Furno, Ivo

Guittienne, Philippe

Howling, Alan

Infoscience - École polytechnique fédérale de Lausanne

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: alan.howling@epfl.ch Frontiers in Low Temperature Plasma Diagnostics XI, 24-28 May 2015 Porquerolles Island, France 1 Outline of talk • Review:  RF antenna diagnostics  • Inductively-coupled plasma (ICP)  • Planar resonant RF antenna  • Partial inductance  • Complex image method  • RF antenna ICP diagnostic "new" device "new" concept "new" theory new to plasma 2 Brief review:  RF antenna diagnostics relative dielectric constant of  plasma J H Kim et al, Appl. Phys. Lett. 83, 4725 (2003) microwave interferometer microwave cavity E Stoffels  et al, Phys. Rev. E 51, 2425 (1995)  wave cutoff method 3 hairpin probe R L Stenzel, Rev. Sci. Instrum. 47, 603 (1976) 𝜖𝑟 = 1 −𝜔𝑝𝑒𝜔2, 𝜔𝑝𝑒 =𝑛𝑒𝑒2𝜖0𝑚𝑒   active plasma resonance spectroscopy  T. Styrnoll et al, Pl. Sources, Sci. Technol. 23, 025013 (2014) Inductively-coupled plasma diagnostic? transformer coupling model  measure the change in primary impedance to deduce plasma conductivity (electron density and collision frequency) plasma OK only for simple geometries! coil 4 I2 I1 Cylindrical (birdcage)  How to model inductive coupling with plasma? 20 cm 55 cm 23 legs 5 Ph. Guittienne et al, Pl. Sources, Sci. Technol. 23, 015006 (2014) Planar resonant network  Planar resonant network, N legs, (N-1) resonances  How to model inductive coupling with screen & plasma? For each resonance: single LC parallel resonant circuit plasma 6 top view side view mode m = 4 Zin frequency [MHz] Mode impedance spectrum measurements m=6 m=8 m=10 m=4, vacuum m=4, plasma m=2 I1 V1 Zin network analyser vacuum Zin "Z-scan" probe plasma Strong effect of plasma = Basis for a plasma diagnostic 7 L R r C r C L R Mn,n+1 str/line Mn,n+1 leg/leg Mn-1,n leg/leg Mn+1,n+1 str/opp L R r C r C L R Planar resonant network  ...must consider mutual inductances 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: self inductance Loop 9 Alternative view of inductance... partial inductance 10 surface integrals line integral Stokes' theorem self partial inductance l I 2h wire 1 wire 2 l I B Y ∞ mutual partial inductance A  A.dl = 0 A=0  A.dl = 0 11 Y ∞ a Mutual partial inductance between parallel wires Mp l I 2h wire 1 wire 2 I Lp Lp I I wire wire wire/wire OK!  partial                 loop inductance loop                partial inductance 12 Mutual partial inductances between antenna elements matrix impedance model Vn 13 Ohm's law for nth leg 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 17 Planar resonant network – with plasma  18 Induced current in a plasma I mutual inductance with plasma? I 19 y plasmacurrent density plasma skin depth d d Induced current in a resistive ground return Bell Syst. Techn. J. 5, 539 (1926) Mutual inductance: infinite converging Fourier integrals  20 Dubanton at Electricité de France (1976), & co.: Complex image theory = real image current at a complex depth complex mutual inductance also includes ohmic dissipation: Complex depth p = complex skin depth.  Complex wavenumber  = 1/p 21 depth IAC Complex image theory = real image current at complex depth... 22 induced current distribution in the plasma ...the magnetic field above the plasma is the same for both cases  Complex image method is used in several domains (but not plasma)  • power transmission • telecommunications • geophysics • microelectronics theory InsulatorInsulatorSemiconductor SubstratePort 1Port 2MetalViaMetal Ground Plane23 The impedance matrix accounts for all coupling to the antenna 24 vacuum plasma 25 mode resonance measurements matrix impedance model Complex image method fits all 5 modes using only 3 physical quantities: 1) distance;   2) electron density;   3) collisionality skin depth depends on: plasma to be measured network analyser 130 135 140 145 150 155 160 165 170051015202530[MHz]Df DR RF network (non-invasive in wall) metal housing dielectric spacer "window" (alumina...) Zin frequency [MHz] Inductively-coupled antenna used as a diagnostic for plasma conductivity  "Method and Device for Determining Plasma Characteristics" 4 May 2015               EP15166251.7 26 A hybrid resonant network antenna probe on a printed circuit board ... and a large area 15 kW antenna (1.2 m2) for large area deposition, etching, packaging applications, etc  increases sensitivity to inductive coupling 27 Measurement of probe Df  as a function of the RF power of the plasma source. The computed relation between the electron density and Df (complex image method and mutual inductance matrix). The electron density as a function of the source injected power. 0 200 400 600 80002468101214power [W]ne [1016 m-3]  ne (interferometer)ne (inductive probe)28 DEVICE + METHOD 0 500 1000 1500 2000 25000.00.51.01.52.02.53.03.5   Ar 1.1Pa gap 12cm N2 1.1 Pa gap 12 cm He 1.1 Pa gap 12 cm Ar 1.1Pa gap 6cmfrequency shift [MHz][Isatsqrt(Mi)]plasma density estimated with Langmuir probe Inductive probe measurements using different gases 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  30 

RF antennas as plasma monitors

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RF antennas as plasma monitors

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Infoscience - École polytechnique fédérale de Lausanne