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Probe Measurements of Electron Energy Distributions in Low Temperature Plasmas

V. A. GodyakRF Plasma Consulting, Brookline, MA 02446, USA

and University of Michigan, Ann Arbor, MI 48109, USA

May 24, Huntsville AL

Introduction

“There is no plasma diagnostics method other than probe diagnostics where the danger of incorrect measurements and erroneous interpretation of results are so great.”

L. Schott, Plasma Diagnostics, Amsterdam,1968

It was true then, it is even more true today, when plasmas are more complicated and the measurement techniques are more sophisticated

The Langmuir probe is the most universal and informative plasma diagnostics tool

However, the simplicity of the probe concept frequently leads to abuse this technique resulting in erroneous results

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Isotropic EVD, a[ln(l/2a)] > λD , Ip

Langmuir probe I/V characteristic(Classical Langmuir technique)

Main problems in using Langmuir procedure:

1. Assumption of Maxwellian EEDF errors in Te and n2. Uncertainty in plasma potential V error in n3. Arbitrariness in the ion current approximation error in Te for high energy electrons (ε > |eVf|)

Shown in textbooks probe characteristics correspond to a large probe which gives a nice looking probe I/V, but prone to large plasma perturbation and distorted data

Ip = Iesexp(-eV/Te) – Ii(V) Ies = (1/4)SenvTe

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• Probe survives (is stable) in plasma

• No global plasma perturbation (rp

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Problems in Langmuir Probe Diagnostics

Majority of the published probe experiments are mediocre and of bad quality

• Bulky probes

• Low frequency noise and drift

• Rf plasma potential

• Probe contamination and sputtering

• Strong plasma rf field

• Probe circuit resistance

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Low temperature plasmas in applications, space and laboratory are not Maxwellian

Electrons are not in equilibrium with ions and neutral gas (Te >> Ti and Tg)

Electrons are not in equilibrium within their own ensemble (not Maxwellian)

Electrons can be in non-equilibrium with electromagnetic field (nonlocal electron kinetics and electodynamics)

The classic Langmuir probe (and spectroscopy) in a real, mom-Maxwellian plasma can give erroneous results. Therefore, the plasma diagnostics, as well the theory and simulation must be done on kinetic level

Probe characteristics and EEDFs in Argon CCPGodyak et al, J. Appl. Phys. 73, 3677 (1993)

Langmuir procedure, Ie (V) Druyvestein procedure, f(ε)

Deviation from Maxwellian EEDF for high energy electrons (ε > ε∗, εi, εw) is typical for gas discharge plasmas. Strong non-equilibrium for bulk electrons (ε < ε∗, εi, εw) in DC and RF discharges in Ramsauer gases makes the classical Langmuir procedure inappropriate for diagnostics of such plasmas

Strongly non-Maxwellian in the elastic energy range, ε < ε*

Te and N are 2.5 and 3 times less than their true values fond from EEDF

14 times!

2.6 times

Plasma parameters for Ar CCP at 30 and 300 mTorr

30 mTorr (bi-Maxwellian) 300 mTorr (Druyvesteyn-like)Langmuir EEDF Langmuir EEDF

Te = 0.73 eV Te = 0.67eV Te = 1.37 ! Te = 3.4 eVn=5.9x109cm-3 n=4.4x109cm-3 n=4.5x109cm-3 n=2.9x109cm-3

The temperatures of cold and fast electrons in bi-Maxwellian plasma found from the Langmuir procedure and those found from the EEDF are different!Tec = 0.73 eV and The = 4.2 eV are found as Te-1 = dlnIe/dV

Tec = 0.50 eV and The = 3.4 eV are found as Te-1 = dlnfe/dV

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Error factor n/nEEDF found by different authors

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.)()(22

)()(22

)()(2

2 εεεεεεεεεε

πdfeV

meS

dFeVm

eSdfeV

meS

IeV

pp

eV

p

eV

pe ∫∫∫

∞∞∞

−=−=−=

Langmuir formula and Druyvesteyn method

Similarly, all plasma parameters (Tesk, λD, JB) and rates of plasma-chemical processes (νea, νee, ν*, νi, ….) can be found as appropriate integrals of the measured EEPF.

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What makes a good EEDF measurement?

• EEDF has to resolve tail electrons (ε > ε*) responsible for excitation, ionization and electron escape to the wall, as well as low energy electrons (ε < Te) accounting the majority of electrons. In the majority of published EEDF, the both groups of electrons are practically absent.

• Due to error augmentation inherent to differentiation procedure, small (invisible) inaccuracy in Ip(V) can bring enormous distortion in the measured EEDF.

• It is important to realize the source of the possible errors and to be able to mitigate them.

• The sources of the errors are well elucidated in the literature, but are insistently ignored in the majority of published papers.

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Problems in probe measurements and their mitigations.

1. Probe size: a[ln(πl/4a)], b is probe holder radius

2. No collisions in the probe sheath: λD

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a = 0.05 mm, b = 1 mm, c = 2-3 mm

Probe constructions

P1 P2

Telescopic probe construction

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Probe circuit resistance (the most frequent problem)

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EEPF Druyvesteynization due to Rcδ = Rc/Rpmin; Rpmin= Te/eIesat

Error in EEPF less than 3% requires Rc/Rpmin < 1% !

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,

106

107

108

109

1010

1011

1012

1013

0 10 20 30 40 50

eepf

(eV

-3/2

cm -3

)

electron energy (eV)

110100

300 mT

0.3ε ε i

6.78 MHz, 50 W

* 1010

1011

1012

1013

0

2

4

6

8

10

10-1 100 101 102 103

plas

ma

dens

ity (c

m-3

)

effe

ctiv

e el

ectro

n te

mpe

ratu

re (e

V)

gas pressure (mT)

6.78 MHz, 50 W

Example of EEPF measurement in argon ICP with a low disturbance probe having Rc and noise compensation

Maximal argon pressure, where measurement was possible, was limited by the chamber surface

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In a high density plasmas, EEPF at low energy must be Maxwellian

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RF plasma potential

Criterion for undistorted by rf sheath voltage EEPF measurement is known for over 30 years (1979)

Zpr/Zf ≤ (0.3-0.5)Te/eVplrfA presence of a filter in the probe circuit does not guarantee undistorted EEPF measurement. To do the job, the filter has to satisfy the following condition for all relevant harmonics:

Zf ≥ (2-3)ZpreVplrf /TeFor filter design we need to know (measure!) Vplrf and minimize Zpr

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Filter design procedure

Zpr is defined by its sheath capacitance at floating potential

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Probe measurement circuit incorporating, dc voltage and low frequency noise suppression, rf compensation and rf filter dc resistance compensation with I/V converter having a negative input resistance

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Example of EEPF measurement demonstrating a paradoxical Te distribution in argon 13.56 MHz CCP

30 mTorr, Teo < Tes 300 mTorr, Teo > Tes

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EEPF and plasma parameters evolution during CCP transition to the γ- mode

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Time resolved EEPF measurementsEEPF measured in afterglow stage of ICP with internal ferrite core inductor

109

1010

1011

1012

0 5 10 15

eepf

(ev

-3/2

cm

-3 )

electron energy (eV)

Ar, 30 mT, 50 W; off cycle

Ton

= 2 µs

Toff

= 20 µs

t = 2.8 µs 3.6 4.4 6.8 9.2 12.4 18.8

0.1

1

1 10 100 1000

elec

trron

tem

pera

ture

(eV)

time (µs)

300

100

303 mT 10

Ar, CW 100 W

p Te(mT) (eV)

3.0 6.510 4.230 3.1 100 2.1300 1.5

25

0

20

40

60

80

0

0.5

1

1.5

0 5 10 15 20

lam

p vo

ltage

(abs

. val

ue V

)

elec

tron

tem

pera

ture

(eV

)

time (µS)

2 A

4

8

50 kHz

2

8

108

109

1010

1011

0 1 2 3 4 5 6 7 8

eepf

(eV

-3 /

2 cm

-3)

energy (eV)

50 kHz, 2 A

t = 1 µS

5 µS

EEPF and Te measured along rf period in an induction lamp operated at 300 mTorr Ar and 7 mTorr Hg

Time resolution δt = 0.5 μS. Note asymmetry in Te(ωt)

Probe sheath capacitance to plasma is the main limiting factor in EEPF measurement speed. The minimal time resolution, δt > (10-30)ωpi

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EEDF in running striations, argon, p = 10 mTorr, Id = 1 A

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Ion current effect

Ip = Ie + Ii and I”p = Ie”+ Ii”Ion current effect occurs in light gases, low density plasmas and small probes, and is maximal at orbital ion motion (a/λD < 1), according to:

Ie”/Ii” = (4πM/m)1/2η3/2exp(-η) η = eV/Teindependently on a/λD

In practice, Ii” effect is essentially smaller and can be neglected

Ratio Ie”/Ii” depends on EEPF and a/λD

28eV/kTe

Ie”, Ii”, Ip”

a/λD

1.0

10

100

Hydrogen

Relative Ii” effect for orbital and radial ion motion for Maxwellian and Druyvesteyn distributions

Orbital motion Radial motion

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Probe surface effects:

• Probe surface work function (changes during probe scan)

• Non conductive layer of reaction product → (Rc)

• Sputtering of electrode and probe and deposition conductive layer on the probe holder → Sp• Strong temperature dependence of all above

REMEDIES

• Continuous probe cleaning with fast probe scan (mS)

• Ion bombardment, electron heating and rf biasing

• Probe cleaning before or after probe scan is ineffective

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EEPF measurements with MFPA in Plasma reactors(Wide specter with large amplitude of rf plasma potential and

high rate of probe contamination are the major problems)

EEPF measured in ICP reactor, H2/CF4 at 30 mTorr with a polymer layer deposition. University of Maryland by N. Fox-Lyon

EEPF in commercial two-inductor ICP in different processing mixtures at 15 mTorr.Mattson Technology,by V. Nagorny

Ar, O2, HBr, HBr+O2 Ar, Ar + H2

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A remarkToday, plasma simulation codes are practically main tool for study plasma electrodynamics, plasma transport and plasma kinetics in commercial plasma reactors, space and lab plasmas. These codes applied to complicated processing gas mixture are missing many cross sections for variety of (accounted and not) plasma-chemical reactions.

They also are missing effects of nonlocal and nonlinear plasma electrodynamics that has been proved can be important and even dominant in rf plasmas at low gas pressure.

In such situation, a feasibility of EEDF measurement in low temperature plasma would give a valuable experimental data for understanding variety of kinetic process in such plasmas and validation of existing numerical codes.

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