Transcript PPT

Probe Measurements of Electron Energy
Distributions in Gas Discharge Plasmas
V. A. Godyak1 and V. I. Demidov2
1
RF Plasma Consulting, Brookline, MA 02446, USA
2West Virginia University, Morgantown, WV 26506, USA
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Electron Distribution Function
f
,
Two-term approximation (small anisotropy, f1 << f0)
Electron Energy Distribution (EEDF) and Electron
Energy Probability (EEPF) Functions
F(t,r ε) =
4
.
3
Langmuir formula and Druyvesteyn method
Ie 
2eS p
m
2

 (  eV ) f ( )d  2
eV
eS p

(  eV )

2m
eV
F ( )

d 
eS p
2

(  eV ) f

2m
p
( )d .
eV
Similarly, all plasma parameters (Tesk, λD, JB) and rates of plasmachemical 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?
• We want to have more than Langmuir method gives us
• EEDF has to resolve tail electrons (ε>ε*) responsible for
excitation, ionization and electron escape, as well as low energy
electrons (ε< Te) accounting the majority of electrons
• 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, λD << le
and
Ip << Id, Ir, Iz
Ir = IB = ScheNsvB, vB = (Te/M)1/2,,,,,.. Iz = eΓe is the current
corresponding to generation rate of electrons with energy ε in
the volume defined by the chamber characteristic size Λ, or by
the electron relaxation length λε,
To neglect the voltage drop across the wall sheath, the
following requirement has to be satisfied:
(SpN0/SchNs)(M/2πm)1/2 << 1
a = 38 μm
b = 175 μm
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Probe constructions
P1
P2
a = 0.05 mm, b = 1 mm, c = 2-3 mm
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Probe circuit resistance (the most frequent problem)
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EEPF Druyvesteynization due to Rc
δ = Rc/Rpmin Rpmin= Te/eIesat
Error in EEPF less than 3% requires Rc/Rpmin < 0.01 !
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Example of EEPF measurement in argon ICP with a low
disturbance probe having Rc and noise compensation
13
Maximal argon pressure,
where measurement was
possible, was limited by the
chamber
surface
50
,
10
12
10
11
10
10
9
10
8
10
7
300 mT
100
* i
10
50
13
6.78 MHz, 50 W
50W
8
-3
plasma density (cm )
10
-3/2
10
10
50W
-3
eepf (eV cm )
6.78 MHz, 50 W
10
1
0.3
.3mT50W
10
12
10
11
10
10
6
4
2
6
0
10
20
30
electron energy (eV)
40
50
10
-1
0
1
10
10
10
gas pressure (mT)
2
0
3
10
10
effective electron temperature (eV)
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Argon, 20 mTorr
VGPS: max = 15-22 eV
Comparison of
EEPF
measured with
different
commercial
probe stations
At maximal
discharge power
of 2 kW, N ≈
1·1012 cm-3, thus
EEPF has to be
Maxwellian
νee ∞ NTe-3/2
Maxwellization
Argon, 20 mTorr
Espion: max = 7-11 eV
“Druyvesteynization””
Distorted @ low energy and lost information @ high energy
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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/eVplrf
A 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 /Te
For 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 measurements
EEPF measured in afterglow stage of ICP with internal ferrite core inductor
10
12
Ar, 30 mT, 50 W; off cycle
Ar, CW 100 W
10
11
10
10
off
= 2 s
p
Te
(mT) (eV)
= 20 s
1
eepf (ev
-3/2
-3
cm )
T
on
10
t = 2.8 s
3.6
4.4
6.8
9.2
12.4
18.8
9
0
5
10
electron energy (eV)
3.0
10
30
100
300
electrron temperature (eV)
T
6.5
4.2
3.1
2.1
1.5
300
0.1
100
30
3 mT
10
15
1
10
100
time (s)
1000
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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)
80
1010
5 S
109
t = 1 S
108
0
1
2
3
4
5
energy (eV)
6
7
8
2
60
8
1
2A
40
4
0.5
8
20
0
0
0
5
10
15
20
time (S)
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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electron temperature (eV)
lamp voltage (abs. value V)
eepf (eV
-3 / 2
-3
cm )
10
50 kHz
50 kHz, 2 A
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1.5
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/Te
independently on a/λD
In practice, Ii” effect is essentially smaller and can be neglected
Ratio Ie”/Ii” depends on EEPF and a/λD
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Relative Ii” effect for orbital and radial ion motion
for Maxwellian and Druyvesteyn distributions
Ie”, Ii”, Ip”
Orbital motion
Radial motion
Hydrogen
a/λ
D
1.0
10
100
eV/kTe
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Accounting for Ii” contribution
In many works and commercial probe instruments, the extrapolated from large
negative probe potential Ii(V) is subtracted from Ip(V) with following
differentiation. Due to uncertainty of the extrapolation and error augmentation
caused by differentiation this way of accounting for Ii” brings more error than
correction.
Ion probe theories used in probe
diagnostics do not account for:
•
Non-Maxwellian EEDF
• Rear collisions that destroy OM
• Two-dimentionality of the probe sheath
• Ambipolar ion drift (Va >> VTe)
• Plasma parameters found from Ii(V) may be
up to an order of magnitude differ from those
found from Ie(V)!
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Probe surface effects
I”p(V)
Φwf (Volt)
Ne + 5%
benzyl
Ar
Mo
Ta
W
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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 VGPS in Plasma reactors
(Wide specter and large amplitude of rf plasma potential and
high rate of probe contamination are the major problems)
Microcrystalline silicon deposition
Ar/SiF4 10 mTorr ECR.
Ecole Polytechnique
H2/CF4 30 mTorr ICP with
polymer deposition.
University of Maryland
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A remark
Today, plasma simulation codes are practically main tool for study
plasma electrodynamics, plasma transport and plasma kinetics in
commercial plasma reactors. 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 plasma
chemical reactors 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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