field reversals in electrically asymmetric capacitively coupled ......in this paper, we present a...

This content has been downloaded from IOPscience. Please scroll down to see the full text.

Download details:

IP Address: 157.182.27.179

This content was downloaded on 21/12/2013 at 19:09

Please note that terms and conditions apply.

Field reversals in electrically asymmetric capacitively coupled radio-frequency discharges in

hydrogen

View the table of contents for this issue, or go to the journal homepage for more

2013 J. Phys. D: Appl. Phys. 46 435201

(http://iopscience.iop.org/0022-3727/46/43/435201)

Home Search Collections Journals About Contact us My IOPscience

iopscience.iop.org/page/termshttp://iopscience.iop.org/0022-3727/46/43http://iopscience.iop.org/0022-3727http://iopscience.iop.org/http://iopscience.iop.org/searchhttp://iopscience.iop.org/collectionshttp://iopscience.iop.org/journalshttp://iopscience.iop.org/page/aboutioppublishinghttp://iopscience.iop.org/contacthttp://iopscience.iop.org/myiopscience

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

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


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


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


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


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


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


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


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


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


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


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


[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

field reversals in electrically asymmetric capacitively coupled ......in this paper, we present a...

Documents