Plasmas rf haute densité Pascal Chabert LPTP, Ecole Polytechnique

Programme Introduction Généralité sur les plasmas Plasmas Capacitifs (CCP) VHF Multi-fréquence Plasmas inductifs (ICP) Plasmas hélicons

Industrial applications of plasmas Depollution Environmental applications Reactions with reactive radicals created in the plasma Deposition Microelectronic Solar cells Flat panel displays Coatings Diamond, silica Plasma Processing Surface treatment Nitriding Polymer films Etching Microelectronic Si, SiO 2 and many others! Optoelectronic MEMS, MOEMS, NEMS

Etching plasmas 3x10-1 m Cl 2 Cl Cl + Cl Plasma + 1-100 mtorr + + Cl + e - Pump sheath Cl Cl x + 3x10-7 m SiCl y Si Need to control stability and uniformity of: Ion flux (plasma density) Ion energy (sheath voltage) Reactive neutral flux

Plasma discharges ~ Positive space charge: sheaths Plasma Potential is maximum at the plasma center: Electrons are confined Negative ions are confined Positive ions are accelerated toward the walls n + = n e + n - <V> Positive ion flux : directed Electron flux : isotropic Neutral flux : isotropic J i J e J N 0

Relative densities and energies n (cm -3 ) n (cm -3 )

Why sheaths? Without sheaths, currents at the wall are : Positive space charge: sheaths J e = en 0 kte 2π m e J + = en 0 kt+ 2π m + ~ Plasma n + = n e + n - Since m e << m + and T e >> T + : J e >> J + loss of electrons <V> The positive space charge builds up an E field directed to the walls which confines electrons and accelerate ions to the wall 0 E

Sheath thickness Positive ion current produced by the plasma (Bohm): Using current continuity and Child law, 4ε 9 0 2 q m j + = 1 2 h en l 0 3 2 + V = 2 + s h kt m en e + l 0 kt m e + + + e - + V s2 >V s1 Plasma + + + + + + V + s1 + e - e - + we obtain the sheath thickness: s λ D = ev k T s e 3 4 - I s

Particle and energy balance Plasma (volume V) Surrounded by a surface A

At low pressure n n 0 n s d Plasma Sheath 0 x s x

at high pressure n n 0 Plasma Sheath n s 0 x s x

h l vs pressure h l 0.5 0 100 P (mtorr)

Plasma Dielectric constant and conductivity Conductor at low frequency (ω < ω p ) Dielectric at high frequency (ω > ω p ) MHz GHz ω pi rf domain ω pe ω

Skin depth Conductor at low frequency (ω < ω pe ) Dielectric at high frequency (ω > ω pe ) MHz GHz ω pi rf domain ω pe ω Waves are absorbed in a skin depth Propagating waves (microwave diagnostics: interferometry, reflectometry etc.) Inertial (low pressure)

Typical etching reactors: CCP s, ICP s MHz rf domain GHz Electrons follow the rf field ω pi 13.56 MHz or higher? ω pe ω Ions follow time-averaged field ~ rf Capacitively-coupled plasma Inductively-coupled plasma ~ rf ~ rf

Magnetic confinement Anisotropic dielectric constant Cyclotron frequency: Larmor radius: ω c = R L = qb m mv qb For typical conditions (B 50 Gauss): Non-magnetized ions: R L 10-20cm Magnetized electrons: R L 1-2 mm

Waves in magnetized plasmas N² Alfven helicons Right-hand polarized Left-hand polarized 1 ω ci ω ce ω pe ω Without B field, no propagation at ω < ω pe

Helicon reactors Helicon antenna Source solenoid 400l/s turbo pump Matching network and source cooling rf 13.56 MHz B 0 Ar, SF 6 Helicons generate high density plasmas. Interesting for: Very deep etching Load lock and cartridge transfer Wafer holder Chamber solenoid Space plasma propulsion 150l/s turbo Water cooling

A model of capacitive discharges V.A. Godyak, Soviet Radiofrequency Discharge Research, Delphic Associates, Fall Church, 1996 M.A. Lieberman, A.J. Lichtenberg, Principles of Plasma Discharges and Materials Processing, 2 nd Edition 2005 Time-averaged potential Z sheath =1/(jc s ω) s a (t) V rf E z Plasma E z Z plasma =R p +jl p ω s b (t) Impedance depends on : Voltage, V rf Electron density, n e Sheath size, s m To find a self-consistent solution: Child law Particle balance Power balance

The homogeneous model Ion density is constant between the electrodes

Plasma equivalent circuit Surface A d Plasma Negligible since displacement current is smaller than conduction current in the plasma

Sheath model

Sheath motion

Voltage across one sheath The voltage across one sheath is non-sinusoidal. Harmonics!

Combination of the two sheaths The combination of the two sheath is sinusoidal

To summarize Each sheath generates harmonics But the combination is sinusoidal The combination of the two sheaths is described by a capacitor

Sheath equivalent circuit What are these resistive terms?

Power dissipated by ions in the sheath

Collisionless electron heating in the sheath Open problem: R p R stoc Collisionless power dissipation in the sheath Kinetic model «Hard wall» M.A. Lieberman, IEEE Plasma Sci. 16 (1988) 638 I.D. Kaganovich, Phys. Rev. Lett. 89 (2002) 265006 Fluid model «pressure heating» G. Gozadinos et al., Phys. Rev. Lett. 87 (2001) 135004

Equivalent circuit for the capacitive discharge

Scaling of absorbed power vs density

The inhomogeneous model Sheaths In reality, the ion density is not homogeneous between the plates In the bulk, there are density gradients

The sheath is inhomogeneous s(t) Ion density decreases towards the electrode due to acceleration But ion density is independent of time I 0 2R stoc + 2R ion + 2R ohm,sh C s

Inhomogeneous circuit element values

Particle and energy balance in CCP s Plasma (volume V) Since s m depends on I 0 Strictly speaking, n e and T e are not decoupled

Results

Contemporary capacitive discharges (Advanced issues) 1. The issue of multiple-frequency excitation 2. Electromagnetic effects at high frequency

Frequency effect 1000 15 mtorr E ion > 500 V : Experiments ----- : model Energie des ions (V) 100 13.56 MHz 40.68 MHz 81.36 MHz V rf E ion < 100 V 10 0,0 0,1 0,2 0,3 0,4 0,5 Flux d'ions J i (ma.cm -2 ) A. Perret et al., Appl. Phys. Lett 86 ( 2005) 021501 HF drive for high flux LF bias for tunable ion energy Dual Frequency Capacitive (DFC)

New physics : multiple-frequency excitation 1. Collisionless heating in the dual frequency sheath M. Turner and P. Chabert, Phys. Rev. Lett. 96 (2006) 205001 z R 0 E z H φ E r r ~ 2. Electromagnetic regime: inductive heating at high frequency P. Chabert, J.-L. Raimbault, P. Levif, J.-M. Rax and M. A. Lieberman, Phys. Rev. Lett. 95 (2005) 205001

Collisionless heating in the DF sheath n 0 0 n s S(t)

Collisionless heating in the DF sheath Enhancement!

Conclusions on heating in the DF sheath Heating in the dual frequency sheath (Collisionless and Ohmic) enhanced by low frequency This is because the low frequency voltage greatly increases the sheath size such that the high frequency produces heating over a larger volume Independent control of ion flux and ion energy is not achieved! Let us now investigate electromagnetic effects at high frequency

The capacitor at high frequency (Feynman Lectures on Physics, chapter 23-2) z r E 0 Field line E

The capacitor at high frequency (Feynman Lectures on Physics, chapter 23-2) z r E 0 B 1 First order Field line E Field line B

The capacitor at high frequency (Feynman Lectures on Physics, chapter 23-2) z r E 0 B 1 E 1 First order Field line E Field line B

The capacitor at high frequency (Feynman Lectures on Physics, chapter 23-2) z 1,0 E 0 r 0,8 E 0 +E 1 (100 MHz) E 0 B 1 E 1 E (u.a.) 0,6 0,4 0,2 Field line E Field line B 0,0-0,4-0,2 0,0 0,2 0,4 r (m) Standing wave profile The electric field is not radially uniform

Electromagnetic regime: λ R and δ d Fields are not radially uniform z R E z 0 H φ Er r M.A. Lieberman et al., Plasma Sources Sci. Technol. 11 (2002) 283 L. Sansonnens et al., Plasma Sources Sci. Technol. 15 (2006) 302 ~ Solve Maxwell s equations for given s and n e (not self-consistent): λ R : Standing wave effect (E z ) δ d : Skin effect (E r ) Edge effects

Transmission line model z R ind L C 0 r R cap 2R i dr dr TL elements depends on: Local voltage and/or current (V rf, I rf ) Electron density, n e Sheath size, s m Use: Child law Particle balance Power balance Self-consistent solutions for: V rf (r) and I rf (r) n e (r) s m (r) P. Chabert et al., Physics of Plasmas 11 (2004) 1775 P. Chabert et al., Physics of Plasmas 11 (2004) 4081 P. Chabert et al., Phys. Rev. Lett. 95 (2005) 205001

Experimental evidence of the effects Top-grounded electrode 3 RFEA Retarding Field Energy Analyser Ion energy uniformity 64 planar probes Cartography of the ion flux

Standing wave effect (1/2) J i /J imax 50 W, 200 mtorr (local heating) J i /J imax 60 MHz J imax = 0.15 ma.cm -2 13.56 MHz J imax = 0.07 ma.cm -2 J i /J imax 81.36 MHz J imax = 0.17 ma.cm -2 A. Perret et al., Appl. Phys. Lett 83 ( 2003) 243

Standing wave effect (2/2) 0,18 Experiments 0,16 0,14 TL Theory Worsening factor J i (ma.cm -2 ) 0,12 0,10 0,08 0,06 0,04 0,02 81.36 MHz 200 mtorr (local heating) 50 W 0,00-20 -10 0 10 20 X (cm) Fairly insensitive to the gas composition P. Chabert et al., Physics of Plasmas 11 (2004) 1775

Skin effect, inductive heating Experiments TL Theory Spatial E to H transitions E mode at the centre, H mode at the edge A. Perret et al., Appl. Phys. Lett 83 ( 2003) 243

Global E to H transitions at low pressure Uniform temperature plasma 2.0 Electrode radius = 0.15 200 MHz 1.5 d dt 3 2 n e kt e = P e ( ne ) Ke( Te ) ne P ind /P cap 1.0 H P loss : Inelastic collisions and energy flux at the wall 0.5 0.0 0 500 1000 1500 2000 V 0 (V) E

Inductive discharges (the issue of instabilities) 1. Principles and equivalent circuit 2. E to H transitions 3. Instabilities at the E-H transition when electronegative gases are being used

Inductive reactors (ICP or TCP) Inductive reactors are routinely being used for silicon and metal etching They allow independent control of ion flux and ion energy They may operate at higher density than capacitive They undertake E to H transitions

Inductive coupling E ~ H ~ kz Decaying wave Inertial skin depth (low-pressure) c δ p = = ω p e m e 2 μ0 n e Coil δ p 1 3 cm Dielectric window Resistive skin depth (high pressure) δ p = 2 ωσ μ p 0

Electromagnetic model

Resistance of the plasma loop Density (m -3 ) Density (m -3 )

This can be explained in a much simpler way This is the high density regime (decaying dashed line on previous slide)

Inductance of the plasma loop Note this L is not due to electron inertia from the L obtained in capacitive discharges

The transformer model

The transformer matrix

Equivalent circuit of ideal inductive discharges

Power balance in ideal inductive discharges

Real inductive discharges E ~ H ~ kz P abs Capacitive (E) Inductive (H) E Ground n e

E H Transitions Power P loss Power Inductive (H) I > I rf 2 rf 1 I rf 1 Capacitive (E) n e Pressure Increasing RF current leads to E H transition

Instabilities at the transition 300 Experiment in CF 4 Light fluctuations 250 Stable Inductive (H) 0,4 Effective power(w) 200 150 100 50 Instabilities Stable Capacitive (E) Intensity (a. u.) 0,2 0,0 2 4 6 8 10 12 14 16 Time (ms) 0 0 5 10 15 20 25 30 Pressure (mtorr) If electronegative gas is used!

Global model of the instability e e n n n + = + Γ = Γ Γ + + ( ) i e T T e e e i B i e V n e V n T u n l / / 4 1 4 1 0.2 1 1.5 Φ Φ + + = Γ = Γ + = Γ λ Particle balance : Power balance : ( ) = n K n K n P kt n dt d e e e abs e e 2 3 What is the form of this term? Loss term V A K n n K n n K n n dt dn e att g e g iz g e e Γ + = det * V A K n n K n n K n n dt dn g rec att g e + Γ = det *

Typical model result SF 6 For appropriate I coil 10 Problems! Densities (10 10 cm -3 ) 1 0,1 n + n e n - Experiment: 10 khz Model: 1.2 khz Model window is smaller Model densities are smaller 0,01 0 1 2 3 4 Time (ms) More about this later

Some aspects of helicon discharges 1. The wave mode and E-H-W transitions 2. Instabilities, Double-layers 3. Space propulsion using Double-layers?

Experimental set-up (ANU-like) Z (cm) Pump Diffusion ch. Source chamber 56 26 0 54 36 B field Grid Double saddle antenna Pyrex tube Movable probes Or analyzer Gas inlet

E H W Transitions (1) Pression (mtorr) 8 7 6 5 4 3 2 SF 6 Régime capacitif (E) Régime inductif (H) Régime hélicon (W) Transition H W 1 Transition E H 0 0 400 800 1200 1600 2000 Puissance rf (W) Capacitive (E) : Low electron density High voltage on the antenna Inductive (H) : Higher electron density Ionization near the antenna Helicon (W) : Even higher electron density Ionization at the center; Wave propagation

E H W Transitions (2) Lost power : P P loss P loss = n e u Absorbed power : B A P = P + abs Ohm ( Ec + Ee ) Kne P Stoc (I rf < I min ) Eq. Inductive H P Absorbed (I rf > I min ) n s P Capacitive E P loss E H W transitions P 3 Equilibrium 2 P Absorbed 1 n s n s

Instabilities with EN gases Power (W) 1800 1600 1400 1200 1000 800 600 400 200 0 0 5 10 15 20 25 I+ saturation (a.u.) 7 6 5 4 3 2 1 0 Downstream instability Source instability Pressure (mtorr) z = 26 cm z = 22 cm z = 18 cm z = 14 cm 0ms 5ms 10ms Time Downstream instability; looks similar to previous work Tuszewski et al. Phys. Plasmas 10 539 I+ saturation (a.u.) 0 0ms 1ms 2ms E-H relaxation oscillations Chabert et al. Plasma Sources 10 478 (2001) Corr et al. Plasma Sources 12 265 (2003) 7 6 5 4 3 2 1 Time z = 26 cm z = 23 cm z = 20 cm z = 16 cm

In addition to downstream instabilities: Double-layers 1mT, 600W, SF6:Ar (1:1) mixture 30 Z axis 25 DOUBLE LAYER 0 0 5 10 15 20 25 30 Z (cm) 18 cm Diffusion chamber 20 15 10 5 Source chamber <Vp> HIGH Vp - + + - - + + + + - - - - - LOW Vp 26 cm 18 cm 0 cm

Plasma potential dynamics Plasma Potential Electropositive High Te Z (mm) 500 450 400 350 300 Vp(z,t) 35 30 25 250 20 200 150 15 100 Electronegative; Low Te 50 0.5 1 1.5 2 t/tinsta 10 26% SF 6, Pressure = 1 mt, Power = 600 W Frequency = 850 Hz

Propagating double layers Propagating speed = 150 m/s

Static double layers Electron density (m -3 ) 10 17 10 16 10 15 4% SF 6 8% SF 6 Diffusion chamber 0 10 20 30 40 50 60 Z (cm) source Electron temperature (ev) 6 5 4 3 2 4% SF 6 8% SF 6 1 Diffusion source chamber 0 0 10 20 30 40 50 60 Z (cm) No DL Stable DL Propagating DL 0 7 13 % SF 6

HDLT Concept (Charles at ANU) Christine Charles and Rod Boswell at ANU have proposed to use a Double Layer for ion acceleration and produce thrust Xe Xe + beam DL The Helicon Double Layer Thruster (HDLT) uses highly diverging B field to generate the DL Charles and Boswell (2003) Appl. Phys. Lett. 82 1356 Charles, 2005 Phys. Plamsas (2005) 12 044508

General conclusion Capacitive discharges have to be excited by more than one frequency to be used as efficient etching tools, which involves a lot of new fascinating issues (Academic point of view!) Inductive discharges produce high density plasmas with independent control of ion flux and ion energy, but are subject to instabilities at the E to H transition Helicon discharges produce even higher plasma densities which is interesting for plasma propulsion. They also have a lot of instabilities (which were not all discussed here) and seem to involve double-layers in some cases