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Experimental investigations of electron heating dynamics and ion energy distributionsin capacitive discharges driven by customized voltage waveformsBirk Berger, Steven Brandt, James Franek, Edmund Schüngel, Mark Koepke, Thomas Mussenbrock, and JulianSchulze Citation: Journal of Applied Physics 118, 223302 (2015); doi: 10.1063/1.4937403 View online: http://dx.doi.org/10.1063/1.4937403 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/118/22?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Simulation study of wave phenomena from the sheath region in single frequency capacitively coupled plasmadischarges; field reversals and ion reflection Phys. Plasmas 20, 073507 (2013); 10.1063/1.4816952 Experimental investigation of ion energy distributions in a dual frequency capacitively coupled Ar / CF 4 plasma Phys. Plasmas 17, 033501 (2010); 10.1063/1.3304186 Reconstruction of ion energy distribution function in a capacitive rf discharge Appl. Phys. Lett. 94, 211503 (2009); 10.1063/1.3147216 Comparison of measurements and particle-in-cell simulations of ion energy distribution functions in a capacitivelycoupled radio-frequency discharge Phys. Plasmas 14, 103510 (2007); 10.1063/1.2795634 Feature of electron energy distribution in a low-pressure capacitive discharge Appl. Phys. Lett. 87, 041501 (2005); 10.1063/1.1928320

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Experimental investigations of electron heating dynamics and ion energydistributions in capacitive discharges driven by customized voltagewaveforms

Birk Berger,1,2 Steven Brandt,1 James Franek,1 Edmund Sch€ungel,1 Mark Koepke,1

Thomas Mussenbrock,2 and Julian Schulze11Department of Physics, West Virginia University, Morgantown, West Virginia 26506-6315, USA2Institute for Theoretical Electrical Engineering, Ruhr University Bochum, D-44780 Bochum, Germany

(Received 2 July 2015; accepted 24 November 2015; published online 14 December 2015)

Capacitively coupled radio frequency plasmas driven by customized voltage waveforms provide

enhanced opportunities to control process-relevant energy distributions of different particle species.

Here, we present an experimental investigation of the spatio-temporal electron heating dynamics

probed by Phase-Resolved Optical Emission Spectroscopy (PROES) in an argon discharge driven

by up to three consecutive harmonics of 13.56 MHz with individually adjustable harmonics’

amplitudes and phases. PROES and voltage measurements are performed at fixed total voltage

amplitudes as a function of the number of driving harmonics, their relative phases, and pressure to

study the effects of changing the applied voltage waveform on the heating dynamics in collisionless

and collisional regimes. Additionally, the ion energy distribution function (IEDF) is measured at

low pressure. In this collisionless regime, the discharge is operated in the a-mode. The velocity ofenergetic electron beams generated by the expanding sheaths is found to be affected by the number

of driving harmonics and their relative phases. This is understood based on the sheath dynamics

obtained from a model that determines sheath voltage waveforms. The formation of the measured

IEDFs is understood and found to be directly affected by the observed changes in the electron

heating dynamics. It is demonstrated that the mean ion energy can be controlled by adjusting the

harmonics’ phases. In the collisional regime at higher pressures changing the number of harmonics

and their phases at fixed voltage is found to induce heating mode transitions from the a- to thec-mode. Finally, a method to use PROES as a non-invasive diagnostic to monitor and detectchanges of the ion flux to the electrodes is developed. VC 2015 AIP Publishing LLC.[http://dx.doi.org/10.1063/1.4937403]

I. INTRODUCTION

Plasma technology has significantly improved our

modern life. Computer chips and smartphones would not

exist without highly controllable plasma etching, sputtering,

and deposition processes as a basis for semiconductor manu-

facturing.1–5 Plasma technology is also becoming more

important for biomedical applications such as sterilization

and wound healing.6–8 For many of these applications capaci-

tively coupled radio frequency (CCRF) discharges or hybrid

combinations of CCRF plasmas with high density remote

sources represent the most important reactor types,9–11 since

such plasmas allow for an efficient processing of dielectric

substrates based on high fluxes of ions and chemically reac-

tive radicals. In particular, the mean ion energy at the electro-

des, which is crucially important for the plasma surface

interaction, can be controlled in this type of plasmas.

In order to improve process control and realize ever

smaller feature dimensions and uniform process rates over

large substrates, e.g., to fulfill Moore’s law,12 advanced

methods to control particle heating dynamics and energy dis-

tribution functions of different particle species in the plasma

and at boundary surfaces must be developed.13 This requires

a detailed fundamental understanding of the plasma physics

and, in particular, of the electron heating dynamics space

and time resolved on a nanosecond timescale within the

RF period.

CCRF discharges can be operated in different electron

heating modes, which strongly affects process-relevant

plasma parameters such as electron and ion energy distribu-

tions: At low pressures and in electropositive gases, CCRF

plasmas are usually operated in the a-mode, where stochasticand ambipolar electron heating during sheath expansion14–28

and electron heating by electric field reversals during sheath

collapse29–33 dominate. At higher pressures and/or applied

voltages the c-mode is present. In this mode, the ionization isdominated by secondary electrons generated at boundary

surfaces and enhanced by collisions inside the sheaths.24,34,35

Electronegative, dusty, and/or high-pressure CCRF plasmas

can be operated in the drift-ambipolar heating mode,36–40

where strong electron heating in the plasma bulk is observed

due to a reduced electrical conductivity and high drift elec-

tric fields. Under these conditions strong ambipolar electric

fields at the sheath edges can be generated that cause signifi-

cant electron heating and ionization, as well.

In single frequency CCRF discharges, there is a strong

coupling between the electron heating, that affects the

plasma density and ion fluxes, and the mean sheath voltages,

which are key quantities for the mean ion energy at the elec-

trodes. Both parameters can be controlled by changing the

0021-8979/2015/118(22)/223302/14/$30.00 VC 2015 AIP Publishing LLC118, 223302-1

JOURNAL OF APPLIED PHYSICS 118, 223302 (2015)


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driving voltage amplitude or power, but they cannot be con-

trolled independently, since an increase of the voltage/power

will enhance both the electron heating and the mean sheath

voltages.41 Therefore, classical dual-frequency discharges

operated at substantially different frequencies (e.g., 1 MHz

and 100 MHz) were developed and became industry-

standard. In these plasma sources, the low frequency (lf)

voltage amplitude mainly controls the sheath voltage while

the high frequency (hf) voltage amplitude mainly controls

the sheath dynamics and, thus, the electron heating. It is

believed that the lf voltage amplitude does not affect the

electron heating while the hf amplitude does not affect the

mean sheath voltage significantly if the hf voltage amplitude

is sufficiently low compared to the lf voltage amplitude.41–46

However, recent investigations discovered strong coupling

mechanisms between both RF sources that limit this separate

control of the ion mean energy and the ion flux due to effects

of the lf voltage on the sheath dynamics and ionization by

secondary electrons.34,41,46,47 One approach to solve these

problems and provide ultimate process control in CCRF

plasmas is RF voltage waveform tailoring.48–60 This concept

is based on driving one electrode with a customized voltage

waveform in order to tailor the sheath dynamics and, thus,

the electron heating dynamics and the shape of the ion

energy distribution function (IEDF) at the electrodes. This

method was pioneered by Wendt et al.61,62 and Baloniaket al.63 at low frequencies and without impedance matchingin high density remote plasma sources by applying arbitrary

waveforms in the kHz-range to an electrode/wafer. This

allows for control of the shape of the ion flux-energy distri-

bution function; however this technology is not widely used

in industry. The idea of RF voltage waveform tailoring is to

generate the plasma capacitively via the customized driving

voltage waveform without any remote source. Such driving

voltage waveforms, /�ðtÞ, can be generated as a finiteFourier series consisting of multiple consecutive harmonics

of a fundamental driving frequency

/�ðtÞ ¼XNk¼1

/k cosð2pkftþ hkÞ: (1)

Here, N is the total number of applied consecutive har-monics, f is the fundamental frequency, /k is the amplitudeof the k-th harmonic, and hk is its phase. The sum of allharmonics amplitudes, /tot ¼

PNk¼1 /k, is defined as the total

amplitude of the driving voltage waveform. This waveform

can be tailored by individually adjusting the harmonics’

amplitudes and phases. For a sufficient number of harmonics

any periodic driving voltage waveform can be generated in

this way.

For N¼ 2, Equation (1) yields the waveform that wasoriginally used to generate a DC self-bias, g, electrically andcontrol it by adjusting the relative phase between the two

driving harmonics via the Electrical Asymmetry Effect

(EAE).64–70 In this way integral quantities of the ion flux

energy distribution, i.e., the ion flux and the mean ion

energy, could be controlled separately of one another and the

parasitic coupling mechanisms between the driving sources

occurring in classical dual-frequency CCRF plasmas could

be widely avoided. Moreover, lateral non-uniformities of the

ion flux across large wafers due to electromagnetic standing

wave effects could be prevented.71 Using multiple consecu-

tive harmonics to tailor the shape of the driving voltage

waveform goes significantly further: It should allow the

customization of the sheath dynamics and, thus, the electron

heating dynamics on a nanosecond timescale and the control

of the shape of the ion distribution function.72,73

Here, we present experimental investigations of the

electron heating dynamics by phase-resolved optical emis-

sion spectroscopy (PROES) in a CCRF discharge driven by

customized voltage waveforms based on a novel RF supply

system with up to three consecutive harmonics of 13.56 MHz

with individually adjustable harmonics’ amplitudes and

phases. The discharge is operated in argon with a small

admixture of neon as a tracer gas for PROES. In combination

with voltage measurements and a model to determine the

sheath voltage waveforms at both electrodes, we use PROES

to study the effects of changing the shape of the driving volt-

age waveform on the electron impact excitation dynamics as

a function of space and time on a nanosecond timescale

within the fundamental RF phase at low and high pressures.

In this way relatively collisionless and collisional regimes

are probed. The waveform is modified by changing the num-

ber of driving harmonics and their relative phases at fixed

voltage amplitudes.

At low pressures we find the discharge to be operated in

the a-mode. The velocity of energetic electron beams gener-ated by sheath expansion heating is affected by the shape of

the driving voltage waveforms via its effects on the sheath

dynamics. Based on this fundamental understanding of the

electron heating dynamics we discuss the physical origin of

the effects of voltage waveform tailoring on the IEDFs meas-

ured by a Retarding Field Energy Analyzer (RFEA) at both

electrodes as well as its integral quantities such as the ion

flux and the mean ion energy. At high pressures an electron

heating mode transition from the c-mode into the a-mode orhybrid combinations of both modes is found to be induced

by adding higher harmonics and/or changing the harmonics’

phases. These findings are again explained by changes of the

sheath dynamics by changing these external control parame-

ters. These results are expected to be highly relevant for both

applications of, and fundamental research on, RF voltage

waveform tailoring in the future.

The manuscript is structured in the following way: In

Section II, the experimental setup including the reactor, the

RF power supply, and impedance matching as well as the

diagnostics are introduced. Additionally, the model used to

determine the sheath voltage waveform based on the measured

voltage drop across the plasma is explained. In Section III, the

results are presented. This section is divided into two parts

according to the two different pressure regimes investigated

here. At both pressures (3 Pa and 200 Pa) the spatio-temporal

measurements of the electron impact excitation rate into a par-

ticularly chosen neon state are discussed as a function of the

number of driving frequencies and the harmonics phases in

combination with the voltage measurements and the model

results. At low pressures, these findings are combined with

223302-2 Berger et al. J. Appl. Phys. 118, 223302 (2015)


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RFEA measurements of the IEDFs at both electrodes to obtain

a complete understanding of the electron heating dynamics

and its effects on IEDF control. Finally, conclusions are drawn

in Section IV.

II. EXPERIMENTAL SETUP AND SHEATH MODEL

A. Plasma source and diagnostics

Figure 1 shows a sketch of the experimental setup.

The experiments are performed in a modified Gaseous

Electronics Conference (GEC) cell74 with a powered elec-

trode at the bottom and a grounded counter electrode. Both

electrodes have a diameter of 10 cm with a gap length d. Thegap length is adjustable by changing the height of the top

grounded electrode, while the position of the powered elec-

trode is fixed. The RF supply system is designed to drive

such a CCRF discharge with multiple consecutive harmonics

and individually adjustable harmonics’ phases and ampli-

tudes.75,76 Here, three consecutive harmonics of 13.56 MHz

are used.

A multi-frequency waveform is applied to the powered

electrode according to Equation (1) with harmonics’ ampli-

tudes according to the following criterion:48

/k ¼ /tot2 N � k þ 1ð Þ

N N þ 1ð Þ : (2)

This criterion maximizes the electrical control range of the

DC self-bias for a given /tot. A total voltage amplitude of/tot ¼ 210 V is used here. Thus, for a triple-frequencydischarge the harmonics’ amplitudes are chosen to be

/1 ¼ 105 V; /2 ¼ 70 V, and /3 ¼ 35 V for the 13.56 MHz,27.12 MHz, and 40.68 MHz signals, respectively. With

two frequencies the amplitudes are set to /1 ¼ 140 V;/2 ¼ 70 V, and /3 ¼ 0 V. Voltage amplitudes at higherharmonics generated by the plasma itself have been meas-

ured with a HV probe and can be neglected due to compa-

rably small values of less than 1%.

Measurements have been performed in a collisionless

and a collisional regime using two different configurations.

In both regimes, argon is used with an admixture of 25%

neon as tracer gas to perform optical emission measure-

ments. The collisionless case is investigated at a pressure of

p¼ 3 Pa with a gap length of d¼ 30 mm. A glass cylinder isused to confine the plasma radially between both electrodes.

Although this cylinder increases the geometrical symmetry

compared to the case of the plasma being confined by the

grounded chamber side wall, the coupling between the glass

cylinder and the grounded chamber side wall effectively

enlarges the surface area of the grounded electrode and, thus,

induces a geometrical asymmetry.66,77,78 The measurements

in the collisional regime are performed at 200 Pa. Here, the

geometrical asymmetry is maximized to facilitate the opera-

tion of the plasma in the c-mode by maximizing/minimizingthe voltage drop across the sheath at the powered/grounded

electrode, respectively. Therefore, the glass cylinder is

removed and the grounded counter electrode is set to its

highest position (d¼ 15 cm). Then, the surface area of thegrounded electrode is the entire chamber wall.

In addition to the reactor, the diagnostics are also shown

in Figure 1. A high voltage probe is connected to the

RF cable close to the powered electrode to measure the time-

resolved voltage drop across the discharge. Using this

measurement the amplitudes and phases for each individual

frequency are determined based on a Fourier Transformation

and a calibration routine described in Refs. 66 and 76.

A RFEA (Impedans Semion79–82) is used to measure the

IEDF at both the powered and grounded electrodes. For this

purpose the RFEA is either placed on top of the powered

electrode or the grounded electrode via a holder. Based on

the measured ion distribution function, f ðeiÞ, the total ionflux, Ci, and the mean ion energy, heii, are calculated66

Ci ¼ðei;max

0

f ðeiÞdei; (3)

heii ¼ C�1iðei;max

0

eif ðeiÞdei : (4)

Here, ei;max is the maximum energy of the ions. Measurementscan only be performed at low pressure due to the high proba-

bility of collisions inside the RFEA at higher pressures.

To perform PROES measurements, the neon emission

line at 585.2 nm originating from the Ne2p1 state is measured

space- and time-resolved using an ICCD (intensified charge-

coupled device) camera (Andor iStar) equipped with an in-

terference filter. The neon transition has been used, because

the Ne2p1 state has a relatively short lifetime of about 15 ns,

which leads to a more accurate calculation of the excitation

rate compared to states with a longer lifetime. Moreover, the

excitation threshold energy of this line is about 19 eV and,

thus, resembles the excitation threshold energy of argon ioni-

zation. To synchronize the camera with the driving voltage

waveform the measured signal of the high voltage probe is

used as the trigger signal for a Digital Delay Generator,

which provides a synchronized output signal. In this way the

high frequency MHz-signal can be reduced to a kHz-signal

that is needed to trigger the camera. All images were binned

in the horizontal direction in order to reduce noise.

Measurements of the emission are performed with a spatial

resolution of about 1 mm in the vertical direction and a time

resolution of 2 ns. Based on a simplified rate equation model

the electron impact excitation rate from the ground state into

the observed excited state is calculated from the measuredFIG. 1. Sketch of the experimental setup including all diagnostics.



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spatio-temporal emission. A detailed explanation of the diag-

nostic can be found in Ref. 83.

B. Model of the sheath voltages

A detailed understanding of the spatio-temporal electron

heating dynamics revealed by the PROES measurements is

facilitated by determining the temporal evolution of the

sheath voltages from measured input parameters based on a

model that has been introduced in Ref. 64 and has been

extensively described in Ref. 67. It is based on the voltage

balance of a CCRF discharge

/plðtÞ ¼ gþ /�ðtÞ ¼ /spðtÞ þ /bðtÞ þ /sgðtÞ: (5)

Here, /pl is the voltage drop across the plasma, which corre-sponds to the sum of the driving voltage waveform, /�ðtÞ,and the DC self-bias, g. /sp; /b, and /sg are the voltagedrops across the powered electrode sheath, the plasma bulk,

and the grounded electrode sheath, respectively. Typically,

the voltage drop across the plasma bulk is negligible in low-

pressure electropositive plasmas.

We adopt a quadratic charge-voltage relation of the

plasma sheaths.64,67 This corresponds to a simplification, as

higher orders may as well play a role,84 but it will allow for

an analytical treatment of the sheath voltages. This yields64

/sp tð Þ � �1

2e�0�nspA2pQ2sp tð Þ; (6)

/sg tð Þ �1

2e�0�nsgA2gQ2sg tð Þ; (7)

for the powered and grounded sheath, respectively. Here,

�nsp; �nsg, Qsp, Qsg, Ap, and Ag are the mean ion densities andthe total charge in the two sheaths and the powered and

grounded electrode surface area, respectively. e and �0 arethe elementary charge and the vacuum permittivity.

A further assumption is that the total net positive space

charge within the discharge volume, Qtot, (i) remains con-stant as a function of time, (ii) is only located in the oscillat-

ing sheath regions adjacent to the powered and grounded

electrodes, and (iii) is found entirely in the opposing sheath

at the time when either sheath is collapsed, i.e., any residual

minimum charge or floating potential is neglected.64,67,85

Certainly, the latter point becomes critical in multi-

frequency plasmas, because the time fraction within the RF

period of a comparatively small sheath voltage and, hence,

of an electron conduction current to the electrodes depends

on the shape of the applied voltage waveform and may

become relatively long. As a consequence, the floating

potential may be enhanced for certain phase angles.48 Such

effects will play a role for the ion dynamics in a low-voltage

sheath, for instance, but are not required for the discussion of

the results in the scope of this paper. Thus, we can define

q ¼ Qsp=Q0 and qtot � q ¼ ðQtot � QspÞ=Q0 (with Q0 ¼ Apffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2e�0 �nsp/tot

pbeing a charge normalization constant67) to be

the normalized charge in the powered and grounded sheath.

This yields

/pl ¼ /tot½�q2ðtÞ þ eðqtot � qðtÞÞ2�: (8)

The symmetry parameter, e, relates the maximum voltagedrops across the powered and grounded sheath. Using

Poisson’s equation, the maximum voltage drop across the

powered and grounded electrodes sheath can be expressed

as j/sp;maxj � Q2sp;max=ð2A2pe�0�nspÞ and /sg;max � Q2sg;max=ð2A2ge�0�nsgÞ. Thus, the symmetry parameter is

64,67

e ¼/maxsg/maxsp

�� ¼ ApAg

� �2 �nsp�nsg

Qsg;maxQsp;max

� �2: (9)

Both the symmetry parameter and the total charge can easily

be determined from the DC self-bias, g, and from the globalextrema of the applied voltage waveform, /�;max and /�;min,which are obtained from the voltage measurements64,67,76

e ¼ �gþ /�;maxgþ /�;min

; (10)

qtot ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi/�;max � /�;min

/tot 1þ eð Þ

s: (11)

Rearranging Equation (8) for q(t),69 the sheath voltages areeventually calculated as /spðtÞ ¼ �/totq2ðtÞ and/sgðtÞ ¼ e/tot½qtot � qðtÞ�2. This yields

/sp tð Þ ¼ �/tot�eqtot þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffieq2tot � 1� eð Þ

/pl tð Þ/tot

s

1� e

264

375

2

; (12)

/sg tð Þ ¼ e/totqtot �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffieq2tot � 1� eð Þ

/pl tð Þ/tot

s

1� e

264

375

2

: (13)

III. RESULTS

A. Low pressure (3 Pa)

In this section, the control of the electron heating

dynamics and the ion flux-energy distribution functions by

voltage waveform tailoring, i.e., by changing the number of

applied harmonics and their relative phases, is investigated

in a low-pressure argon plasma. The gap distance is

d¼ 30 mm. Measurements at N¼ 2 and N¼ 3 are comparedwith each other to demonstrate the effect of adding a third

harmonic.

Figure 2(a) shows the DC self-bias normalized by the

total applied voltage amplitude, �g ¼ g=/tot, as a function ofthe phase of the second and third harmonics. The minimum

DC self-bias is found at h2 ¼ 0� and h3 ¼ 0�, while the maxi-mum value is found at h2 ¼ 180� and h3 ¼ 0�. This is in goodqualitative agreement with previous results.76 In order to tune

�g between these extrema, the easiest option is to keep the thirdharmonic at h3 ¼ 0� and vary h2. Thus, in the following, wefocus on this variation to control the DC self-bias and the

mean ion energy at the electrodes. Figure 2(b) shows �g forN¼ 3 and h3 ¼ 0� (squares), N¼ 3 and a phase-unlocked



157.182.27.250 On: Tue, 22 Dec 2015 20:18:42

third harmonic (circles), and for N¼ 2 (triangles), as a func-tion of the second harmonics phase. In the phase-unlocked

case, the trigger signal of the synchronization unit, which is

part of the RF power supply and impedance matching system

and ensures the phase-locking,76 is removed from the high fre-

quency RF generator. This leads to a high frequency of

40.685 MHz, which is slightly off the integer harmonics fre-

quency of the first harmonic of 40.680 MHz. Thereby, it is not

possible to obtain the third harmonics voltage amplitude from

the measurement with the high voltage probe, as the voltage

waveform changes in every RF cycle and no stable signal can

be measured to perform a Fourier transformation. However, a

temporal mean waveform can be measured over sufficient RF

cycles to obtain information about the first and second har-

monics amplitudes and phases. In order to estimate the voltage

amplitude of the third harmonic, we used the following proce-

dure: When the discharge is operated with all harmonics being

phase-locked, the power delivered by the 40.68 MHz genera-

tor needs to be changed by approximately 10% for different

values of h2 and h3 in order to deliver constant voltage of thethird harmonic to the electrode. For the phase-unlocked case a

mean value of these applied powers is calculated and the

generator is set to this value. As in all other cases the DC self-

bias is normalized by the sum of all harmonics’ voltage ampli-

tudes. Overall, we did not observe any instabilities of the

discharge induced by phase-unlocking the high frequency

driving voltage waveform.

Figure 2(b) shows that the DC self-bias is shifted

towards negative values, i.e., there is a non-negligible DC

self-bias at h2 ¼ 90�, although the absolute values of theglobal extrema of the applied voltage waveform are equal

(/�;max ¼ �/�;min). This is caused by the geometrical asym-metry, which can only be reduced but not completely elimi-

nated by the confinement glass cylinder.76 For N¼ 2 the DCself-bias, �g, can be varied from �g ¼ �42 % at h2 ¼ 0� to

�g ¼ 3 % at h2 ¼ 180�. Thus, it can be varied over a controlrange of 45%. By adding a third harmonic this control range

is extended to 55%, i.e., an increase of the control range of

about 20% compared to the control range with two consecu-

tive harmonics is realized. In the phase-unlocked case the

DC self-bias is the average of all values obtained at different

h3 for each value of h2 in Figure 2(a), which results in adecreased control range of 33%. This is a reduction of 40%

compared to the phase-locked case with N¼ 3. While addinga third harmonic might generally affect the plasma proper-

ties, e.g., the density, this comparison shows the importance

of phase-locking the third harmonic in order to maximize the

control range of the DC self-bias and, thus, the control range

of the mean ion energy at the electrodes. As a large control

range of the mean ion energy is important for applications,

we limit our investigations in the following to the phase-

locked scenario and set h3 ¼ 0� in the triple-frequency case.A more detailed study of all phase combinations is signifi-

cantly beyond the scope of this work.

Figure 3 shows the measured electron-impact excitation

rate from the ground- into the Ne2p1-state for N¼ 2 and fordifferent values of the phase of the second harmonic, h2.These excitation rates are temporally resolved within one

period of the fundamental driving frequency and spatially

resolved between both electrodes. Below these plots, the

total voltage drop across the discharge (/pl, black solid line)and the voltage drop across the sheaths in front of the pow-

ered (/sp, red dashed line) and grounded electrode (/sg, bluedotted line) obtained from the model are plotted. The time

axes of the voltage and the excitation plots are shifted with

respect to each other based on previous simulation results

under similar conditions, i.e., the time axis of the voltage

plot is shifted so that the excitation maximum caused by the

expansion of the sheath at the powered electrode happens at

the same time within the RF period as it does in PIC/MCC

FIG. 2. (a) Normalized DC self-bias as a function of the second and third harmonic’s phase measured for N¼ 3. The arrows indicate how the average values in(b) have been calculated; (b) Comparison of the normalized DC self-bias with three (h3 ¼ 0�, solid line) and two (dotted line) consecutive harmonics as a func-tion of the second harmonics phase. The dashed line shows �g in the case of N¼ 3 with a phase-unlocked third harmonic. The crosses show the average over allvalues for h3 at each value of h2 in the phase-locked mode for N¼ 3. Discharge conditions: Ar, 3 Pa; d ¼ 30 mm; /tot ¼ 210 V.



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simulations.49 For all phase shifts, the maximum sheath

voltage at the grounded electrode is significantly lower com-

pared to the maximum sheath voltage at the powered

electrode due to the geometric discharge asymmetry (e < 1).The discharge is operated in the a-mode for all phase shifts,i.e., sheath expansion heating causes most of the excitation.

At h2 ¼ 0� the sheath at the grounded electrode expandsbetween 60 ns� t� 74 ns. This results in an acceleration ofelectrons towards the powered electrode. As the sheath adja-

cent to the grounded electrode expands relatively slowly

compared to the sheath expansion adjacent to the powered

electrode and electrons have not been heated by sheath

expansion heating for a significant fraction of the fundamen-

tal RF period before the grounded sheath expands, most of

these beam electrons are not accelerated to energies above

the excitation threshold of the observed state (19 eV) and are

hardly visible in Figure 3(a). Nevertheless, these warm elec-

trons propagate towards the bottom electrode. Upon arrival,

the sheath at the bottom electrode expands quickly

(0 ns� t� 20 ns) due to a high maximum sheath voltage atthis electrode. The warm beam electrons originating from the

sheath expansion at the top electrode are now reflected and

again accelerated by the sheath expansion at the bottom elec-

trode. Consequently, they reach energies above the excitation

threshold, i.e., the beam becomes visible. This beam propa-

gates towards the grounded electrode, where it hits the col-

lapsing local sheath and is reflected back into the bulk.

Meanwhile, the beam is scattered by electron-neutral colli-

sions. Changing the phase to h2 ¼ 90� (Figure 3(b)) causesthe sheath at the bottom powered electrode to expand more

slowly when the beam electrons originating from a prior

sheath expansion at the top electrode arrive. Consequently,

the excitation rate is reduced during this time (0 ns� t� 20 ns). As demonstrated in detail later, this leads to areduction of the ion flux and plasma density and, thus, causes

a reduction of the excitation rate also at different times within

one fundamental RF period. Changing the phase to h2 ¼180� (Figure 3(c)) causes a further attenuation of the excita-tion caused by the beam generated by sheath expansion heat-

ing at the powered electrode (30 ns� t� 50 ns) relative to theexcitation caused by the beam generated at the top electrode

(60 ns� t� 74 ns), although the bottom sheath expands morequickly compared to h2 ¼ 90�. This is caused by the fact thatthe bottom sheath expands shortly before the grounded sheath

at h2 ¼ 180�, while the situation is reversed at 0� and 90�.Thus, cold electrons are accelerated by the expanding sheath

at the bottom electrode at h2 ¼ 180� and weaker excitationis observed, while warm electrons originating from the

grounded sheath expansion are accelerated by sheath expan-

sion heating at the bottom electrode at 0� and 90�.Consequently the velocity of the beam generated at the bot-

tom electrode, uB, determined from the slope of the arrowindicating its trajectory might be lower at 90� (uB � 1:38�106 m=s) and 180� (uB � 1:80� 106 m=s) compared to 0�(uB � 2:20� 106 m=s). The specific beam velocity can beestimated from the excitation profiles only roughly.

Figure 4 shows the measured spatio-temporal excitation

rate for N¼ 3 and different phase shifts h2. The total drivingvoltage amplitude is kept constant compared to the dual-

frequency scenario investigated before and the harmonics’

amplitudes are still chosen according to Equation (2). While

changing h2 has similar consequences on the excitation

FIG. 3. Spatio-temporally resolved plots of the Ne2p1 excitation rate for N¼ 2 atdifferent phase shifts, h2 (h1 ¼ h3 ¼ 0�): (a) h2 ¼ 0�, (b) h2 ¼ 90�, and (c)h2 ¼ 180�. The arrows mark the trajectory of the electron beams. The voltage dropsacross the plasma, /pl, and across the sheaths, /sp; /sg as a function of time withinone period of the fundamental frequency are shown at the bottom of each figure.

Discharge conditions: Arþ 25% Ne, 3Pa, d¼ 30mm, N¼ 2, /tot ¼ 210 V.



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dynamics observed in the dual-frequency case (Figure 3),

adding the higher harmonic of 40.68 MHz at fixed total volt-

age amplitude leads to higher excitation rates due to faster

sheath expansion velocities caused by the higher driving fre-

quency. Consequently, the velocity of the electron beams

obtained from their trajectories in Figure 4 might always be

higher compared to the dual-frequency case at a given value

of h2. With N¼ 3 beam velocities of uB � 2:62� 106 m=s;uB � 1:69� 106 m=s, and uB � 2:19� 106 m=s at h2 ¼ 0�;h2 ¼ 90�, and h2 ¼ 180 � are found, respectively. Overall,these results indicate that the ion flux and plasma density are

increased by adding a higher harmonic at fixed total voltage

amplitude.

These experimental findings of the effect of h2 on thespatio-temporal excitation dynamics agree qualitatively well

with previous kinetic simulations performed under compara-

ble conditions49 and correspond to their first experimental

verification. The only major difference between the experi-

ment and these simulation results is the experimental geo-

metric discharge asymmetry, which is not present in the

simulations. In the experiment, the asymmetry reduces all

excitation rates adjacent to the effectively larger grounded

electrode relative to the excitation rates at the powered

electrode.

The results of the RFEA measurements at the powered

and grounded electrodes are shown in Figure 5 for N¼ 2 andN¼ 3. The measurements were taken in pure argon andunder otherwise identical discharge conditions as before

(d ¼ 30 mm; p ¼ 3 Pa and /tot ¼ 210 V). Under these condi-tions the mean free path of the ions is shorter than the maxi-

mum thicknesses of the RF sheaths adjacent to the

electrodes, which results in a relatively high probability for

collisions within the sheaths. Therefore, a broad shape of the

IEDF between ei ¼ 0 eV and ei ¼ emax develops. The IEDFbecomes narrower at the powered electrode for an increasing

h2. This is due to the increasing DC self-bias and, thus, adecreasing mean sheath voltage. The effect is stronger for

N¼ 3 compared to N¼ 2, since the control range of the DCself-bias is enlarged by adding higher harmonics. At the

grounded electrode a reversed effect is observed.

A flux peak at the high energy end is visible in most of

the measured IEDFs at the powered and grounded electrodes.

This peak can be associated with ions that do not collide dur-

ing their motion through the sheath electric field. The transit

time of the ions through the several millimeters thick sheath

is much larger than the time of one fundamental period

(74 ns). Using Equation (9) in Ref. 86 the energy gap DEi ofa possible bimodal structure for the IEDF due to collisionless

transits of ions through the sheath can be estimated. With

typical values (cf. Figures 3 and 4) DEi reaches values of afew eV only. Such structures can hardly be resolved with aRFEA. Thus, the highest possible energy the ions can reach

corresponds approximately to the mean sheath voltage.80

The redistribution of the energy of ions in collisions within

the sheath leads to fluxes at lower energies. The flux of ions

that is measured at energies above the energy of the high

energy peak at the powered electrode is an artifact of the

RFEA caused by imperfect electrical filtering of the RF sig-

nal from the RFEA data. Another indication for the presence

of an artifact is that it is not evidenced by measurements at

the grounded electrode. The resulting error for the mean ion

FIG. 4. Spatio-temporally resolved plots of the Ne2p1 excitation rate for N¼ 3 atdifferent phase shifts, h2 (h1 ¼ h3 ¼ 0�): (a) h2 ¼ 0�, (b) h2 ¼ 90�, and (c)h2 ¼ 180�. The arrows mark the trajectory of the electron beams. The voltage dropsacross the plasma, /pl, and across the sheaths, /sp; /sg, as a function of time withinone period of the fundamental frequency are shown at the bottom of each figure.

Discharge conditions: Arþ 25% Ne, 3Pa, d¼ 30mm, N¼ 3, /tot ¼ 210 V.



157.182.27.250 On: Tue, 22 Dec 2015 20:18:42

energy and the total ion flux in further analysis of the IEDFs

is negligible.

The mean ion energy and the total ion flux to the electro-

des can be calculated according to Equations (3) and (4). In

Figure 6, the results for N¼ 2 and N¼ 3 are depicted assquares and circles, respectively. The solid lines represent

the results for the mean ion energy and the flux at the pow-

ered electrode, while the results for the grounded electrode

are shown as dashed lines. The mean ion energy at the

powered electrode decreases as a function of the phase h2

due to the increasing DC self-bias as mentioned before. For

the same reason, the opposing trend can be observed at the

grounded electrode. Increasing the number of applied har-

monics leads to a larger total ion flux to both electrodes.

This can be explained by the increased plasma density in a

triple-frequency discharge compared to a dual-frequency dis-

charge. This is because the electron heating is enhanced,

resulting in higher ionization rates and plasma densities.

This effect has been observed in the measurements of the ex-

citation rate by PROES (see Figures 3 and 4). Additionally, a

FIG. 5. Ion energy distribution functions as a function of the phase of the second harmonic for two (N¼ 2, (a) and (b)) and three (N¼ 3, (c) and (d)) appliedconsecutive harmonics measured at the powered ((a) and (c)) and grounded ((b) and (d)) electrode, respectively. Discharge conditions: Ar, 3 Pa; d ¼ 30 mm;/tot ¼ 210 V; h1 ¼ h3 ¼ 0�.

FIG. 6. (a) Mean ion energy and (b) total ion flux as a function of the phase of the second harmonic obtained from the measured IEDF at the powered (p, solid

lines) and grounded (g, dashed lines) electrode for two (squares) and three (circles) consecutive harmonics. Discharge conditions: Ar, 3 Pa; d ¼ 30 mm;/tot ¼ 210 V; h1 ¼ h3 ¼ 0�.



157.182.27.250 On: Tue, 22 Dec 2015 20:18:42

higher plasma density results in a reduced sheath width.

Thus, the probability for collisions in the sheaths becomes

smaller and the number of ions hitting the electrode at high

energies increases. This explains the change in the shape of

the IEDF as a function of N (see Figure 5), as it leads to themeasured larger ion flux fraction at relatively high energies

at N¼ 3 compared to N¼ 2.Changing h2 is also found to affect the total ion flux. At

first it decreases as a function of h2 at both the powered andgrounded electrodes and then increases again at different

phases depending on N and the electrode. In comparison tothe simulations by Derzsi et al. these changes are relativelylarge. They are caused by the geometrical asymmetry that is

present in the experiment87 and absent in the simulation. In

the following, we demonstrate that the ion flux can be corre-

lated with the observed excitation profiles, E(x, t), by exam-ining the mean excitation rates adjacent to the powered and

grounded electrodes: Assuming that the PROES measure-

ments of the excitation probe the ionization rate qualita-

tively, the discharge is divided into two spatial regions of

interest (ROI) by finding the center of the plasma bulk, xc,for each phase, h2 according to the following procedure: Dueto the electrical and geometrical asymmetry, the bulk center

does not have to be located in the middle of the electrode

gap and its position changes for different conditions. First,

the mean excitation profile during one RF period hEðxÞi¼Ð T

0Eðx; tÞdt is calculated, keeping the spatial resolution.

Then, the two points at which the mean excitation profile

drops to 1/e of its maximum (adjacent to the powered andgrounded sheath regions) are identified in order to estimate

the maximum sheath widths at both electrodes. Finally, the

middle position between these two points is identified as the

bulk center, xc. In a good approximation, xc hereby corre-sponds to the point of maximum density in the spatial ion

density profile, which is located in the center of the plasma

bulk where the electrical field is almost zero.57 Hence, the

ions motion is mostly due to diffusion, i.e., ions located

closer to the grounded electrode than xc diffuse towards thegrounded electrode and ions located closer to the powered

electrode move towards the powered electrode. Thus, the ex-

citation below and above this point can be related to the ioni-

zation in either half of the plasma bulk and, therefore, to the

number of ions flowing towards the powered and grounded

electrodes, respectively. A spatially averaged value for both

parts can be calculated as h �Epi ¼Ð xc

0hEðxÞidx (powered elec-

trode) and h �Egi ¼Ð d

xchEðxÞidx (grounded electrode).

FIG. 7. Temporally and spatially averaged measured mean excitation rate in

two spatial regions of interest (ROI) adjacent to the powered (p) and

grounded electrode (g), h �Ep;gi, as a function of the phase of the second har-monic for two (N¼ 2, squares) and three (N¼ 3, circles) consecutive har-monics. The ROIs are defined by 0� x� xc and xc� x� d at the poweredand grounded electrodes, respectively. Here, xc is the center of the plasmabulk. Discharge conditions: Arþ 25% Ne, 3 Pa; d ¼ 30 mm; /tot ¼ 210 V;h1 ¼ h3 ¼ 0�.

FIG. 8. Spatio-temporally resolved plots of the measured excitation rate for

(a) N¼ 1, (b) N¼ 2, and (c) N¼ 3 consecutive harmonics. /pl; /sp, and /sgare shown at the bottom of each figure. Discharge conditions: Arþ 25% Ne,200 Pa; d ¼ 30 mm; /tot ¼ 210 V; h1 ¼ h2 ¼ h3 ¼ 0�.



157.182.27.250 On: Tue, 22 Dec 2015 20:18:42

The results of this approach are shown in Figure 7. The

dependence of hEpi and hEgi on h2 is almost identical to thecorresponding dependence of the ion flux (Figure 6(b)).

Thus, the change of the ion flux to either electrode as a func-

tion of h2 can be explained by the excitation dynamics in thecorresponding half of the plasma bulk. These results show

that PROES can be used as a simple non-intrusive (real-

time) diagnostic to monitor and detect changes of the ion

flux to the electrodes.

In general, the RFEA measurements indicate how the

IEDF can be controlled by driving a CCRF discharge with

customized voltage waveforms, which is an important result

for applications.61,88–90 By varying the phase the mean ion

energy can be controlled. The mean value for the mean ion

energy with two consecutive harmonics is 64 eV and can be

varied by 35%, while the flux varies by 615 %. With N¼ 3the mean value of the mean ion energy is 60 eV with an

increase of the control range to 47%. Hereby, the relative

FIG. 9. Spatio-temporally resolved plots of the measured excitation rate for two (N¼ 2: (a) and (b)) and three (N¼ 3: (c) and (d)) consecutive harmonics anddifferent phases of the second harmonic: (a) h2 ¼ 90�, (b) h2 ¼ 180�, (c) h2 ¼ 90�, and (d) h2 ¼ 180�. /pl; /sp, and /sg are shown at the bottom of each figure.Discharge conditions: Arþ 25% Ne, 200 Pa; d ¼ 30 mm; /tot ¼ 210 V; h1 ¼ h3 ¼ 0�.



157.182.27.250 On: Tue, 22 Dec 2015 20:18:42

variation of the ion flux is almost the same compared to two

harmonics (616 %).

B. High pressure (200 Pa)

Spatio-temporal plots of the electron-impact excitation

rate obtained from PROES measurements at a high pressure

of 200 Pa are shown in Figure 8 for N¼ 1, 2, 3 and h2 ¼ 0�.The glass cylinder has been removed and the upper electrode

has been moved to its highest possible position (d¼ 15 cm).Therefore, the whole chamber wall can be regarded as coun-

ter electrode for the powered electrode and the discharge

becomes as asymmetric as possible in order to facilitate the

operation of the plasma in the c-mode, since the voltage dropacross the powered electrode sheath and, thus, the accelera-

tion and multiplication of secondary electrons is increased

in this sheath due to a stronger geometrically induced DC

self-bias. The applied total voltage amplitude is the same as

before (/tot ¼ 210 V) and the harmonics’ amplitudes arechosen according to Equation (2). The measured data are

shown only in the region close to the powered electrode,

because this is the only region of significant emission.

Figure 8(a) shows the excitation rate at N¼ 1 andp¼ 200 Pa. Similar to the measurements at lower pressures,the excitation caused by energetic electrons accelerated by the

expanding sheath is visible for 10 ns� t� 20 ns. Compared tothe measurements at lower pressure this excitation is, how-

ever, strongly localized at the sheath edge due to a reduced

mean free path of the electrons at this high pressure.

Moreover, around the time of most negative driving voltage

and maximum sheath voltage at the powered electrode

(23 ns� t� 45 ns), a second excitation maximum developsthat is stronger than the one during sheath expansion. This

second maximum can be associated with secondary electrons

emitted from the electrode surface. These electrons are accel-

erated in the sheath towards the bulk and excite the observed

neon state. The excitation becomes strongest when the sheath

potential is maximum, as can be seen in the figure, leading to

the conclusion that the single-frequency discharge is predomi-

nantly operated in the c-mode. Increasing the number ofapplied harmonics leads to a stronger a-mode excitation dueto a higher slope of the voltage drop across the powered elec-

trode sheath and, thus, a faster sheath expansion (Figure 8(b)).

At N¼ 2 the a-mode excitation is much stronger than thec-excitation. Adding a third harmonic further enhances thea-mode heating during the quick expansion phase of the pow-ered electrode sheath, so that the c-mode excitation becomescomparatively small (Figure 8(c)). As the peak-to-peak

voltage of /pl is reduced by increasing N for /tot ¼ const:,the maximum sheath voltage is slightly reduced when the

number of harmonics is increased and the excitation by sec-

ondary electrons is slightly reduced, too. Overall, a heating

mode transition from the c-mode to the a-mode is induced byadding more harmonics to the driving voltage waveform at

fixed total voltage and pressure.

Generally, these measurements show that the strength of

an individual electron heating mechanism within one funda-

mental RF period strongly depends on the shape of the driv-

ing voltage waveform. Similarly, the electron heating mode

is affected by the shape of the voltage waveform for fixed N,i.e., by changing the phases of the applied harmonics, as

shown in Figure 9. Compared to h2 ¼ 0� an increase of thephase of the second harmonic to h2 ¼ 90� leads to a strongerexcitation rate caused by secondary electrons relative to the

excitation caused by sheath expansion heating for N¼ 2 andN¼ 3. This is due to the decreasing slope of the voltage dropacross the powered electrode and, thus, a reduced speed of

the sheath expansion at the beginning of the fundamental

RF period. This slope increases again at a phase shift of

h2 ¼ 180�, leading to an increase of the a-heating. Here, theexcitation caused by electrons heated at the expanding

sheath edge partially merges with the one caused by second-

ary electrons occurring shortly afterwards. In contrast to the

low-pressure case discussed before, the maximum excitation

rate remains almost constant as a function of h2. This is dueto the fact that the plasma operates in a strongly localized re-

gime in which the excitation is not modulated by electron

confinement or sheath-to-sheath interaction effects. Our find-

ings of a mode transition from the c-mode at N¼ 1 to ahybrid mode dominated by the a-mode at N¼ 2, 3 (h2 ¼ 0�)as well as the phase dependence of the spatio-temporal exci-

tation for different N agree qualitatively well with previouskinetic simulations on this topic performed by Derzsi et al.49

and correspond to their first experimental verification.

IV. CONCLUSION

Electron heating dynamics probed by PROES and ion

energy distribution functions have been investigated in a

capacitively coupled argon discharge driven by up to three

consecutive harmonics of 13.56 MHz with individually ad-

justable harmonics’ amplitudes and phases. The driving volt-

age waveform was customized using a novel RF power

supply including impedance matching for each individual

harmonic. The phase of the second harmonic, h2, was tunedto change the shape of the applied voltage waveform. The

spatio-temporally resolved electron impact excitation rate

measured by PROES was discussed in conjunction with the

temporal evolution of the sheath voltages obtained from a

model under low- and high-pressure conditions and was used

as a basis to explain the effects of changing the shape of the

applied voltage waveform on the measured IEDFs at both

electrodes.

At a low pressure of 3 Pa, the PROES measurements

show that the discharge is operated in the a-mode and theelectron heating is dominated by the non-local interaction of

electrons with the expanding sheaths and the corresponding

generation of energetic beam electrons. It was found that the

shape of the driving voltage waveform controlled via the

number of consecutive harmonics, their amplitudes, and

phases strongly affects the electron heating dynamics via its

effects on the sheath dynamics. Increasing the number of

driving harmonics at fixed total applied voltage and harmon-

ics’ phases was found to increase the sheath expansion ve-

locity and, thus, the excitation rate and the ion fluxes to the

electrodes. Changing the harmonics phases at a fixed num-

ber of harmonics and at fixed total voltage amplitude was

also found to affect the excitation dynamics and the ion



157.182.27.250 On: Tue, 22 Dec 2015 20:18:42

fluxes by affecting the sheath expansion velocities and the

interaction of energetic electron beams with both boundary

sheaths.

The electrical control range of the DC self-bias via the

Electrical Asymmetry Effect, i.e., by tuning h2, is found tobe enhanced by adding more consecutive harmonics to the

driving voltage waveform at fixed total voltage amplitude.

Consequently, the electrical control range of the mean ion

energy at the electrodes by phase control is found to be

enhanced significantly. Increasing the number of driving fre-

quencies also causes the sheaths to shrink and, therefore, to

become less collisional at a given pressure and total applied

voltage due to its effect on the electron heating dynamics.

This leads to a more pronounced high energy peak in the ion

distribution function at a high number of driving harmonics.

The ion flux at both electrodes was found to change as a

function of h2. This change was again understood based onthe effect of changing this phase on the electron heating dy-

namics revealed by PROES. Finally, at low pressure PROES

was demonstrated to be an efficient non-invasive (real-time)

diagnostic to monitor/detect changes of the ion flux to both

electrodes.

At a high pressure of 200 Pa, the electron heating

dynamics is dominated by local effects, i.e., excitation

occurs spatially and temporally close to the position of

energy gain of electrons by their interaction with the sheath

electric field. The discharge is operated in the c-mode ifdriven by a 13.56 MHz single-frequency voltage, whereas

electron heating is dominated by the a-mode heating ifhigher harmonics are added to the driving voltage waveform

at fixed total voltage amplitude, i.e., if a multi-frequency

voltage waveform is used. The PROES measurements show

that the strength of both the a- and c-mode heating change asa function of the phase of the second harmonic, since they

depend on the temporal evolution of the sheath voltage and,

hence, on the shape of the customized driving voltage

waveform.

These findings demonstrate how driving a CCRF plasma

with tailored voltage waveforms allows for control, tailoring,

and optimization of the electron and ion dynamics, which is

highly relevant for surface processing applications. This

should be tested experimentally by examining the effect of

the multi-frequency driving voltage waveform on plasma

etching and deposition rates in future works based on the

fundamental understanding of the particle heating dynamics

obtained here.

ACKNOWLEDGMENTS

This work was supported by the Ruhr University

Research School PLUS, funded by Germany’s Excellence

Initiative [DFG GSC 98/3].

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