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May 24, 2015 - Mutual partial inductance between parallel wires. M p l. I. 2h wire 1 wire 2. I. L p. L p. I. I wire wire wire/wire. OK! ☺ partial loop inductance loop.
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

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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

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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! 

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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

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Method of images:

baseplate screen

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Method of images

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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

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25

DR

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

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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