Bmax¼ 245 G at x¼ 7.5 cm, reaching

its minimal value there. From the position of x¼ 1 cm

to x¼ 7.5 cm, the electron temperature changes from 4.3 eV

to 0.5 eV.

Behind the magnetic field maximum, in the interval

between x¼ 7.5 cm and x¼ 12 cm, the electron temperature

remains practically unchanged and close to its minimal

value. Thus, in the present experiment, the essential electron

cooling effect takes place only along the positive gradient of

the magnetic field.

Measurements in a wide range of argon pressure (not

presented here) showed that the electron temperature near

the window (x¼ 1 cm), where magnetic field is negligible, is

defined by the argon pressure and varies between 6.7 eV at

1 mTorr and 2.1 eV at 100 mTorr. On the other hand, the

electron temperature measured at the centre and behind the

magnetic filter (x� 7.5 cm) is practically the same (0.5 eV)

in this pressure range. The independence of the minimal

electron temperature is probably due to mutual compensation

of the initial electron temperature drop and reduction of the

magnetic field effect with growing gas pressure. Separating

the magnets in the z-direction, such that the maximum filter

field is 150 G in the centre, results in the minimal electron

temperature at 10 mTorr increasing up to 2.0 eV.

Plasma density profiles n(x) along the x direction with-

out and with magnetic field are shown in Fig. 3(b). In both

cases, the plasma density decays along the x direction mainly

due to diffusion to the walls and partly in the x direction.

With the magnetic field present, the plasma density decays

faster in front of the magnetic filter (x< 7.5 cm), with forma-

tion of a local minimum behind it (x> 7.5 cm). Such behav-

iour of the plasma density distribution is probably due to

plasma repelling by the magnetic field hump (the effect op-

posite to magnetic trapping) imposed on the plasma decay

along the x direction.

In conclusion, we have studied electron cooling along

magnetic filters in inductively coupled plasma, without

plasma expansion. The EEDF measurements were carried

out free of plasma perturbing effect caused by a large probe

in magnetic field and by probe characteristics distortion due

to RF plasma potential. We found Maxwellian EEDFs in the

elastic energy range with corresponding electron temperature

decreasing along the positive gradient of the magnetic field.

At the maximum of the magnetic field, the electron tempera-

ture reaches its minimum and remains nearly constant in the

area of the negative gradient of the field, where plasma den-

sity distribution exhibits a double-layer-like structure.

We are grateful for the expert technical assistance by J.

Guillon and M. Baudier. This work is part of the PEGASES

project at LPP which is partially funded EADS Astrium. V.

Godyak’s work was supported in part by the DOE OFES

(Contract No DE-SC0001939).

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