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: [email protected].
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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