Control of ion and electron distribution functions by the ...doeplasma.eecs.umich.edu/files/PSC_Czarnetzki1.pdf · •Assuming for flux balance approximately a full collapse of

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Control of ion and electron distribution functions by the Electrical Asymmetry Effect

U. Czarnetzki

Institute for Plasma and Atomic Physics

64th GEC, Salt Lake City, 14 -18 November 2011

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Process RequirementsIon energy: - deposition or etching/sputtering

- quality and selectivity

Ion flux: - process speed, substrate heating

Ideal concept: Independent control of ion energy and flux.

This can be achieved by the Electrical Asymmetry Effect.

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Voltage Balance Model of CCP Discharges

• Balance of all voltages.• One-dimensional model (plane-parallel, cylinder, sphere).• Unequal electrode areas included in non-planar geometries.• All voltages φ are expressed as functions of q(t), the positive

space charge in the sheath at the powered electrode.

RF bulksheath g

bsgspCRF φφφφφ +++=

Csheath p

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Simplified System

• The total positive space charge qt in both sheaths isapproximately constant.

• Sheaths are well characterized by a quadratic charge-voltage relation:

• The bulk voltage is negligible in most cases.• The time varying part of the capacitor voltage is also

negligible.• A single parameter characterizes the symmetry of the

system by the ratio of areas and mean sheath ion densities:

sg

sp

g

p

nn

AA

2

=ε

2qsp −=φ

( ) ( ) ( ) ( )( )ε

ηϕφεεεϕεηφ

−+−−+−

=⇒−+−=+1

1222 RFtt

tRFqq

qqqq

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Self-bias and total charge• Assuming for flux balance approximately a full collapse of

the sheaths at times of the applied voltage extremes determines the total charge qt and the self-bias η :

εφεφη

εφφ

++

−=+−

=1

and1

2121 mmmmtq

0.0 0.2 0.4 0.6 0.8 1.0-1.0

-0.8

-0.6

-0.4

-0.2

0.0

η

ε

In a single-frequency dischargethe self-bias is: • determined by the

area ratio Ap / Ag.• vanishes in a geometrically symmetric discharge (ε = 1).

εεη

+−

−=11

Heil B G, Czarnetzki U, Brinkmann R P and Mussenbrock T, 2008 J. Phys. D: Appl. Phys. 41 165202

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The Electrical Asymmetry Effect (EAE)• Unequal voltage extremes lead to a self-bias for any value

of the symmetry parameter ε.• This can be realized by a two successive harmonics:

( ) ( ) ( )( )00)(~)(~

2/2coscos,

21 ≠⇒≠+

++=

ηθφθφ

ϕθϕθϕφ

mm

The phase θ is the control parameter!

0.5

1.0

1.5

Ε0.0

0.5

1.0

1.5

Θ

�0.4�0.20.00.20.4

Η .

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Bias Variation by the Phase

• The bias varies almost linearly with the phase.• The bias can be varied over a large range.• The role of the two electrodes can interchanged.

high potential at ground,low potential at the electrode

low potential at ground,high potential at the electrode

Z. Donkó, J. Schulze, B.G. Heil and U. Czarnetzki,Journal of Physics D: Applied Physics 42, 025205 (2009)

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PIC-MC: Ion Energy Distribution(Argon, 2.7 Pa, d = 6.7 cm, φ0 = 315 V )

powered electrode grounded electrode

• Ion energy distribution can be well controlled by the phase.• The role of the two electrodes can be reversed.

Donkò Z, Schulze J, Heil B G, Czarnetzki U 2009 J. Phys. D: Appl. Phys. 42 025205

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Experimental Ion Energy Distributions

0 10 20 30 40 50 60

0500100015002000250030003500

9075

6045

3015

0

10 Pa

Ion

flux

[a.u

.]

θ [D

egree

]

E [eV]

0 10 20 30 40 50 60

01000200030004000500060007000

9075

6045

3015

0

4 Pa

Ion

flux

[a.u

.]

θ [D

egree

]

E [eV]

The experiment very well confirms theory and simulation.

Schulze J, Schüngel E, Czarnetzki U 2009 J. Phys. D: Appl. Phys. 42 092005

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Mean Sheath PotentialsThe massive ions react only on the mean sheath potential.Therefore, the mean sheath potential controls the ion energy.

.

5.029.0

5.029.02

const

q

sgsp

spsg

sp

≈+⇒

+≈+=

−≈=

φφ

ηηφφ

ηφ

• The mean sheath potentials are approximately linearfunctions of the self bias.

• The sum of the absolute values is approximately constant.• Ion energies can be varied complimentary at the electrodes.

E. Schüngel, J. Schulze, Z. Donkó, and U. CzarnetzkiPhysics of Plasmas 18, 013503 (2011)

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PIC Simulation of the Mean Sheath Potentials

Argonp = 100 Paφ0 = 100 Vd = 1 cm

-0.2 -0.1 0.0 0.1 0.20.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

I<φ s>I

η

powered ground

sum

• Linear variation of the mean sheath potential.• Sum is approximately constant.• Good agreement with the model.• This explains the linear variation of the mean ion energy.


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Mean Ion EnergiesPIC (100 Pa) Experiment

• Linear variation of the mean ion energy by the phase angle.• Good agreement with the mean sheath potential.

0 15 30 45 60 75 900

10

20

30

40

50

4 Pa, 2.5 cm 10 Pa, 2.5 cm 20 Pa, 1 cm

<εi>

[eV

]θ [Degree]

J. Schulze, E. Schüngel and U CzarnetzkiJournal of Physics D: Applied Physics 42, 092005 (2009)

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Mean Ion and Total Power

• The mean sheath voltages vary linearly with the bias.• The power dissipated by the ions is proportional to the

power dissipated by the electrons.• Then the same applies also to the total power.

( )

ei

sgsp

eei

isgspi

PP

const

Pn

P

∝⇒

≈+

∝∝Γ

Γ+∝

.φφ

φφ

eie PPPP ∝+=⇒0 20 40 60 80 100

0

2

4

6

8

10

12

14

Θ [Degrees]

Abs

rbed

pow

er d

ensi

ty [

kW m

-3 ]

Electrons Ions Total


o

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Electron velocity distribution functions

The applied voltage waveform leads apparently to complicate sheath dynamics and electron distribution functions.

Ionization rate:V0 = 200 V, f = 13.56 MHz, Theta = 0 deg, L = 2.5 cm, p = 3 Pa (argon), T = 400 K The powered electrode is at x=0, time covers one period of the 13.56 MHz cycle. The grey lines indicate equipotential contours (spacing = 20 V).

Z. Donkó, Plasma Sources Sci. Technol. 20, 024001 (2011)

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Simulated and measured Excitaiton

• As expected, the complex time-space structure of thesheath voltage waveforms leads to similar complexity inexcitation.

• Positions and strengths of the various maxima are varying with the phase, i.e. with the form of the waveform.

J. Schulze, E. Schüngel, Z. Donko, and U CzarnetzkiPlasma Sources Sci. Technol. 19, 045028 (2010)

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Non-local contribution to thedistribution function

• The distribution function in the bulk has a local, basicallyconstant part and a non-local part caused by ballisticelectrons from the sheath.

• The relative contribution is scaled by the ratio of the sheathto the bulk density αz.• The part originating from the sheath is expanded in the timevarying drift velocity uz. J. Schulze, E. Schüngel, Z. Donko, and U Czarnetzki

Plasma Sources Sci. Technol. 19, 045028 (2010)

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Excitation Rates

• The excitation rate E in the bulk can be split into a constantand a time varying part.

• Of particular interest is the ration between peak values atboth sheaths.

• A similar argument could be made for ionization, althoughmore difficult to measure.

• The velocity u can be related to the derivative of q and soto the derivative of the applied voltage φ.


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Ratio of the absolute maxima at both sheaths

• Experiment, simulation, and model agree very well.• Excitation is clearly related to the beam electrons from the

sheaths.• The excitation can be well described by the calculated q(t).


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Phase dependence of the absolute maximum

Again, very good agreement is found, supporting the rathersimple model description, i.e. the physical picture related tothe model.


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a) Experiment (I2)b) PIC simulationc) Analytical Model Identical results throughout!

Variations by θ cancel out almostentirely in the integral over ϕ.

Power Dissipated by the Electrons

22 qI &∝


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Mean Electron Power

Not more than 10 % variation of the mean power!


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Ion FluxPIC (2.7 Pa)

0 20 40 60 80 1000

2000

4000

6000

8000

10000

Ion

flux

[a.u

.]

θ [Degree]

Grounded electrode

Experiment (4 Pa)

• The ion flux is nearly independent of the phase angle.

• Ion energy and flux can be controlled separately.

Z. Donkó, J. Schulze, B.G. Heil and U. Czarnetzki,Journal of Physics D: Applied Physics 42, 025205 (2009)

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Summary

• The electrical asymmetry effect allows a convenient controlof ion energy distribution functions.

• Increasing the ion energy at one electrode reduces correspondingly the ion energy at the counter electrode, allowing even for a full reversal.

• The control parameter is the phase between the two RF frequencies.

• Electron energy distribution functions and correspondinglyexcitation and ionization show a complicate spatial-temporal behavior.

• The temporal and spatial average is, however, approximately constantleading to a constant density and ion flow.

Support by the DFG in the frame of SFB 591, GK 1051, the RUB Research School, the Federal Ministry for Environment and the Hungarian Fund for Scientific Research is gratefully acknowledged. Commercialization and licensing is via RUBITEC.

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More about the EAE on this meeting• Shinya Iwashita, Tuesday 15.00 ET4 4

• Edmund Schüngel, Thursday 15.30 QRP1 45

• Julian Schulze, Thursday 15.30 QRP1 46

• Sebastian Mohr, Thursday 15.30 QRP1 47

• Julian Schulze, Friday 08.30 SF1 2

Documents

Control of ion and electron distribution functions by the ...doeplasma.eecs.umich.edu/files/PSC_Czarnetzki1.pdf · •Assuming for flux balance approximately a full collapse of