Plasmas rf haute densité Pascal Chabert LPTP, Ecole Polytechnique

Transcription

1 Plasmas rf haute densité Pascal Chabert LPTP, Ecole Polytechnique Pascal Chabert, 2006, All rights reserved

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

3 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

4 Etching plasmas 3x10-1 m Cl 2 Cl Cl + Cl Plasma 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

5 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

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

7 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

8 Sheath thickness Positive ion current produced by the plasma (Bohm): Using current continuity and Child law, 4ε q m j + = 1 2 h en l 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 I s

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

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

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

12 h l vs pressure h l P (mtorr)

13 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

14 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)

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

16 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

17 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

18 Helicon reactors Helicon antenna Source solenoid 400l/s turbo pump Matching network and source cooling rf 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

19 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

20 The homogeneous model Ion density is constant between the electrodes

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

22 Sheath model

23 Sheath motion

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

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

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

27 Sheath equivalent circuit What are these resistive terms?

28 Power dissipated by ions in the sheath

29 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) Fluid model «pressure heating» G. Gozadinos et al., Phys. Rev. Lett. 87 (2001)

30 Equivalent circuit for the capacitive discharge

31 Scaling of absorbed power vs density

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

33 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

34 Inhomogeneous circuit element values

35 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

36 Results

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

38 Frequency effect mtorr E ion > 500 V : Experiments : model Energie des ions (V) MHz MHz 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) HF drive for high flux LF bias for tunable ion energy Dual Frequency Capacitive (DFC)

39 New physics : multiple-frequency excitation 1. Collisionless heating in the dual frequency sheath M. Turner and P. Chabert, Phys. Rev. Lett. 96 (2006) 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)

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

41 Collisionless heating in the DF sheath Enhancement!

42 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

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

44 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

45 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

46 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

47 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

48 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)

49 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

50 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 MHz J imax = 0.07 ma.cm -2 J i /J imax MHz J imax = 0.17 ma.cm -2 A. Perret et al., Appl. Phys. Lett 83 ( 2003) 243

51 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, MHz 200 mtorr (local heating) 50 W 0, X (cm) Fairly insensitive to the gas composition P. Chabert et al., Physics of Plasmas 11 (2004) 1775

52 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

53 Global E to H transitions at low pressure Uniform temperature plasma 2.0 Electrode radius = 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 V 0 (V) E

54 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

55 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

56 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

57 Electromagnetic model

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

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

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

61 The transformer model

62 The transformer matrix

63 Equivalent circuit of ideal inductive discharges

64 Power balance in ideal inductive discharges

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

66 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

67 Instabilities at the transition 300 Experiment in CF 4 Light fluctuations 250 Stable Inductive (H) 0,4 Effective power(w) Instabilities Stable Capacitive (E) Intensity (a. u.) 0,2 0, Time (ms) Pressure (mtorr) If electronegative gas is used!

68 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 / / 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 *

69 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, Time (ms) More about this later

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

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

72 E H W Transitions (1) Pression (mtorr) SF 6 Régime capacitif (E) Régime inductif (H) Régime hélicon (W) Transition H W 1 Transition E H 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

73 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

74 Instabilities with EN gases Power (W) I+ saturation (a.u.) 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 I+ saturation (a.u.) 0 0ms 1ms 2ms E-H relaxation oscillations Chabert et al. Plasma Sources (2001) Corr et al. Plasma Sources (2003) Time z = 26 cm z = 23 cm z = 20 cm z = 16 cm

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

76 Plasma potential dynamics Plasma Potential Electropositive High Te Z (mm) Vp(z,t) Electronegative; Low Te t/tinsta 10 26% SF 6, Pressure = 1 mt, Power = 600 W Frequency = 850 Hz

77 Propagating double layers Propagating speed = 150 m/s

78 Static double layers Electron density (m -3 ) % SF 6 8% SF 6 Diffusion chamber Z (cm) source Electron temperature (ev) % SF 6 8% SF 6 1 Diffusion source chamber Z (cm) No DL Stable DL Propagating DL % SF 6

79 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 Charles, 2005 Phys. Plamsas (2005)

80 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