RF antennas as plasma monitors A. A. Howling1*, Ph. Guittienne2, R. Jacquier1, I. Furno1 1Centre
de Recherches en Physique des Plasmas, EPFL, Lausanne, Switzerland 2Helyssen
Sàrl, Switzerland
*Contact e-mail:
[email protected]
Frontiers in Low Temperature Plasma Diagnostics XI, 24-28 May 2015 Porquerolles Island, France
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Outline of talk • Review: RF antenna diagnostics • Inductively-coupled plasma (ICP) • Planar resonant RF antenna "new" device • Partial inductance
"new" concept
• Complex image method
"new" theory
new to plasma
• RF antenna ICP diagnostic
2
Brief review: RF antenna diagnostics microwave interferometer
wave cutoff method
J H Kim et al, Appl. Phys. Lett. 83, 4725 (2003)
microwave cavity
active plasma resonance spectroscopy E Stoffels et al, Phys. Rev. E 51, 2425 (1995) T. Styrnoll et al, Pl. Sources, Sci. Technol. 23, 025013 (2014)
hairpin probe
𝜖𝑟 = 1 −
𝜔𝑝𝑒 2 𝜔
, 𝜔𝑝𝑒 =
𝑛𝑒 𝑒 2 𝜖0 𝑚 𝑒
R L Stenzel, Rev. Sci. Instrum. 47, 603 (1976)
relative dielectric constant of plasma 3
Inductively-coupled plasma diagnostic? transformer coupling model
coil plasma
I1 I2
OK only for simple geometries!
measure the change in primary impedance to deduce plasma conductivity (electron density and collision frequency) 4
Planar resonant network
Cylindrical (birdcage)
Ph. Guittienne et al, Pl. Sources, Sci. Technol. 23, 015006 (2014)
23 legs 55 cm
20 cm
How to model inductive coupling with plasma? 5
Planar resonant network, N legs, (N-1) resonances top view
mode m = 4 For each resonance: single LC parallel resonant circuit
side view plasma
How to model inductive coupling with screen & plasma? 6
Mode impedance spectrum measurements
m=10
m=2
m=4, vacuum
m=6
m=8 m=4, plasma
Zin frequency [MHz] plasma
vacuum
Zin
Zin
"Z-scan" network analyser probe
I1 V1
Strong effect of plasma = Basis for a plasma diagnostic
7
Planar resonant network C
r
L
L
R
R C
r
...must consider mutual inductances C leg/leg L Mn-1,n
r leg/leg Mn,n+1
R
str/line Mn,n+1
L str/opp Mn+1,n+1
R
C
r 8
Loop and partial inductance – basic concepts "Inductance: Loop and Partial" by Clayton Paul (2010)
What is the self inductance L of a metal leg? Conventionally, (loop) inductance is only defined for a closed circuit Consider a rectangular circuit:
Loop self inductance
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Alternative view of inductance... surface integrals Stokes' theorem line integral
partial inductance 10
self partial inductance A.dl = 0 ∞
B
l
A
A=0
Y
a A.dl = 0
I
mutual partial inductance wire 2
l
wire 1
I
Y
2h 11
∞
Mutual partial inductance between parallel wires l wire 1 I
partial
loop inductance
loop
partial inductance
2h
I
wire 2
Lpwire
I
I
Mpwire/wire Lpwire OK!
12
Mutual partial inductances between antenna elements
Ohm's law for nth leg
Vn
matrix impedance model 13
Mutual inductance with the baseplate screen in vacuum (no plasma) side view
screen
14
Method of images:
baseplate screen
15
Method of images
16
Planar resonant network – no plasma mode frequencies calculated by a
matrix impedance model using partial inductances
good agreement for mode frequencies in vacuum
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Planar resonant network – with plasma
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Induced current in a plasma
plasma skin depth d
I I plasma current density
mutual inductance with plasma?
d 19
y
Induced current in a resistive ground return
Bell Syst. Techn. J. 5, 539 (1926)
Mutual inductance: infinite converging Fourier integrals
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Dubanton at Electricité de France (1976), & co.: Complex image theory = real image current at a complex depth Complex depth p = complex skin depth. Complex wavenumber = 1/p
complex mutual inductance also includes ohmic dissipation: 21
Complex image theory = real image current at complex depth... ...the magnetic field above the plasma is the same for both cases
depth
induced current IAC distribution in the plasma
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Complex image method theory is used in several domains (but not plasma) • • • •
power transmission telecommunications geophysics microelectronics Port 1
Metal
Via Port 2 Insulator Insulator Semiconductor Substrate Metal Ground Plane
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The impedance matrix accounts for all coupling to the antenna
plasma
vacuum
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Complex image method fits all 5 modes using only 3 physical quantities: 1) distance; 2) electron density; 3) collisionality skin depth depends on: mode resonance measurements
matrix impedance model
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Inductively-coupled antenna used as a diagnostic Df for plasma conductivity "Method and Device for Determining Plasma Characteristics" 4 May 2015 EP15166251.7
30
25
DR
20
Zin
network analyser
15
10
5
metal housing
0 130
135
140
145
150
155
160
165
170
[MHz]
frequency [MHz] RF network (non-invasive in wall) dielectric spacer "window" (alumina...) plasma to be measured 26
A hybrid resonant network antenna probe on a printed circuit board
increases sensitivity to inductive coupling
... and a large area 15 kW antenna (1.2 m2) for large area deposition, etching, packaging applications, etc 27
The computed relation between the electron density and Df (complex image method and mutual inductance matrix).
Measurement of probe Df as a function of the RF power of the plasma source.
DEVICE
14
12
+
METHOD
ne (interferometer) ne (inductive probe)
8
ne [10
16
-3
m ]
10
6 4 2 0 0
200
400 power [W]
600
800
The electron density as a function of the source injected power. 28
Inductive probe measurements using different gases 3.5
frequency shift [MHz]
3.0 2.5 2.0 1.5 1.0
Ar 1.1Pa gap 12cm N2 1.1 Pa gap 12 cm
0.5
He 1.1 Pa gap 12 cm Ar 1.1Pa gap 6cm
0.0 0
500
1000
1500
2000
2500
[Isatsqrt(Mi)]
plasma density estimated with Langmuir probe 29
Conclusions • Planar resonant antenna used as a plasma source • Partial inductance method
• Complex image method • Planar resonant antenna used as a plasma sensor for plasma conductivity general method for ICP
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