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Field reversals in electrically asymmetric capacitively coupled
radio-frequency discharges in
hydrogen
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2013 J. Phys. D: Appl. Phys. 46 435201
(http://iopscience.iop.org/0022-3727/46/43/435201)
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IOP PUBLISHING JOURNAL OF PHYSICS D: APPLIED PHYSICS
J. Phys. D: Appl. Phys. 46 (2013) 435201 (13pp)
doi:10.1088/0022-3727/46/43/435201
Field reversals in electrically asymmetriccapacitively coupled
radio-frequencydischarges in hydrogenSebastian Mohr, Edmund
Schüngel, Julian Schulze and Uwe Czarnetzki
Institute for Plasma and Atomic Physics, Ruhr University Bochum,
44780 Bochum, Germany
Received 2 July 2013, in final form 27 August 2013Published 1
October 2013Online at stacks.iop.org/JPhysD/46/435201
AbstractIn this paper, we present a simulation study of
electrically asymmetric capacitively coupledradio-frequency
hydrogen discharges using the hybrid plasma equipment model
operated atthe combined frequencies of 10 and 20 MHz. We find that,
in such discharges, field reversalscause ionization near the
electrodes during the sheath collapse. In the case of the
investigatedasymmetric voltage waveforms, the field reversals are
asymmetrically distributed over thesheaths, which causes asymmetric
ionization and density profiles. The asymmetry of theseprofiles can
be controlled by the phase angle between the two frequencies. As a
result, thepossibility to control the ion energy independently from
the ion flux via the electricalasymmetry effect (EAE) is reduced in
discharges displaying strong field reversals, as theasymmetric
field reversals compensate the electrically induced asymmetry. The
reason for thisis understood by an analytical model. Furthermore,
we demonstrate, that the EAE can berestored by the addition of
specific gases to a pure hydrogen discharge.
(Some figures may appear in colour only in the online
journal)
1. Introduction
For many technological products, from microchips over
paneldisplays to solar cells, the controlled manipulation of
surfacesis an important production step. Capacitively coupled
radio-frequency (rf) discharges are often used to induce
surfaceprocesses like the etching of structures or the deposition
of thinfilms. In order to control the process efficiency and the
qualityof the processed surfaces, the independent control of the
ionflux to the surfaces and the ion bombarding energy is
desired.Dual-frequency discharges with two substantially
differentfrequencies are frequently used to achieve this
independentcontrol [1–5]. In these discharges, the independent
control ofion energy and ion flux is limited by frequency coupling
[6–15]and secondary electrons [16], however.
Another method, which has been proposed, is theelectrical
asymmetry effect (EAE) [17–35]. It allows to adjustthe dc self-bias
and, therefore, the sheath voltages and the ionenergy without
affecting the plasma density and, consequently,the ion fluxes to
the surfaces. This is most conveniently done bycombining a
fundamental frequency with its second harmonic.By adjusting the
phase angle between the two frequencies, one
can influence the symmetry of the voltage waveform and
thedischarge. The applicability of this effect has been shown
invarious gas mixtures and Johnson et al recently succeededin
manipulating the characteristics of Si : H films with thismethod
[35].
Investigations on electronegative [33, 36] and secondaryelectron
driven discharges [16, 34] have shown that the electronheating
mechanisms and the associated ionization dynamicshave a significant
impact on the symmetry of the dischargeand the applicability of the
EAE. In this work, we investigatethe influence of field reversals
which lead to ionization nearthe electrode surfaces during the
sheath collapse [37–46] andcan potentially alter the sheath
properties and the symmetryof the discharge. Field reversals will
occur, if the electronmotion to the electrodes is hindered, and an
electric field, whichaccelerates the electrons towards the
electrodes is needed tobalance the positive ion flux on time
average. Thus, fieldreversals are favoured by a high electron
collisionality andmobile ions. Hydrogen discharges display both, so
fieldreversals appear frequently in hydrogen discharges.
Sincehydrogen is also part of many gas mixtures used in
surfaceprocessing, hydrogen discharges are the subject of this
paper.
0022-3727/13/435201+13$33.00 1 © 2013 IOP Publishing Ltd Printed
in the UK & the USA
http://dx.doi.org/10.1088/0022-3727/46/43/435201http://stacks.iop.org/JPhysD/46/435201
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J. Phys. D: Appl. Phys. 46 (2013) 435201 S Mohr et al
Figure 1. Schematic of the idealized mesh used in the
simulations. The contour plot displays the electron density in cm−3
for a pressure of100 Pa, a voltage amplitude and 260 V and a phase
angle of 90◦.
We conduct a simulation study of electrically asymmetrichydrogen
discharges using the hybrid plasma equipment model(HPEM) [47–49] by
Mark Kushner. These simulations arecarried out at a pressure of 100
Pa. By comparing differentvoltage amplitudes between 150 and 500 V,
under which theamount of ionization caused by field reversals
differs, wesystemically study the effect of field reversals on
electricallyasymmetric discharges, and employ an analytical model
toidentify the mechanisms behind this. First, we present the partof
the theory behind the EAE which is necessary to understandthe
influence of field reversals. This will be followed by ashort
description of the simulation methods. Next, the electronheating
and ionization mechanisms in electrically asymmetrichydrogen
discharges will be presented, and the effect on the dcself-bias and
the control of the ion energy will be discussed.As industrial
applications usually use gas mixtures, we brieflydiscuss the
addition of other gases, in this case silane andhelium as two gases
with substantially different characteristics,to hydrogen discharges
before finally drawing conclusions.
2. The electrical asymmetry effect
The EAE has already been discussed in detail in
severalpublications, a good overview can be found in [28]. So
inthis work, we only highlight the parts which are necessary
tounderstand the influence of field reversals.
If the voltage drop across the bulk and the floatingpotentials
can be neglected, the dc self-bias, η, is given by
η = − φ̃max + εφ̃min1 + ε
. (1)
η depends on the maximum, φ̃max, and minimum, φ̃min, ofthe
applied voltage waveform. Note, that the voltages arenormalized to
the amplitude of the applied voltage waveform.The symmetry
parameter, ε, is given by:
ε =∣∣∣∣φg,maxφp,max
∣∣∣∣ =(
Ag
Ap
)2n̄p
n̄g
(Qg,max
Qp,max
)2Isg
Isp. (2)
Here, φg,p,max denotes the maximum sheath voltage,respectively,
for the grounded and powered sheath, Ag,p theelectrode areas, n̄g,p
the mean ion densities in the sheaths atthe moment of maximum
sheath expansion and Qg,p,max themaximum positive space charges in
the sheaths, which are
reached at the moment of maximum sheath expansion. Isg,pare the
sheath integrals whose values depend on the shapesof the ion
densities in the sheaths. Reference [18] discussesthe sheath
integral thoroughly. Briefly, the sheath integral cantheoretically
be in the range between 1 and 2, and is bigger thesteeper the ion
density increases towards the bulk. Typically,|(Isg/Isp) − 1| <
0.1.
If φ̃max = −φ̃min, a dc self-bias only develops, if ε �=
1.Externally this is most commonly done by differently
sizedelectrodes. On the other hand, if ε = 1, a dc self-bias can
beinduced by voltage waveforms with different absolute valuesof
φ̃max and φ̃min. Such waveforms, φ̃(t), are for example givenby
[17, 18]
φ̃(t) = φ̃02
[sin (2πf t + θ) + sin (4πf t)] , (3)
where φ̃0 is the voltage amplitude, f the fundamental
drivingfrequency and θ a fixed, but adjustable phase angle
betweenthe two sines. Tuning θ gives us control over η [18]. Thisis
known as the EAE. This control over η translates into acontrol over
the mean ion energy at the electrode, usuallyby a factor of 2,
while the ion flux is constant, whichhas been successfully
demonstrated by various simulationsand experiments. However,
internal processes such asstrongly localized ionization can alter
the sheath properties andtherefore ε, which may be phase-dependent.
If this is the case,an increasing ε as a function of θ in the range
45◦ � θ � 135◦leads to a bigger control range, a decreasing ε to a
smaller one.
3. Setup of the simulation
In our simulations of pure hydrogen discharges, thefundamental
driving frequency, f , is 10 MHz and the neutralgas pressure is 100
Pa. We use voltage amplitudes φ̃0 of 150,260, and 500 V. The phase
angle θ is varied between 45◦ and135◦. We use an idealized mesh
with two opposing electrodeswith a separation ofd = 1.4 cm and a
radius of 10 cm (figure 1).There is a dielectric pump port in front
of the outer metalside wall to ensure a geometric symmetry. We
still observea small geometric asymmetry, however, which is caused
bya capacitive coupling to the side metal wall [50, 51].
Thisasymmetry causes a shift of the bias towards more
negativevalues, so effectively ε < 1 in otherwise symmetric
cases.The electron density shown in figure 1 is peaked at the
edge,
2
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J. Phys. D: Appl. Phys. 46 (2013) 435201 S Mohr et al
Figure 2. Spatio-temporal plots of the radially averaged
electronpower absorption in 10−2 W cm−3 over one rf-period T for
differentphase angles and φ̃0 = 260 V.
but otherwise uniform in radial direction. The peak is causedby
two mechanisms: first, the electrical field will be enhancedat the
boundary between the metal electrodes and the dielectricwall.
Second, a sheath also develops between the plasma bulkand the
dielectric wall, so at the edge two perpendicular sheathmotions
overlap, resulting in an effective diagonal sheath
motion with a higher sheath velocity. Both mechanisms leadto an
enhanced heating of the electrons and ionization.
We use the HPEM by the group of Mark Kushner [47–49]along with
the incorporated hydrogen chemistry. This 2Dsimulation tool
consists of several modules which addressdifferent physical
phenomena such as particle transport orparticle collisions.
Reference [47] gives a good overviewof the modules along with the
used equations, so herewe will only present the module choices we
made for oursimulations. We make use of the fluid kinetics Poisson
module(FKPM) to address the particle transport, temperatures
andreactions of heavy particles and electric fields, and the
electronenergy transport module (EETM) to obtain the electron
energydistribution functions and electron impact source
functions.Within the FKPM, the electron fluxes are calculated using
adrift–diffusion approximation. This is justified by the
highcollision frequencies compared to the driving frequency of10
MHz. The ion transport, on the other hand, is governedby the
momentum balance equation. The temperature ofneutrals is kept
constant at 300 K. For their transport, adiffusion approximation
was used, resulting in an effectivelyconstant gas background of the
feed gas H2. Since we donot expect electrodynamic effect at these
frequencies, theelectric potential and fields are obtained by
solving Poisson’sequation. In the EETM, we opt for the electron
Monte Carlosimulation. We also use a Monte Carlo simulation,
whichgives the effective ion temperature and transport
coefficients,to treat the H+3 ions, since kinetic effects cannot be
ignoreddue to the high mobility of these ions. Due to their
negligibledensities, we do not carry out Monte Carlo simulations
for H+2and H+, but employ the energy balance equation instead.
Thisneed not be the case in the sheaths of capacitively coupledrf
discharges due to the collisionally induced dissociation ofH+3 .
This cannot be properly addressed in fluid models becauseof the
stark energy dependence of these reactions. However,simulations and
experiments have shown, that H+3 remainsby far the dominant ion in
the sheaths at similar pressures[52–54]. Secondary electrons are
not taken into account,as their influence on electrically
asymmetric discharges hasalready been investigated [34] and we want
to be able to clearlydistinguish between the effects of field
reversals and secondaryelectrons. The electron reflection
coefficient at the electrodeswas set to 0.1.
To calculate the sheath voltages, sheath integrals, chargesand
mean ion densities in the sheaths, the sheath widths haveto be
known. They are calculated using
∫ s0
ne(x) dx =∫ d
2
s
(ni(x) − ne(x)) dx, (4)
with the sheath width s, the electrode distance d, and
theelectron or ion density ne,i, respectively [55]. We use
radiallyaveraged values of the densities in this equation. It
should benoted, that in the presented cases, this criterion is not
alwaysapplicable, due to the presence of negative space
chargesduring the field reversals, which can lead to a negative
valueof the integral on the right-hand side. If this is the case,
thesheath width and connected parameters are set to zero.
3
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J. Phys. D: Appl. Phys. 46 (2013) 435201 S Mohr et al
Figure 3. Axial electric field (left) and charge density (right)
in front of the powered electrode at different moments of the
rf-cycle T duringthe sheath collapse for θ = 45◦.
4. Results
4.1. Electron heating and ionization in electricallyasymmetric
hydrogen discharges
Let us first discuss the electron power absorption and
ionizationdynamics in electrically asymmetric hydrogen
discharges.Figure 2 shows spatio-temporal plots of the electron
powerabsorption at 100 Pa for a voltage amplitude of 260 V and
threedifferent phase angles. In all cases, we observe both
electronheating during the sheath expansion and during the
sheathcollapse. The heating during the sheath expansion is causedby
the interaction of the electron ensemble with the expandingsheath;
electrons, which have diffused into the sheath regionduring the
sheath collapse are driven back into the bulk andaccelerated. The
heating during the sheath collapse is causedby field reversals.
These field reversals occur, because theelectrons cannot reach the
electrodes by diffusion alone, astheir motion is hindered by
collisions. However, the ion fluxto the electrodes has to be
balanced, so an electric field, whichaccelerates the electrons
towards the electrodes, develops. Thereversed electric field is
accompanied by a region of negativespace charges. This process is
visualized in figure 3 for thepowered sheath with θ = 45◦.
Qualitatively, the evolution ofthe electric field and the charge
density show good agreementwith the measurements in [43].
Due to the asymmetric voltage waveform, the electronheating by
field reversals can be highly asymmetric, i.e.different in front of
each electrode, dependent on the phaseangle. At a phase angle of
45◦, only the sheath collapse onthe powered side displays a
significant field reversal, while itis the other way around at a
phase angle of 135◦. In between,exemplary at a phase angle of 90◦,
field reversals can be seenin both sheaths and are more or less
evenly distributed. Sostarting at a phase angle of 45◦, the field
reversals shift frombeing concentrated on the powered side to an
even distributionand finally to being concentrated on the grounded
side at aphase angle of 135◦.
Figure 4 shows the voltage waveform for a phase angle of45◦. Two
maxima and two minima can be identified. However,only one of the
two maxima has a significantly positive value;the other one is
zero. On the other hand, the two minima haveboth significantly
negative values. As a consequence, thereis only one sheath collapse
at the powered electrode, but two
Figure 4. The normalized applied voltage for different
phaseangles θ .
at the grounded [25]. Thus, at the grounded side, the
totalelectron flux over one rf-period is distributed over two
sheathcollapses, resulting in two rather weak field reversals. On
thepowered side, the whole electron flux over one rf-period hasto
reach the electrode in only one sheath collapse which
isconsequently characterized by a strong field reversal. This isa
consequence of the different time intervals, during whichelectrons
can reach the respective electrodes. A shorter timeinterval
necessitates a higher current density j0, which resultsin a higher
field strength E for the reversed electric field inaccordance with
[43]
E = j0eniµe
(5)
for the collisional case with the elementary charge e, the
iondensity ni, and the electron mobility µe. If the phase angle
isnow changed to greater values, the waveform will first becomemore
symmetric and then show a reversed asymmetry. Asa result, the field
reversals on the powered side will becomeweaker and the ones on the
grounded side stronger until theexact opposite is reached at a
phase angle of 135◦. In thepresented cases, the field reversals in
the powered sheath arestronger than their equivalents in the
grounded sheath due tothe geometric asymmetry.
4
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J. Phys. D: Appl. Phys. 46 (2013) 435201 S Mohr et al
Figure 5. Spatio-temporal plots of the normalized and
radiallyaveraged electron power absorption in the powered sheath
over onehalf rf-period T for different voltage amplitudes and a
phase angleof 45◦.
We also observe a dependence of the field reversal strengthon
the amplitude of the applied voltage (figure 5). At lowvoltages the
electron heating by the sheath expansion stillexceeds the one by
the field reversal. If we raise the voltage
Figure 6. The voltage drop over the powered sheath over
onerf-period T for different voltage amplitudes and a phase angle
of 45◦.
amplitude, the electron heating by the field reversal will
bemore pronounced and finally surpass the electron heatingby sheath
expansion. This happens, because higher voltageamplitudes shorten
the time interval, in which the sheathvoltage is low enough for
electrons to reach the electrodes(figure 6). This necessitates a
higher electron current density tobalance the ion current and,
therefore, a higher reversed electricfield to drive this electron
current. Since both the electroncurrent density and the electric
field strength is increased,the electron heating during the field
reversal will naturally beenhanced.
As figure 7 shows, the asymmetrically distributed fieldreversals
lead to asymmetric ionization profiles. The amount ofionization in
the powered sheath, that is in the region betweenthe powered
electrode and the mean sheath width, decreases asa function of the
phase angle, while the amount of ionizationin the grounded sheath
increases (figure 8). Furthermore, theoverall amount of ionization
in the sheaths also depends onthe voltage amplitude. The chosen
voltage amplitudes give usthree cases: at 150 V, ionization in the
bulk region dominatesover the ionization in the sheaths, the
intermediate voltageamplitude of 260 V yields similar amounts of
ionization in thebulk and in the sheaths, and finally, the
ionization in the sheathsdominates at the highest voltage amplitude
of 500 V.
As a direct consequence of this, the ion fluxes to theelectrodes
are now dependent on the phase, qualitativelyshowing the same
dependence on the phase as the ionizationin the sheaths (figure 8).
There is also a second effect, thatcontributes to the phase
dependence of the ion fluxes; sincehydrogen ions have a small mass,
they can follow the time-dependent electric field to a certain
extent in contrast to heavierions such as argon. This leads to
temporally modulatedion fluxes (figure 9); the ion flux is high
during the sheathexpansion and low during the sheath collapse. At a
phase angleof 45◦, the powered sheath collapses once and is
effectivelyexpanded over about three-thirds of the rf-cycle,
resulting in along time interval of high ion fluxes to the powered
electrode.At a phase angle of 135◦, the powered sheath collapses
twiceand is effectively expanded for only about one quarter of
5
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J. Phys. D: Appl. Phys. 46 (2013) 435201 S Mohr et al
Figure 7. Radially and temporally averaged axial ionization
profiles for different voltage amplitudes and phase angles.
Figure 8. Top: the amount of ionization in the sheaths in
relation to the overall ionization plotted for each of the sheaths
as a function of θfor the different voltage amplitudes. Bottom: the
radially and temporally averaged ion flux as a function of θ for
the different voltageamplitudes. For a better comparison, the ion
fluxes are normalized to their respective minimum values.
the rf-cycle, leading to a much smaller time interval of highion
fluxes. Consequently, the temporally averaged ion fluxesto the
powered electrode are higher for 45◦. The temporaldependence of the
ion flux is particularly pronounced at highvoltage amplitudes.
4.2. Symmetry parameter and dc self-bias in
electricallyasymmetric hydrogen discharges
As figure 10 shows, ε is a decreasing function of θ with a
rangedepending on the voltage amplitude. The range is bigger,
thehigher the voltage amplitude, i.e. the more ionization is
causedby the field reversals. This ionization influences ε in two
ways.First, it directly alters the ion density profile and,
therefore,
the ion mean densities and the sheath integrals; secondly,it
indirectly affects the maximum charges in the sheaths viathe charge
dynamics. Let us first discuss the changes in theion density
profiles. Figure 11 shows the temporally andradially averaged axial
ion density profiles for 45◦ and 135◦
with different voltage amplitudes. As we can see, the iondensity
in the sheath, which shows no significant ionization(the grounded
at 45◦ and the powered at 135◦), monotonouslyincreases towards the
bulk. On the other hand, the ionizationinside the sheaths causes
the ion density to be rather constantat low voltage amplitudes and
even showing an elevation infront of the electrode at higher
voltage amplitudes. Usually,such structures would flatten due to
diffusion. In these cases,the diffusion towards the bulk is
hindered by the electric field
6
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J. Phys. D: Appl. Phys. 46 (2013) 435201 S Mohr et al
Figure 9. Temporal development of the H+3-flux to the
poweredelectrode over one rf-period T for θ = 45◦ and φ0 = 500
V.
in the sheaths, so the ions pile up in front of the
electrode.This elevation does not occur at low voltage amplitudes,
asthe ion source in the sheath competes with an effect known
asself-amplification of the EAE [18]. This causes the ion densityin
the sheath with the higher mean sheath voltage to decreasemore
rapidly and has been observed in low-pressure argondischarges. As
hydrogen ions are more mobile, this effect isstill observed at
higher pressures in hydrogen. So without theadditional ion source
in the sheath, the ion density would showa steeper gradient in the
powered sheath than in the groundedsheath for θ = 45◦. The
self-amplification also leads to thephase-dependent bulk location
seen in figure 11, as the steeperion density gradients necessitate
a bigger maximum sheathwidth, even if the maximum sheath voltages
are equal, as isthe case for φ̃0 = 150 V. In the case of high
voltage amplitudes,the bulk displacement shows a different
behaviour as a resultof the elevated ion densities and a
phase-dependent ε �= 1. Theion source provided by the field
reversals counteracts the self-amplification, leading to the either
rather constant ion densitiesor the elevation in front of the
electrode. This difference inthe ion density profiles in the
sheaths causes the part of thesymmetry parameter ε, which describes
the ion density profile,
εi = n̄pn̄g
Isg
Isp(6)
to turn from an increasing function of θ at low
voltageamplitudes (self-amplification dominates) to a decreasingone
at higher voltage amplitudes (ionization in the sheathsdominates)
(figure 12). The interested reader can find a moredetailed and
separate discussion of Isg/Isp and n̄g/n̄p in theappendix.
The ratio of the maximum charges in the
sheaths,(Qg,max/Qp,max)
2, is also a decreasing function of θ (figure 13).Forφ0 = 150 V,
(Qg,max/Qp,max)2 shows a different qualitativebehaviour than for
the higher voltage amplitude by displayinga linear decrease. This
is caused by the axial distribution of thespace charge at the
moments of maximum sheath expansion,
Figure 10. The symmetry parameter ε as a function of the
phaseangle θ for different applied voltage amplitudes.
which are shown in figure 14. Besides the obviously
differentmaximum space charges, we see that there is a small amount
ofpositive space charge Qg,p,min left in the respective
collapsedsheaths, as at the low voltage amplitude, electrons have
ampleof time to overcome this barrier. Due to the different
timeintervals, during which electrons can reach the
electrodes,these space charges differ (Qp,min < Qg,min).
Furthermore,we observe regions of negative space charges in the
collapsedsheath regions Qg,p,neg, due to the field reversals. As
the fieldreversals are of different strength, these negative space
chargesalso differ (Qp,neg < Qg,neg < 0 C cm−3). As the total
positivecharge in the discharge is approximately constant in this
case(see figure 15 (left)), the maximum positive space charges
inthe expanded sheaths differ because of these two effects,
asQg,max + Qp,min + Qp,neg = Qp,max + Qg,min + Qg,neg.
Now, we will discuss the behaviour of (Qg,max/Qp,max)2
for the cases with higher voltage amplitudes. It displays a
steepdecrease between 45◦ and 60◦ and a more modest one for
highervalues of θ . The cause of this behaviour can be found in
thecharge dynamics. Between sheath collapses, only ions leavethe
discharge, so the total uncompensated charge decreases.During the
sheath collapses, a lot more electrons than ionsreach the
electrode, resulting in a sudden increase in theuncompensated
charge. In symmetric discharges, each sheathcollapse and the
resulting electron loss has an equivalent at theother electrode.
Thus, the maximum charges in the respectivesheaths, which roughly
equal the total charges at the momentsof maximum sheath expansion,
are equal. Due to the differentnumber of sheath collapses on the
respective sides, this isgenerally not the case in electrically
asymmetric discharges.For example, with θ = 45◦, more electrons
leave the dischargeduring the only sheath collapse on the powered
side thanduring each of the two sheath collapses on the grounded
side(figure 15). If the ion loss between sheath collapses is high,
thisleads to a phase-dependent (Qg,max/Qp,max)2 which can also
beobserved in low-pressure argon discharges as described in
[25],which also gives a more detailed discussion of this effect.
Ashydrogen ions are highly mobile, we see a similar behaviourin
hydrogen discharges at higher pressures.
7
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J. Phys. D: Appl. Phys. 46 (2013) 435201 S Mohr et al
Figure 11. The axial, radially and temporally averaged ion
density profile for different phase angles and voltage amplitudes.
The verticallines depict the maximum sheath widths for θ = 45◦.
Figure 12. The symmetry parameter εi as a function of θ
fordifferent voltage amplitudes.
Figure 13. The maximum charge ratio is a decreasing function of
θ .In case of high voltage amplitudes (strong field reversals), it
does notdecrease linearly, but shows a steeper slope between 45◦
< θ < 60◦.
Furthermore, this effect is amplified by the field reversals,as
figure 15 shows. This is a consequence of the differentfluxes to
the respective electrodes. If the ion flux at thepowered electrode
is higher, as is the case for example for
Figure 14. The axial space charge profile for θ = 45◦ at
themoment of the maximum space charges in the respective
sheaths.
θ = 45◦, the electron flux must also be higher. So in
thisexample, even more electrons will leave the discharge duringthe
one collapse of the powered sheath than without a strongfield
reversal. Consequently, the change in the total chargewill be
bigger compared to the changes in the total chargeduring the other
sheath collapses, leading to a greater rangeover which
(Qg,max/Qp,max)2 varies in the case of φ̃0 = 500 Vin comparison to
φ̃0 = 260 V or to a case with no field reversalsas in [25]. In
hydrogen, this is enhanced by the aforementionedmodulated ion
fluxes at high voltage amplitudes, which lead tohigher ion losses
during the second half of the rf-cycle. This isespecially apparent
for the voltage amplitude of 500 V. Sincethe transition from one
sheath collapse on the powered sideand two on the grounded side to
one sheath collapse on eachside takes place between 45◦ and 60◦,
the slope in figure 13 isbigger in this interval. (Qg,max/Qp,max)2
varies over a widerrange than εi (6), so the enhanced charge
dynamics are mainlyresponsible for the decreasing ε as a function
of θ . This effectis a result of the high ion mobility, so it
stands to reason that itwill be more pronounced at low pressures
and less pronouncedat higher pressures. Furthermore, we can
conclude, thatfield reversals are a self-amplifying phenomenon; the
fieldreversals cause ionization in the sheaths which result in
higher
8
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J. Phys. D: Appl. Phys. 46 (2013) 435201 S Mohr et al
Figure 15. Left: the temporal development of total uncompensated
charge over one rf-period T for θ = 45◦. Right: the minimum
totalcharge normalized to the maximum total charge as a function of
the relative amount of ionization within the sheaths.
Figure 16. Normalized dc self-bias, η, as a function of the
phaseangle, θ , for different applied voltage amplitudes. The
symbolsdepict the results of the simulation, the lines the results
ofequation (1) with ε calculated using the maximum sheath
voltagesgiven by the simulation.
ion fluxes to the electrodes. Consequently, higherelectron
fluxes are also needed, resulting in stronger fieldreversals.
The altered ion density profiles and the enhanced chargedynamics
result in a limited control range of the dc self-bias(figure 16)
and the mean ion energy of H+3 (figure 17) which wastaken from the
in situ ion Monte Carlo simulation in the last cellin front of the
electrodes. The plotted values are normalizedto their respective
minimums to allow a direct comparison.The difference between the
model and the simulated values ofthe dc self-bias for the 150 V
case are caused by the ratherlow electron density and conductivity
in the bulk region,which induces a significant, temporal voltage
drop over thebulk, similar to a reduction of the conductivity by
negativeions [33]. In combination with the phase dependence of
thefluxes (figure 8), we conclude, that the application of theEAE,
control of the ion energy independently from the ionfluxes, is
limited in discharges displaying strong field reversalsin
combination with a highly dynamic uncompensated totalcharge.
5. Gas mixtures
So far we have demonstrated, that the EAE does not work wellin
pure hydrogen discharges under conditions, in which fieldreversals
contribute significantly to the ionization. However,in industrial
applications other gases are usually admixed toinduce the desired
surface processes. To investigate how theaddition of other gases
influences the heating and ionizationmechanisms and finally the dc
self-bias, we discuss now thecase with a voltage amplitude of 260 V
and add 1% of eithersilane or helium as examples of two gases with
differentcharacteristics.
Silane is much heavier than hydrogen and has a lowerionization
threshold (12.2 eV) than H2 (15.48 eV). On theother hand, the mass
of helium ions is only marginally higherthan that of H+3 , and
helium has a higher ionization threshold(24.58 eV). As a result,
fewer helium ions are created byelectron impact than silane ions,
respectively, compared tohydrogen ions. To put this in numbers, the
ratio of electronimpact ionization of hydrogen to that of helium is
about 2000,in the hydrogen/silane mixture the respective ratio is
only about30. Additionally, more helium ions than silane ions are
lost tothe walls due to their lower mass. To quantify this, we
calculatethe relative ion loss �i,rel. We define �i,rel as the
ratio of thetemporally and radially averaged ion fluxes to the
respectiveelectrodes, 〈�i,g,p〉, and the volume averaged ion
density, 〈ni〉:
�i,rel =〈�i,g
〉+
〈�i,p
〉〈ni〉 . (7)
The ratio of the relative loss of hydrogen ions to heliumions �∑
H+i ,rel/�He+,rel ≈ 5, for hydrogen and silane ions�∑ H+i ,rel/�∑
SiH+i ,rel ≈ 35. Finally, H+3 , the dominanthydrogen ion species,
reacts efficiently with silane [56, 57],but not with helium [58].
Thus, the hydrogen/helium mixtureis dominated by hydrogen ions,
while the hydrogen/silanemixture is dominated by silane ions
(figure 18).
Figure 19 shows the electron power absorption in frontof the
powered electrode for θ = 45◦ for a pure hydrogendischarge and the
two gas mixtures. For the hydrogen/heliumcase, no discernible
difference to the pure hydrogen case canbe observed, as the
discharge is in essence a pure hydrogendischarge. On the other
hand, the electron power absorptioncaused by the field reversals is
reduced in the hydrogen/silane
9
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J. Phys. D: Appl. Phys. 46 (2013) 435201 S Mohr et al
Figure 17. Left: mean ion energy at the powered electrode.
Right: mean ion energy at the grounded electrode. Both are
normalized to therespective minimum values.
Figure 18. Radially and temporally averaged ion density profiles
for θ = 45◦ and φ0 = 260 V in the different gas mixtures.
case. This happens, because the various silane ions are
muchheavier than hydrogen ions, resulting in a smaller ion flux
tothe electrodes. This can again be quantified by the relative
ionlosses; in the hydrogen/helium mixture, the relative ion lossfor
all ion species �i,rel ≈ 5 × 105 cm s−1, in hydrogen/silane�i,rel ≈
5×104 cm s−1. This reduces the needed compensatingelectron flux
and, therefore, the field reversals. The sametrend can be seen in
the ionization profiles (figure 20); inthe hydrogen/silane case,
the ionization peak in the sheathvanishes, while it is still
present in the hydrogen/heliumcase. As a consequence, the dc
self-bias can be controlledover a wider range in hydrogen/silane
case, but not in thehydrogen/helium mixture (figure 21).
6. Conclusions
We have demonstrated, that field reversals can affectthe
symmetry of capacitively coupled radio-frequencydischarges by the
example of electrically asymmetric hydrogendischarges. In these
discharges, the field reversals areasymmetrically distributed over
the sheaths, because of thedifferent number of the sheath collapses
as a consequence ofthe asymmetric voltage waveform, which result in
differenttime intervals during which electrons can reach the
electrodes.The field reversals cause ionization in the sheaths
which isalso asymmetric. Generally, this asymmetry counteracts
theelectrically induced asymmetry and limits or even reverses
theintended use of the EAE, control of the ion energy with
constant
ion fluxes. The reduced dc self-bias control range limits
thecontrol over the ion energy, while the asymmetric
ionizationprofiles induce a dependence of the ion flux on the phase
angle.This dependence is amplified by the modulated ion flux to
theelectrodes due to the low ion mass.
This is caused by two mechanisms; first, the ionizationin the
sheaths directly influences the mean ion density inthe sheaths and
the shape of the density profile. As theionization is asymmetric,
the effect on the ion density profilesis also asymmetric,
compensating the electrically inducedasymmetry. Secondly, the
charge dynamics limit the EAE.The high ion mobility leads to a
varying total uncompensatedcharge and to different maximum charges
in the sheaths.This is amplified by the field reversals, as the
ionization inthe sheaths leads to asymmetric ion fluxes and,
therefore, toasymmetric electron losses during the sheath collapses
at therespective electrodes. The charge dynamics have a
greaterimpact on the dc self-bias than the altered ion density
profiles,so we can conclude that a severe reduction of the dc
self-bias control range only appears if field reversals dominate
theionization at high voltage amplitudes and the ion mobility
ishigh enough to induce significant charge dynamics.
Finally, we have shown, that the addition of other gaseschanges
the electron heating mechanisms and restores the dcself-bias
control range, if the added gas is carefully chosen.In order to
induce these changes, the ions generated fromthe added gas, have to
surpass the hydrogen ions in densityand have a much higher mass
than the hydrogen ions. Thisreduces the ion fluxes to the
electrodes and, consequently, the
10
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J. Phys. D: Appl. Phys. 46 (2013) 435201 S Mohr et al
Figure 19. Spatio-temporal plot of the radially
averaged,normalized electron power absorption in front of the
poweredelectrode for θ = 45◦ and φ0 = 260 V in different gas
mixturesover one half rf-period.
needed balancing electron flux and field reversals. Apart
fromthe higher mass, a low ionization threshold and a
reactionchannel with H+3 is favourable to reduce the relative
densityof hydrogen ions.
Figure 20. Radially and temporally averaged ionization
profilessummed over all ion species in different gas mixtures for θ
= 45◦and φ0 = 260 V.
Figure 21. Normalized dc self-bias η for different gas
mixtures.
Acknowledgments
The authors like to thank the German Ministry for
theEnvironment, Nature Conservation, and Nuclear Safety forfunding
this work (0325210B) and Mark J Kushner for theuse of and fruitful
discussions about HPEM.
Appendix
Figure 22 shows Isg/Isp as a function of θ for the
differentvoltage amplitudes. In all cases, Isg/Isp decreases, since
forsmall phase angles, only the powered sheath is affected by
fieldreversals, and for big phase angles only the grounded
sheath.As is noted in [18], Isg/Isp usually only varies by a very
smallamount, as is the case for φ̃0 = 150 V. However, this only
holdsfor density profiles which are constant or steadily
increasingtowards the bulk. Figure 11 shows that the ionization in
frontof the electrode leads to an elevated density at this
position,
11
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J. Phys. D: Appl. Phys. 46 (2013) 435201 S Mohr et al
Figure 22. The ratio of the sheath integrals as a function of θ
.
Figure 23. The ratio of the mean ion densities in the sheaths at
themoment of maximum sheath expansion as a function of θ .
i.e. the ion density decreases towards the bulk in a small
partof the affected sheath. This leads to the great range over
whichIsg/Isp varies.
n̄p/n̄g, on the other hand, is not a decreasing function ofθ in
these cases (figure 23); for the two smaller amplitudes,it
increases, and it is almost constant for φ̃0 = 500 V. Thisseems
counterintuitive to the presence of ionization in thepowered sheath
at small phase angles and in the groundedsheath at bigger phase
angles. This is a result of theself-amplification. In figure 11 we
see, that the ion densityfor example increases in the grounded
sheath steadily towardsthe bulk due to the self-amplification. In
the powered sheath,the self-amplification is counteracted by the
ionization sourcewhich results in a rather constant ion density in
the sheathand a smaller mean ion density, as a comparison of the
iondensities at the maximum sheath widths shows. Increasing
thevoltage amplitude increases the weight of the ion source in
thesheath compared to the self-amplification and yields the
ratherconstant n̄p/n̄g for φ̃0 = 500 V.
References
[1] Boyle P C, Ellingboe A R and Turner M M 2004 PlasmaSources
Sci. Technol. 13 493
[2] Kitajima T, Takeo Y, Petrovic Z L and Makabe T 2000
Appl.Phys. Lett. 77 489
[3] Denda T, Miyoshi Y, Komukai Y, Goto T, Petrovic Z L
andMakabe T 2004 J. Appl. Phys. 95 870
[4] Lee J K, Manuilenko O V, Babaeva N Yu, Kim H C andShon J W
2005 Plasma Sources Sci. Technol. 14 89
[5] Booth J P, Curley G, Marić D and Chabert P 2010
PlasmaSources Sci. Technol. 19 015005
[6] Gans T, Schulze J, O’Connell D, Czarnetzki U, Faulkner
R,Ellingboe A R and Turner M M 2006 Appl. Phys. Lett.89 261502
[7] Schulze J, Gans T, O’Connell D, Czarnetzki U, Ellingboe A
Rand Turner M M 2007 J. Phys. D: Appl. Phys. 40 7008
[8] Schulze J, Donkó Z, Luggenhölscher D and Czarnetzki U
2009Plasma Sources Sci. Technol. 18 034011
[9] Turner M M and Chabert P 2006 Phys. Rev. Lett. 96 205001[10]
Ahn S K and Chang H Y 2009 Appl. Phys. Lett. 95 111502[11] Olevanov
M, Proshina O, Rakhimova T and Voloshin D 2008
Phys. Rev. E 78 026404[12] Li X S, Bi Z H, Chang D L, Li Z C,
Wang S, Xu X, Xu Y,
Lu W Q, Zhu A M and Wang Y N 2008 Appl. Phys. Lett.93 031504
[13] Wang S, Xu X and Wang Y N 2007 Phys. Plasmas 14 113501[14]
Georgieva V and Bogaerts A 2006 Plasma Sources Sci.
Technol. 15 368[15] Yang Y and Kushner M J 2010 J. Appl. Phys.
108 113306[16] Donkó Z, Schulze J, Hartmann P, Korolov I,
Czarnetzki U and
Schüngel E 2010 Appl. Phys. Lett. 97 081501[17] Heil B G,
Schulze J, Mussenbrock T, Brinkmann R P and
Czarnetzki U 2008 IEEE Trans. Plasma Sci. 36 1404[18] Heil B G,
Czarnetzki U, Brinkmann P R and Mussenbrock T
2008 J. Phys. D: Appl. Phys. 41 165202[19] Donkó Z, Schulze J,
Heil B G and Czarnetzki U 2009 J. Phys.
D: Appl. Phys. 42 025205[20] Czarnetzki U, Heil B G, Schulze J,
Donkó Z, Mussenbrock T
and Brinkmann R P 2009 IOP Conf. Ser. 162 012010[21] Schulze J,
Schüngel E, Donkó Z and Czarnetzki U 2009
J. Phys. D: Appl. Phys. 42 092005[22] Donkó Z, Schulze J,
Czarnetzki U and Luggenhölscher D
2009 Appl. Phys. Lett. 94 131501[23] Longo S and Diomede P 2009
Plasma Process. Polym. 6 370[24] Schulze J, Schüngel E, Donkó Z
and Czarnetzki U 2009
J. Appl. Phys. 106 063307[25] Schulze J, Schüngel E, Donkó Z
and Czarnetzki U 2010
J. Phys. D: Appl. Phys. 43 225201[26] Schüngel E, Schulze J,
Donkó Z and Czarnetzki U 2011 Phys.
Plasmas 18 013503[27] Schulze J, Schüngel E, Donkó Z and
Czarnetzki U 2010
Plasma Sources Sci. Technol. 19 045028[28] Czarnetzki U, Schulze
J, Schüngel E and Donkó Z 2011
Plasma Sources Sci. Technol. 20 024010[29] Johnson E V, Verbeke
T, Vanel J-C and Booth J-P 2010
J. Phys. D: Appl. Phys. 43 412001[30] Zhang Q-Z, Jiang W, Hou
L-J and Wang Y-N 2011 J. Appl.
Phys. 109 013308[31] Schulze J, Schüngel E, Czarnetzki U,
Gebhardt M,
Brinkmann R P and Mussenbrock T 2011 Appl. Phys. Lett.98
031501
[32] Schüngel E, Zhang Q-Z, Iwsahita S, Schulze J, Hou L-J,Wang
Y-N and Czarnetzki U 2011 J. Phys. D: Appl. Phys44 285205
[33] Schulze J, Derzsi A and Donkó Z 2011 Plasma Sources
Sci.Technol. 20 045008
[34] Schulze J, Donkó Z, Schüngel E and Czarnetzki U
2011Plasma Sources Sci. Technol. 20 045007
12
http://dx.doi.org/10.1088/0963-0252/13/3/016http://dx.doi.org/10.1063/1.127020http://dx.doi.org/10.1063/1.1636527http://dx.doi.org/10.1088/0963-0252/14/1/012http://dx.doi.org/10.1088/0963-0252/19/1/015005http://dx.doi.org/10.1063/1.2425044http://dx.doi.org/10.1088/0022-3727/40/22/022http://dx.doi.org/10.1088/0963-0252/18/3/034011http://dx.doi.org/10.1103/PhysRevLett.96.205001http://dx.doi.org/10.1063/1.3223593http://dx.doi.org/10.1103/PhysRevE.78.026404http://dx.doi.org/10.1063/1.2945890http://dx.doi.org/10.1063/1.2780136http://dx.doi.org/10.1063/1.3517104http://dx.doi.org/10.1109/TPS.2004.924575http://dx.doi.org/10.1088/0022-3727/41/16/165202http://dx.doi.org/10.1088/0022-3727/42/2/025205http://dx.doi.org/10.1088/1742-6596/162/1/012010http://dx.doi.org/10.1088/0022-3727/42/9/092005http://dx.doi.org/10.1063/1.3110056http://dx.doi.org/10.1002/ppap.200800219http://dx.doi.org/10.1063/1.3223310http://dx.doi.org/10.1088/0022-3727/43/22/225201http://dx.doi.org/10.1063/1.3535542http://dx.doi.org/10.1088/0963-0252/19/4/045028http://dx.doi.org/10.1088/0963-0252/20/2/024010http://dx.doi.org/10.1088/0022-3727/43/41/412001http://dx.doi.org/10.1063/1.3530626http://dx.doi.org/10.1063/1.3544541http://dx.doi.org/10.1088/0022-3727/44/28/285205http://dx.doi.org/10.1088/0963-0252/20/4/045008http://dx.doi.org/10.1088/0963-0252/20/4/045007
-
J. Phys. D: Appl. Phys. 46 (2013) 435201 S Mohr et al
[35] Johnson E V, Pouliquen S, Delattre P-A and Booth J-P
2012Japan. J. Appl. Phys. 51 08HF01
[36] Schulze J, Derzsi A, Dittmann K, Hemke T, Meichsner J
andDonkó Z 2011 Phys. Rev. Lett 107 275001
[37] Sato A H and Lieberman M A 1990 J. Appl. Phys. 68 6117[38]
Vender D and Boswell R W 1992 J. Vac. Sci. Technol. A
10 1331[39] Turner M M and Hopkins M B 1992 Phys. Rev. Lett. 69
3511[40] Belenguer Ph and Boeuf J P 1990 Phys. Rev. A 41 4447[41]
Salabas A, Marques L, Jolly J and Alves L L 2004 J. Appl.
Phys. 95 4605–20[42] Leroy O L, Stratil P, Perrin J, Jolly J and
Belenguer Ph 1995
J. Phys. D: Appl. Phys. 28 500[43] Czarnetzki U, Luggenhölscher
D and Döbele H F 1999
Plasma Sources Sci. Technol. 8 230[44] Mahony C M O, Wazzan R Al
and Graham W G 1997
Appl. Phys. Lett. 71 608[45] Petrović Z Lj, Tochikubo F, Kakuta
S and Makabe T
1992 J. Appl. Phys. 71 2143[46] Schulze J, Donkó Z, Heil B G,
Luggenhölscher D,
Mussenbrock T, Brinkmann R P and Czarnetzki U2008 J. Phys. D:
Appl. Phys. 41 105214
[47] Kushner M J 2009 J. Phys. D: Appl. Phys. 42 194013[48] Wang
M and Kushner M J 2011 J. Vac. Sci. Technol. A
29 051306[49] Shoeb J and Kushner M J 2011 J. Vac. Sci. Technol.
A
29 051305[50] Coburn J W and Kay E 1972 J. Appl. Phys. 43
4965[51] Lieberman M A and Savas S E 1990 J. Vac. Sci. Technol.
A
8 1632[52] Diomede P, Capitelli M and Longo S 2005 Plasma
Sources
Sci. Technol. 14 459[53] Muta H, Kishida S, Tanaka M, Yamauchi
Y, Baba T,
Takeuchi Y, Takatsuka H and Kawai Y 2009 PlasmaProcess. Polym. 6
S792
[54] Nunomura S and Kondo M 2007 J. Appl. Phys.102 093306
[55] Brinkmann R P 2007 J. Appl. Phys. 102 093303[56] Kushner M
J 1987 J. Appl. Phys. 63 2532[57] Perrin J, Leroy O and Bordage M C
1996 Contrib. Plasma
Phys. 36 3[58] Aquilanti V, Galli A, Giardini-Guidoni A and
Volpi G G
1965 J. Chem. Phys. 43 1969
13
http://dx.doi.org/10.1143/JJAP.51.08HF01http://dx.doi.org/10.1103/PhysRevLett.107.275001http://dx.doi.org/10.1063/1.346899http://dx.doi.org/10.1116/1.578248http://dx.doi.org/10.1103/PhysRevLett.69.3511http://dx.doi.org/10.1103/PhysRevA.41.4447http://dx.doi.org/10.1063/1.1690488http://dx.doi.org/10.1088/0022-3727/28/3/009http://dx.doi.org/10.1088/0963-0252/8/2/004http://dx.doi.org/10.1063/1.119808http://dx.doi.org/10.1063/1.351137
http://dx.doi.org/10.1088/0022-3727/41/10/105214http://dx.doi.org/10.1088/0022-3727/42/19/194013http://dx.doi.org/10.1116/1.3626533http://dx.doi.org/10.1116/1.3626534http://dx.doi.org/10.1063/1.1661054http://dx.doi.org/10.1116/1.576778http://dx.doi.org/10.1088/0963-0252/14/3/007http://dx.doi.org/10.1002/ppap.200931901http://dx.doi.org/10.1063/1.2809345http://dx.doi.org/10.1063/1.2772499http://dx.doi.org/10.1002/ctpp.2150360102http://dx.doi.org/10.1063/1.1697061
1. Introduction2. The electrical asymmetry effect3. Setup of the
simulation4. Results4.1. Electron heating and ionization in
electrically asymmetric hydrogen discharges4.2. Symmetry parameter
and dc self-bias in electrically asymmetric hydrogen discharges
5. Gas mixtures6. Conclusions Acknowledgments Appendix
References