Fluctuation in a helicon plasma with additional immersed antenna

Abstract

Fluctuations in the floating potential are measured in a cylindrical magnetised plasma, as the phase between a "primary" Helicon antenna and a "secondary" immersed antenna is varied. The two antennas are powered by separate radio frequency (RF) generators of 13.56 MHz controlled by a single oscillator and phase shifter. The Helicon antenna is separated from the plasma by a glass tube, while the immersed copper antenna is in direct contact with the plasma. The image presented here shows floating potential fluctuations of ∼100 Hz where the amplitude of the fluctuations vary dramatically with the phase between the two RF generators.

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INSTITUTE OF PHYSICS PUBLISHING
JOURNAL OF PHYSICS D: APPLIED PHYSICS
J. Phys. D: Appl. Phys. 37 (2004) 1334–1341PII: S0022-3727(04)65066-2
Helicon plasma with additional immersed
antenna
A Aanesland1,2, C Charles1,3, R W Boswell1and Å Fredriksen2
1Plasma Research Laboratory, Research School of Physical Sciences and Engineering,
Australian National University, ACT 0200, Australia
2Physics Department, University of Tromsø, N-9037 Tromsø, Norway
E-mail: ane@phys.uit.no
Received 23 June 2003
Published 14 April 2004
Online at stacks.iop.org/JPhysD/37/1334
DOI: 10.1088/0022-3727/37/9/006
Abstract
A ‘primary’ RF power (H-power) at 13.56MHz is coupled to a plasma
source excited by an external double saddle field Helicon antenna.
A ‘secondary’ RF power (S-power), also at 13.56MHz but with variable
phase, is additionally coupled by inserting a second antenna in contact with
the plasma through one end of the source. The immersed antenna can be
grounded or floating, allowing a self-bias to form in the latter case. Changes
in the plasma density and electron temperature are measured in both cases
with varying power on the immersed antenna. The plasma potential
increases dramatically with S-power in the grounded case, and is found to be
similar in size to the sum of the plasma potential and the self-bias formed in
the floating case for all powers. Hence, the sheath between the immersed
antenna and the plasma is shown to be equal in both the grounded and
floating cases. Although the power efficiency does not vary significantly as a
function of the S-power, it is consistently lower for the grounded case
possibly as a result of a dc current to ground. The plasma parameters are
drastically changed as the phase between the two antennae are varied
(floating case), and a sinusoidal function was fitted to the plasma parameters
as a function of the phase shift. The calculated power loss to the antenna
indicates that the power efficiency of the immersed antenna, as the phase is
changed, is altered from 80% to 10%.
1. Introduction
In general, high density, low pressure plasma sources are
excited by rf fields generated by antennae exterior to and
physically separated from the actual plasma.
separation medium is simply a glass vacuum vessel and
theplasmamaybeexcitedbycapacitivecouplingofthevoltage
difference across the antenna or by inductive coupling of the
electric fields induced by currents in the antenna. A so-called
‘inductively coupled’ plasma will have both phenomena
operating, although the inductive electric field is generally
dominant. As it is generally difficult (and often undesirable)
to eliminate capacitive coupling, the glass dielectric vacuum
vesselincontactwiththeplasmanexttotheantennawillcharge
up negatively [1] to form a bias voltage. This will accelerate
Usually, the
3Also at: D´ epartement Sciences Pour l’Ing´ enieur Centre National de la
Recherche Scientifique, France.
ionslocallyintotheglassandproducesecondaryelectronsthat
willsubsequentlybeacceleratedbythesamebiasfieldintothe
plasma bulk, thereby providing an extra source of ionization.
Astheareaoftheantennaisusuallymuchsmallerthanthearea
oftheplasmasource,theseareasofnegativebiasarequitesmall
and, in general, can be neglected compared to the inductive
coupling. Hence, the majority of inductively (and microwave)
coupled plasmas have a low plasma potential of a few tens of
volts and floating potentials close to 0V.
For processing applications, a rf biased substrate can be
introducedintotheplasmaproducedbytheinductivecoupling,
allowingtheionenergiesimpinginguponthesubstratesurface
to be controlled independently of the current to the substrate,
which is determined by the rf power to the inductive coupling
[2]. This effect is made use of in some industrial, capacitively
coupled plasmas to etch insulators using ion bombardment or
reactiveionetching. Thepoweredelectrodeinthesesystemsis
0022-3727/04/091334+08$30.00© 2004 IOP Publishing LtdPrinted in the UK
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Helicon plasma with additional immersed antenna
incontactwiththeplasmabutinthematchingnetworkthereis
a tune capacitor that plays the role of a DC block, allowing the
electrode to develop a negative self-bias with current flowing
only during the charge up stage of the capacitor (some tens of
µs). Thisphenomenonisessentiallythesameasthatdescribed
by Butler and Kino [1] with the glass vacuum vessel playing
the role of the blocking capacitor.
Antennae are also usually situated inside the vacuum
vessel in plasma fusion experiments and are often in contact
with the plasma. In particular, in the H1 Heliac experiment at
theAustralianNationalUniversity[3], therfantennaisshaped
like a loop in the plane of the last closed flux surface (LCFS)
and is in contact with the plasma. One end of the loop is
grounded, allowing direct currents to flow from the plasma.
For typical conditions of 70kW of rf at 7MHz, the plasma
potential at the LCFS is over 100V while at the plasma centre
it is about 0V. A current of about 90A of electrons has been
measured going to earth, which probably maintains the edge
plasma potential at +100V. Similar effects have been noted
in experiments on plasma immersion ion implantation (PI3)
wheretherfantennaisgenerallyinsidealargemetallicvacuum
chamber [4,5].
If the plasma source and biased substrate frequencies are
significantly different from each other there is little or no
interaction between the two frequencies [6]. However, the
substrate is sometimes biased with the same rf frequency as
the source, and to avoid beating, the phase difference between
the two rf voltages (to the plasma source and the substrate)
is controlled electronically. Thomas and Singh [7] showed
that the phase of the rf voltage applied to the electrodes in
a balanced triode etching system had a profound effect on
the resulting plasma and etch rate.
sputtering model together with experiments showed that the
phase delay between a cathode and a substrate affect both
the electron and ion energies, the peak-to-peak voltages on the
A rf glow discharge
Ext. Helicon antenna
(H–antenna)
Int. small antenna
(S–antenna)
DC block
(Floating)
Cl
Ct
Gas
RF
Phase box
RF
Matching box
Pump
H–power S–power
10nF
LP
Figure 1. A schematic diagram of the experimental set-up ‘Chi-Kung’. For better clarity SWR meters inserted between the rf generators
and the matching circuits are not shown in the figure.
electrodesandtherfinputpoweronthesubstrate[8]. Ithasalso
been reported that phase regulation in inductively coupled and
unbalancedmagnetronrfbiasedsputteringsystemscanchange
the self-bias at substrate samples as well as the ion energy
distribution [9,10].
In this work, we measure the influence on the plasma
parameters of the rf power supplying a copper antenna (biased
substrate) immersed into a plasma generated by an external
helicon antenna (source). The immersed antenna can be either
grounded or floating. The influence on the plasma parameters
ofthephaseshiftbetweentherfsupplyingtheexternalhelicon
antenna and the immersed copper antenna is investigated.
2. Experimental set-up
The helicon system used for the experiments reported here has
been described previously [11,12] but has been modified by
the insertion of a second copper antenna which is immersed
in, and in contact with, the plasma [13]. A sketch of the
system is shown in figure 1. Briefly, the plasma is excited by
a 20cm long double saddle type helicon antenna surrounding
and outside the 15cm diameter glass source tube. A 6cm
long bare copper antenna is inserted through the aluminium
source end plate and extends 8cm into the plasma.
helicon and small immersed antennae will be referred to as
the H-antenna and S-antenna, respectively. Both antennae are
fedbyrfpowerat13.56MHzwithseparatematchingnetworks
and rf generators. The power on the S-antenna is 10–100W
and capacitively and/or inductively coupled to the plasma.
The power on the H-antenna is 150W, which is generally low
comparedtocommonheliconsystems,andthepowerismainly
inductively coupled to the plasma [13, 14]. However, for a
plasma density of 1011cm−3in a magnetic field of 100G, the
helicon wavelength would be around 50cm, so helicon fields
would be present throughout the system, although previous
The
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A Aanesland et al
experience with this system has shown that it is unlikely that
theheliconentersintotheionizationprocessatthislowpower.
The S-antenna can be directly connected to ground,
allowing a direct current to flow, or it can be isolated from
ground by a blocking capacitor as shown in figure 1. In the
latter case, the blocking capacitor can charge up and impose a
negative self-bias on the S-antenna. The differences between
these two situations will be discussed in this paper.
The phase difference between the two antennae is
electronically controlled and can be changed from 0 (in phase)
to ±180˚ out of phase, by a common phase control unit
connected between the two rf generators. For convenience,
the rf signal to the helicon antenna is maintained at a fixed
phase, while the phase of the rf signal from the generator to
theimmersedantennaisvariedwithrespecttothisfixedphase.
The phase difference between the two antennae is calibrated
by measuring the phase of the input voltages with a directional
coupler between the generators and the matching networks.
The argon feed gas is introduced into the diffusion
chamber, and the turbomolecular/rotary pumping system is
connected to the sidewall of the chamber. The base pressure
is a few 10−6Torr, the pressure being measured with an ion
gauge and a Baratron gauge. Two solenoids situated around
the source are used to create a dc magnetic field. A pressure of
4mTorrandamagneticfieldof100Ginthesource,decreasing
to a few Gauss in the diffusion region, were used.
Alowpassfilterconnectedtotheimmersedantennainside
the matching box was used to measure the antenna self-bias
(Vsb). The peak-to-peak value of the rf current (Ipp) in the
matching box was measured using a rf current coil (Rogowsky
coil) around the high voltage side of the immersed antenna.
A Langmuir probe (LP) was inserted 1cm from the
S-antenna, in the horizontal plane of the antenna, to obtain
the plasma density (ni), the electron temperature (Te), the
plasma (Vp) and floating potentials (Vf).
thickness in front of the S-antenna is typically 0.02cm the
LP results taken 1 cm away from the antenna will reflect
the bulk plasma parameters. The Langmuir characteristics
As the sheath
Figure 2. (Left) The LP characteristic, the 1st derivative and the absolute values of the 2nd derivative. (Right) The half-logarithmic plot of
the electron current. The dotted lines are the floating and plasma potentials. This data is obtained with the S-antenna floating at 90W.
are obtained using a Labview acquisition system, where the
probe voltage, Vpr, is swept from +40 to −30V with an
increment of 0.7V (100 steps), and the voltage is kept at
−30V between the sweeps. The ions are unmagnetized at a
maximum magnetic field of <100G, hence a non-magnetized
theory to obtain the plasma density from the ion saturation
current can be used [15]. The plasma potential is found by the
maximumofthefirstderivativetogetherwiththezerocrossing
of the second derivative of the characteristics. RF plasma
potential fluctuations can alter the characteristics measured
by a Langmuir probe, but in our case the second derivative
of the characteristic, typically has a maximum and minimum
separated by less than 2kTe, and the amplitude of the floating
potential fluctuations is less than kTe, which indicates that
the effect of RF on the LP measurements are negligible [16].
Te is found from the half-logarithmic plot of the electron
current, and the straight line was extended over two or more
decades. An experimental curve is shown in figure 2 where
the linearity of the plot is quite clear and strongly suggests
that rf interference is very small. The errors were deduced
from repeated analysis of the same IV characteristics, and
were found to be of the order of ?Vp= 0.5V, ?Vf= 0.7V,
?Te = 0.5eV. The results for niare correct to within 20%,
including the errors in both the ion saturation current and the
electron temperature. The LP acquisition system and analysis
are described in more detail in previous studies [13,17].
3. Results and discussion
3.1. Grounded immersed antenna
The initial results were obtained with the S-antenna grounded.
The power on the Helicon antenna (H-power) was 150W and
the two antennae were in phase (0˚ phase shift). Figures 3 and
4showtheresponseofVp, Vf, Teandnitoincreasingpoweron
the S-antenna (S-power). When the S-power increases from
10to50Wtheplasmapotential,floatingpotentialandelectron
temperature increase from 30V to 80V, 20V to 50V and
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Helicon plasma with additional immersed antenna
Figure 3. (a) Plasma potential Vp, (b) floating potential Vfand
(c) electron temperature Teas a function of S-power. The results are
obtained with the LP 1cm away from the grounded immersed
S-antenna. H-power and argon pressure are 150W and 4mTorr,
respectively. The phase shift between the H- and S-antennae is zero.
Figure 4. Plasma density nias a function of S-power, for the same
conditions as in Figure 3.
4.2eV to 5.7eV, respectively, and then slightly decrease for
powers above 50W. We note here that the plasma potential,
the floating potential, and the electron temperature trace each
otherwell. TheplasmadensityincreaseslinearlywithS-power
by one order of magnitude from about 2×1010cm−3to 1.8×
1011cm−3. These measurements were made quite close to the
S-antenna (1cm), and for the working pressure of 4mTorr, the
plasma density decreased axially away from the S-antenna.
Themostinterestingphenomenonistheincreaseintheplasma
and floating potentials as the S-power is increased. At the
higherpowers,manysmallpinpointdischargescouldbeseenin
the diffusion chamber. This phenomenon had been previously
seeninourlaboratorywhentherewasnoblockingcapacitorin
a capacitively driven discharge. To set the background for this
phenomenon, it is worthwhile to recall that in an asymmetric
discharge(suchaswehavehere), thevoltagedivisionbetween
the sheath on the powered electrode (here the S-antenna) and
thesheathonthegroundelectrode(herethediffusionchamber)
is given by
Z = Z1+ Z2=
1
C1ω+
1
C2ω,
(1)
where C1and C2are the capacitances of the two sheaths. The
capacitance is given by ε0A/d, where A is the electrode area
andd isthesheaththicknessinfrontoftheelectrodes. Sincethe
area of the grounded electrode is much larger than that of
the powered S-electrode, and the thickness of the sheath on
the grounded electrode is much less than that of the powered
S-electrode, the capacitance of the sheath on the S-antenna is
ordersofmagnitudessmallerthanthatoftheearthedelectrode.
Hence, its impedance will dominate that of the earthed sheath
andmostoftherfvoltageontheS-electrodewillappearacross
the S-electrode to the plasma sheath.
good conductor, this high rf voltage will lead to a high dc
voltagethatwillappeareverywhereintheplasma,inparticular,
in the diffusion chamber. As the impedance of the earthed
sheath is very small, it supports only a small rf potential
difference but the plasma enforces a much higher dc potential
difference. It would appear that, under these circumstances,
the pinpoint discharges are observed. The detailed physics of
their appearance and evolution is not yet known.
As the plasma is a
3.2. Dc isolated immersed antenna
A second set of experiments was carried out with the same
experimental conditions as above, but with the S-antenna
isolated from ground by a 10nF blocking capacitor. Figures 5
and 6 show the response of Vp, Vf, Te, ni, and Vsbto increasing
power on the S-antenna (S-power). In this case, the plasma
and floating potentials remain relatively constant. When the
S-power increased from 5 to 100W, the increase of Teand
niby 2eV and a factor of 10, respectively, is similar to the
grounded S-antenna case. However, the density in the floating
case remains one to three times higher than that measured for
the grounded case.
Below 30W, the self-bias shows a linear dependence on
the S-power. A linear relationship between a substrate self-
biasandRFpowerfrom0to30Wtogetherwithanunchanged
plasma potential has been obtained previously in a dual RF
excitation plasma [18]. A self-consistent, three moment, fluid
model of a dually driven rf plasma also confirms this behavior
[19]. It was shown by both authors that this dependence
is independent of substrate frequency.
explained by Goto et al [18] as follows. The substrate power
(S-power) is given by
The relationship is
PS= Idc· Vdc
(2)
and roughly
Idc∝ ni·
?
Te.
(3)
Because of the small powers, the substrate or antenna does
not perturb the plasma and hence niand Teare unchanged (as
confirmed by the results in figures 2 and 3 for powers ?30W).
The combination of the above equations shows that
Vdc∝ Vsb∝ PAS.
(4)
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Figure 5. (a) Plasma potential Vp, (b) floating potential Vfand
(c) electron temperature Teas a function of S-power. The results are
obtained with the LP 1cm away from the floating immersed
S-antenna. The H-power and argon pressure are 150W and 4mTorr,
respectively. The phase shift between the H- and S-antennae is zero.
Figure 6. (a) Plasma density niand (b) self-bias Vsbas a function of
S-power, for the same conditions as in figure 5. The values for
Vp(float) − Vp(ground) are shown as open squares.
Goto et al concluded that if the substrate power (S-power)
becomes comparable to the ‘plasma generating power’
(H-power)theaboveargumentisincorrect. Toourknowledge,
there have been no investigations previously on dually driven
rf plasma sources showing the effect on the self-bias when the
rf substrate power and the plasma generating power become
commensurate. However, as can be seen from our results,
above 30W the S-antenna indeed affects the bulk plasma as
boththeplasmadensityandtemperatureincrease, andIdcisno
longer constant. We observe that above 30W, Vsbis constant
and PAS∝ Idc. Hence, as soon as the S-power is high enough
the power goes to increasing the plasma density and electron
temperature and the self-bias is kept constant. The constant
Vsbmight be due to a capacitive-to-inductive transition at this
power for the floating case. When the antenna is grounded, a
direct current can flow from the plasma through the match box
to ground and results in an additional Ohmic loss term that can
reduce the plasma density.
The self-bias (Vsb) on the S-antenna is almost exactly
a mirror image of the plasma potential for the grounded
S-antenna case.The plasma potential, Vp (grounded), in
the grounded case is related to the one in the floating case,
Vp(float) by
Vp(ground) = Vp(float) − Vsb.
(5)
Thevaluesof[Vp(float)−Vp(ground)]versusS-power, shown
by open squares in figure 6(b), are very similar to the values
of Vsb. A possible way of viewing this phenomenon is
by using the impedance division argument between a small
powered antenna and a large earth, presented previously. In
theasymmetriccapacitivedischargewithablockingcapacitor,
a self-bias develops on the small powered electrode with a
magnitude close to that of the rf voltage applied. Whilst the
capacitor is charging, a current flows with electrons going
to the capacitor and ions being lost from the discharge to
the earthed walls. It is commonly accepted that this occurs
because of the differences in impedances between the sheath
capacitances on the powered and earthed electrodes. If the
antenna is earthed, the rf on the antenna will force a dc voltage
component to appear on the plasma in much the same way
as in a symmetric capacitively coupled discharge. This dc
potential would play the role of a plasma potential which we
measure. It would appear from our results, that for the present
experimental configuration, the potential difference between
the antenna and the plasma must be maintained, whether the
antenna be grounded or floating. We do not have a detailed
explanation but apparently this phenomenon can give rise to
dangerous discharges separated by some distance from the
powered (small immersed) antenna. Similar results of large
plasma potentials have been reported on previously in PI3
systems, with internal dc grounded antennae [4], and in the
H1 Heliac experiment also using a dc grounded antenna [3].
However, the above relation has not been previously reported
and at the first glance it might seem surprising.
There is some evidence to support this hypothesis. Smith
et al [20] showed that following plasma breakdown there is a
net current flowing in the system, which charges the blocking
capacitor and forms the self-bias. During the period where
the capacitor is charging, the plasma potential is very large,
the self-bias voltage on the S-antenna becomes larger and the
averageplasmapotentialdecreasesuntilthesystemapproaches
steady state and no current is flowing in the system [20]. For
a grounded antenna, the blocking capacitor no longer exists
andthecurrentflowinginthesystemfollowingthebreakdown
will continue to go from the plasma through the antenna to
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Helicon plasma with additional immersed antenna
ground. The plasma potential will remain large as electrons
are continuously lost to the antenna and the plasma adjusts by
losing positive charge as quickly as possible.
We can estimate the plasma loss PS-antenna due to
ionization, excitation and the kinetic energy carried by
electrons and ions to the S-antenna, using the following
equation [14];
PS-antenna= 0.6niACse(Vi+ Vex+ 2Te+ Vp− Vsb),
where 0.6ni is the sheath edge density [2], A = 40cm2
is the area of the S-antenna, Cs =
acoustic velocity where k is the Boltzmann constant and mi
is the argon ion mass. The ionization energy Viis 15eV, the
excitation energy Vexis about 13eV and each electron takes
2Tewith it as it leaves. To this we must add the negative bias
voltage |Vsb| on the S-antenna (in the floating case), which
generally dominates over all the other terms. The PS-antenna
calculated for the grounded and floating cases as a function
of the S-power is shown in figure 7. The range for power
efficiency(PS-antenna/PS−power)is40–80%forthefloatingcase
and 20–40% for the grounded case, possibly as a result of
the expected dc current flowing from the plasma to ground,
which lowers the plasma density in the latter case. Suzuki
et al [21] investigated the power efficiency of an external
and internal one loop rf antenna and showed that the power
efficiencydependsontheplasmadensity. Thepowerefficiency
calculated in the floating case as a function of the measured
plasma density shows a trend similar to that of the internal
antenna, and suggests that the power transfer changes from
a capacitively dominant to an inductively dominant power
coupling at about 30W. The power transfer efficiency in the
grounded case is low and indicates that the power coupling is
capacitive for the whole power range. The similarity between
our ‘magnetized’ plasma, with a differently shaped immersed
antenna, to their unmagnetized plasma results suggests that
there is similar underlying physics occurring, at least on the
general scale of description we are presenting here.
The increase in electron temperature seen in figures 3(c)
and 4(c) as the S-power is increased (up to 60W) is
probably due to transit time heating effects close to the
antenna (stochastic heating). It has been recently shown [14]
that a theoretical estimate of the stochastic heating a few
times smaller than an experimental estimate was found in a
helicon source. Additional power deposition terms related to
capacitive and/or inductive rf currents flowing in the plasma
bulkandgeneratedbytheS-antennaand/ortheH-antennamay
(6)
√kTe/mi is the ion
Figure 7. PS-antennacalculated from equation (5) as a function of the
input power on the S-antenna for the grounded (? ?) and floating (◦)
cases.
be present [2,22]. At a pressure of 4mTorr, this effect would
be limited to the environs of the S-antenna.
WhentheimmersedS-antennawasgrounded,manysmall
pinpoint discharges and arcing could be seen in the diffusion
chamber at the higher powers (?30W), probably due to
the large Vp, and unfortunately resulted in the breakage of
the glass source tube. Therefore, the following experiments
were performed with the antenna floating, but similar results
were seen in the grounded case.
3.3. Phase shift effects
Measurements of the plasma parameters as a function of the
phase shift between the H- and S-antennae were obtained with
theS-antennafloating. TheS-antennawastunedforeachphase
change while tuning of the H-antenna was unnecessary as its
standing wave ratio (SWR) was always close to 1. Figure 8
shows Vp, Vfand Teand figure 9 shows ni, Vsband Ippas a
functionofthephasedifferencebetweentheH-andS-antenna.
TheH-andS-powerswere150Wand100W,respectively. For
thephaseshiftof0˚,adecreaseofbothniandVsbbyafactorof
about 3 is measured compared to the values shown in figure 6
at 100W S-power. As detailed in a previous publication [13],
some sputtering of the copper antenna occurs for 100W on
the S-antenna, which induces a copper coating on the source
tube and a power transfer decrease from the H-antenna to the
plasma. Consequently, starting with a clean tube, a density
°
Figure 8. (a) Plasma potential Vp, (b) floating potential Vf, and
(c) electron temperature Te, as a function of the phase shift between
the H-antenna and the immersed S-antenna. The H-power is 150W,
S-power is 100W, argon pressure is 4mTorr and the S-antenna is
floating.
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Figure 9. (a) Plasma density ni, (b) self-bias Vsb, and (c) rf current
Ippas a function of the phase shift between the H-antenna and the
immersed S-antenna, for the same conditions as in figure 8.
decrease of a factor of about 3 is measured during the first
30min of operation. Subsequently, the density remains stable
versus time. To prevent any undesirable density drift due to
copper re-deposition, the phase shift series was performed in
a continuous run over a period of 10min following the initial
density decrease.
Figures 8 and 9 show that there are harmonic sinusoidal
likevariationswithphase-shiftbetweentheantennae,whereni
and Vsbchange in phase and Ippchanges in anti-phase (180˚).
Vpand Vf are 90 ± 15˚ out of phase with respect to ni. Te
seems to change sinusoidally as well, but the amplitude is
very small and the frequency is doubled compared to how the
other parameters change. The most dramatic variations are
evident in the plasma density changing by 80%, and the self-
bias and floating potential changing by 40%, while Ipp, Vpand
Techangeby10–20%. Notethatthesearelocalmeasurements
close to the immersed antenna (1cm). However, at 25cm
downstream from the antenna, in the diffusion chamber, the
ionsaturationcurrentandthefloatingpotentialweremeasured
asafunctionofthephaseshiftandthesinusoidallikevariation
was still noticeable. The abrupt change at the phase between
−80˚ and −90˚, evident in all measured parameters and most
pronounced in the plasma density measurements, might be
due to a capacitive-to-inductive or inductive-to-helicon mode
transition for either the S- or H-antenna.
As the density decreases, the self-bias increases, as would
be expected since the power to the S-antenna is kept constant.
However, the plasma loss to the S-antenna, PS-antenna, as a
function of phase is calculated using equation (5) with the
°
Figure 10. PS-antennacalculated from equation (5) as a function of
the phase shift between the H-antenna and the immersed S-antenna,
for the same conditions as in figure 8.
results from figures 8 and 9, and is shown in figure 10. Even
though the S-power is kept constant, a periodic sinusoidal like
variation is found and is in phase (±10˚) with the plasma
densityandself-bias. Themaximumcalculatedpowerof80W
agrees well with the power input to the immersed S-antenna of
about 100W (measured at the rf generator), but the minimum
calculated power is only about 10W. A calibration of the rf
generator with a high impedance HF-probe was also carried
out, and for 100W at the generator the HF-probe measured
172V peak-to-peak over 50?, giving P = V2
and for 20W we measured 87V which corresponds to 19W.
The plasma loss, PS-antenna, is similar to the power input,
S-power, for most values of the phase, except for phases
between −110˚ and −30˚. In that phase range the calculated
power is about 10W and it remains unclear where the rest of
the power goes. A rf power loss of many tens of watts may
occur in the matching box/antenna (eddy and skin currents
and antenna radiation) as observed by many authors [14,21].
This result also agrees with a maximum measured current Ipp
circulating in the S-antenna/matching box for phases between
−110˚ and −30˚ (figure 9(c)).
Thomas and Singh [7] also report on sinusoidal variation
in the electrode voltages (rf peak to peak) and self-bias as a
function of phase between the electrodes in a balanced triode
plasma etching reactor. The phase between two electrodes in
rf sputtering systems have also been shown to influence both
particle concentration, ion energy distribution, and self-bias
potentials previously [9, 10, 23]. Although the influence of
the phase between rf antennae/substrates has been known and
reported on previously, the effect on the plasma parameters
are still not very well understood. Interference and dephasing
between the two rf sources might occur, and it has been shown
theoretically that two rf sources can nonlinearly interact if the
frequencies are sufficiently close. The resulting plasma and
electricalcharacteristicscanthenbesignificantlydifferent[6].
Thevariationofthefloatingandplasmapotentialsis90˚outof
phase with the self-bias and with the density. This behaviour
suggests that the system is acting as a forced oscillator and
may be open to theoretical interpretation. The changes in
density with phase are probably due to changes in the phase
difference between the rf on the plasma potential and that of
the S-antenna. For angles around −90˚ the oscillations in the
plasma potential generated by the helicon antenna (which are
not small [12]) might serve to decrease the electron heating
effect of the S-antenna fields. For phase angles around +90˚,
the two potential variations would appear to be in phase and
thus add to the heating efficiency of the S-antenna [22].
pp/8R = 74W,
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Helicon plasma with additional immersed antenna
The substrate rf power including the matching network
losses has been modelled (empirically) as a function of the
‘delay cable length’ between the substrate and cathode in an rf
sputtering system [8]. The ‘delay cable length’ corresponds to
the phase delay between the substrate and the cathode, and the
calculation showed a sinusoidal variation similar to the one in
figure 10. The authors also find that the cable length affects
theionandelectronenergies, thepeak-to-peakvoltageonboth
the substrate and cathode and the rf plasma voltage, and all
parameters have a sinusoidal variation in agreement with the
results presented here. It is possible that a modification of the
rf equivalent circuit model proposed by Logan et al [8] could
be used to predict the phase-shift dependence on the plasma
parameters in our system as well, by the use of two oscillators.
This will be the subject of further work.
4. Conclusion
For a magnetic field of 100G presented here, the effect of the
immersed antenna is felt all over the plasma and not only on
the field lines which intersect it. This is different to magnetic
fields of kilo-Gauss where the electron heating seems more
localized and confined to magnetic field lines connected to the
antenna. We believe that the phenomenon described in this
paper may also be present in the H1 Heliac.
The behaviour of an antenna immersed in, and in contact
with, a plasma is very different when it is electrically floating
and when it is grounded. In the former case, a self-bias forms
on the antenna and the floating and plasma potentials change
little with increasing power. In the latter case, the plasma
charges up and a dc current can flow from the plasma to the
antenna to ground. It is shown that the plasma potential in
the grounded case is equal to the sum of the plasma potential
and self-bias in the floating case. Hence, the sheath generated
between the S-antenna and the plasma is equal in both cases.
In the floating case, as long as the S-power is low, and not
affecting the bulk plasma, the self-bias increases linearly with
S-power, while at larger powers when the power is coupled
inductively to the plasma the self-bias is fairly constant.
Asthephaseshiftbetweenthe13.56MHzheliconantenna
andtheimmersedcopperantenna(withthesamefrequency)is
varied,theplasmaparameterschangedramatically:theplasma
density, plasma and floating potential, self-bias and rf-current
are all observed to change markedly, and can be fitted to a
sinusoidal function. The variation of the measured parameters
wasinternallyconsistent,andshowedthatthecalculatedpower
to the immersed antenna changed in a similar manner to the
self-biasandtheplasmadensityandinverselytotherf-current.
The calculated maximum power on the S-antenna was in quite
good agreement with the actual power from the generator.
Acknowledgments
This work has been carried out in the Plasma Research
Laboratory, attheAustralianNationalUniversity. Theauthors
are grateful for the technical assistance of Peter Alexander.
Ane Aanesland was supported by the Norwegian Research
Council(GrantNo131953/432),andextendsherthankstoRod
Boswell and Christine Charles for their friendly hospitality
during her stay at ANU.
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