RF antennas as plasma monitors

Transcription

1 RF antennas as plasma monitors A. A. Howling 1 *, Ph. Guittienne 2, R. Jacquier 1, I. Furno 1 1 Centre de Recherches en Physique des Plasmas, EPFL, Lausanne, Switzerland 2 Helyssen Sàrl, Switzerland *Contact alan.howling@epfl.ch Frontiers in Low Temperature Plasma Diagnostics XI, May 2015 Porquerolles Island, France 1

2 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

3 Brief review: RF antenna diagnostics wave cutoff method microwave interferometer J H Kim et al, Appl. Phys. Lett. 83, 4725 (2003) microwave cavity ε r = 1 ω pe ω active plasma resonance spectroscopy T. Styrnoll et al, Pl. Sources, Sci. Technol. 23, (2014) 2, ωpe = n ee 2 ε 0 m e relative dielectric constant of plasma E Stoffels et al, Phys. Rev. E 51, 2425 (1995) hairpin probe R L Stenzel, Rev. Sci. Instrum. 47, 603 (1976) 3

4 Inductively-coupled plasma diagnostic? transformer coupling model coil plasma I 1 I 2 OK only for simple geometries! measure the change in primary impedance to deduce plasma conductivity (electron density and collision frequency) 4

5 Planar resonant network Ph. Guittienne et al, Pl. Sources, Sci. Technol. 23, (2014) Cylindrical (birdcage) 55 cm 23 legs 20 cm How to model inductive coupling with plasma? 5

6 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

7 Mode impedance spectrum measurements m=6 m=4, vacuum m=2 m=10 m=8 m=4, plasma Z in frequency [MHz] plasma vacuum I 1 Z in "Z-scan" probe Z in network analyser V 1 Strong effect of plasma = Basis for a plasma diagnostic 7

8 Planar resonant network C r L R L R...must consider mutual inductances C r C r M str/line n,n+1 M leg/leg n-1,n L R M leg/leg n,n+1 L R M str/opp n+1,n+1 C r 8

9 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 9

10 Alternative view of inductance... surface integrals Stokes' theorem line integral partial inductance 10

11 wire 1 wire 2 self partial inductance A.dl = 0 l A Y B A=0 I a A.dl = 0 mutual partial inductance I l Y 2h 11

12 Mutual partial inductance between parallel wires wire 1 I 2h I wire 2 l partial loop inductance loop partial inductance wire L p I I wire/wire M p wire L p OK! 12

13 Mutual partial inductances between antenna elements Ohm's law for n th leg V n matrix impedance model 13

14 Mutual inductance with the baseplate screen in vacuum (no plasma) side view screen 14

15 Method of images: baseplate screen 15

16 Method of images 16

17 Planar resonant network no plasma mode frequencies calculated by a matrix impedance model using partial inductances good agreement for mode frequencies in vacuum 17

18 Planar resonant network with plasma 18

19 Induced current in a plasma mutual inductance with plasma? I I plasma current density plasma skin depth d d 19 y

20 Induced current in a resistive ground return Bell Syst. Techn. J. 5, 539 (1926) Mutual inductance: infinite converging Fourier integrals 20

21 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

22 Complex image theory = real image current at complex depth......the magnetic field above the plasma is the same for both cases induced current I distribution AC in the plasma depth 22

23 Complex image method theory is used in several domains (but not plasma) power transmission telecommunications geophysics microelectronics Port 1 Metal Via Insulator Insulator Port 2 Semiconductor Substrate Metal Ground Plane 23

24 The impedance matrix accounts for all coupling to the antenna plasma vacuum 24

25 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 25

26 Inductively-coupled antenna used as a diagnostic for plasma conductivity Df "Method and Device for Determining Plasma Characteristics" 4 May 2015 EP DR network analyser Z in metal housing plasma to be measured [MHz] frequency [MHz] RF network (non-invasive in wall) dielectric spacer "window" (alumina...) 26

27 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 m 2 ) for large area deposition, etching, packaging applications, etc 27

28 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). DEVICE + METHOD ne (interferometer) ne (inductive probe) n e [10 16 m -3 ] power [W] The electron density as a function of the source injected power. 28

29 Inductive probe measurements using different gases frequency shift [MHz] Ar 1.1Pa gap 12cm N Pa gap 12 cm He 1.1 Pa gap 12 cm Ar 1.1Pa gap 6cm [I sat sqrt(m i )] plasma density estimated with Langmuir probe 29

30 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