pascal chabert lptp, ecole polytechniqueplasmasfroids.cnrs.fr/img/pdf/plasmasrf.pdfplasma processing...

Plasmas rf haute densité

Pascal ChabertLPTP, Ecole Polytechnique

chabert@lptp.polytechnique.fr

©Pascal Chabert, 2006, All rights reserved

Programme

• Introduction – Généralité sur les plasmas

• Plasmas Capacitifs (CCP) – VHF – Multi-fréquence

• Plasmas inductifs (ICP)

• Plasmas hélicons

Industrial applications of plasmas

EtchingMicroelectronicSi, SiO2 and many others!

OptoelectronicMEMS, MOEMS, NEMS

DepollutionEnvironmental applicationsReactions with reactive

radicals created in the plasma

DepositionMicroelectronicSolar cellsFlat panel displaysCoatingsDiamond, silica

PlasmaProcessing

Surface treatmentNitridingPolymer films

Plasma1-100 mTorr

+

+ +

++

e-

sheath

Etching plasmas

Cl

Si

SiClyClx+

Cl

Cl

Cl

Cl

3x10-1 m

Cl2 Pump

• Ion flux (plasma density)

• Ion energy (sheath voltage)

• Reactive neutral flux

Need to control stabilityand uniformity of:

3x10-7 m

Plasma discharges

• Potential is maximum at the plasma center:

– Electrons are confined– Negative ions are confined– Positive ions are accelerated

toward the walls

Ji

Je JN

• Positive ion flux : directed• Electron flux : isotropic• Neutral flux : isotropic

Plasma

n+ = ne+ n-

<V>

~

Positive space charge: sheaths

0

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

Why sheaths?

• Without sheaths, currents at the wall are :

e

ee m

TkneJπ20=

+

++ =

mTkneJ

π20

• Since me << m+ and Te >> T+ :– Je >> J+ ⇒ loss of electrons

• The positive space charge builds up an E field directed to the walls which confines electrons and accelerate ions to the wall

Plasma

n+ = ne+ n-

<V>

~

Positive space charge: sheaths

0

E

Sheath thickness

• Positive ion current produced by the plasma (Bohm):

• Using current continuity and Child law,

we obtain the sheath thickness:

43

⎟⎟⎠

⎞⎜⎜⎝

⎛=

e

s

D TkVes

λ

++

+ =⎟⎟⎠

⎞⎜⎜⎝

⎛mTkneh

sV

mq e

l 02

23

21

0 29

4ε

++ =

mTknehj e

l 0

Plasma

Vs1

Vs2>Vs1

+-

Is

++

+

+ +

+

+

+

e-+ +

+e- e-

Particle and energy balance

Plasma (volume V)

Surrounded by a surface A

At low pressure…

Sheath

xxs

ns

n0

0

Plasma

n

d

at high pressure…

She

ath

xxs

ns

n0

0

Plasma

n

hl vs pressure

P (mTorr)100

0.5

0

hl

Plasma Dielectric constant and conductivity

Dielectric at high frequency (ω > ωp)Conductor at low frequency (ω < ωp)

ωpi ωωperf domain

MHz GHz

Skin depth

Dielectric at high frequency (ω > ωpe)Conductor at low frequency (ω < ωpe)

ωpi ωωperf domain

MHz GHz

Waves are absorbed in a skin depth Propagating waves (microwave diagnostics: interferometry, reflectometryetc.)

Inertial (low pressure)

Capacitively-coupled plasma

~ rf

Inductively-coupled plasma

~ rf

~ rf

Typical etching reactors: CCP’s, ICP’s

• Electrons follow the rf field

• Ions follow time-averaged fieldωpi ωωpe

rf domainMHz GHz

13.56 MHz or higher?

Magnetic confinement

mqB

c =ω

qBmRLv

=

Cyclotron frequency:

Larmor radius:

For typical conditions (B ≈ 50 Gauss):

• Non-magnetized ions: RL≈10-20cm

• Magnetized electrons: RL≈1-2 mm

Anisotropic dielectric constant

Waves in magnetized plasmas

N²

ω

helicons

Right-hand polarizedLeft-hand polarized

ωpeωci ωce

1

Alfven

Without B field, no propagation at ω < ωpe

Helicon reactors

Water cooling

rf13.56 MHz

Matching networkand source cooling

Helicon antenna

Wafer holder

Load lock and cartridge transfer

Sourcesolenoid

400l/sturbopump

150l/s turbo

Ar, SF6

Chambersolenoid

B0Helicons generate high density plasmas. Interesting for:

• Very deep etching

• Space plasma propulsion

A model of capacitive discharges

PlasmaVrf

Time-averaged potential Zsheath=1/(jcsω)

Zplasma=Rp+jLpω

Impedance depends on :• Voltage, Vrf• Electron density, ne• Sheath size, sm

To find a self-consistent solution:• Child law• Particle balance• Power balance

V.A. Godyak, “Soviet Radiofrequency Discharge Research”, Delphic Associates, Fall Church, 1996M.A. Lieberman, A.J. Lichtenberg, “Principles of Plasma Discharges and Materials Processing”, 2nd Edition 2005

sb(t)

sa(t)

EzEz

The homogeneous model

Ion density is constant between the electrodes

Plasma equivalent circuit

Plasmad

Surface A

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

Rp Rstoc

Collisionless power dissipation in the sheath

Open problem:

• Kinetic model « Hard wall »M.A. Lieberman, IEEE Plasma Sci. 16 (1988) 638I.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

In the bulk, there are density gradients

In reality, the ion density is not homogeneous between the plates

Sheaths

The sheath is inhomogeneous

s(t)

Cs

2Rstoc + 2Rion + 2Rohm,sh

I0

• Ion density decreases towards the electrode due to acceleration

• But ion density is independent of time

Inhomogeneous circuit element values

Particle and energy balance in CCP’s

Plasma (volume V)

Since sm depends on I0

Strictly speaking, ne and Te are not decoupled

Results

1. The issue of multiple-frequency excitation2. Electromagnetic effects at high frequency

Contemporary capacitive discharges(Advanced issues)

0,0 0,1 0,2 0,3 0,4 0,510

100

1000

13.56 MHz

40.68 MHz

81.36 MHz

Ene

rgie

des

ions

(V)

Flux d'ions Ji (mA.cm-2)

15 mTorr

Frequency effect

■●▲ : Experiments----- : model

Eion < 100 V

Eion > 500 V

HF drive for high fluxLF bias for tunable ion energy

Dual Frequency Capacitive (DFC)

Vrf

A. Perret et al., Appl. Phys. Lett 86 ( 2005) 021501

New physics : multiple-frequency excitation

1. Collisionless heating in the dual frequency sheath

2. Electromagnetic regime: inductive heating at high frequency

M. Turner and P. Chabert, Phys. Rev. Lett. 96 (2006) 205001

P. Chabert, J.-L. Raimbault, P. Levif, J.-M. Rax and M. A. Lieberman, Phys. Rev. Lett. 95 (2005) 205001

~

z

r0

R

Hφ

Ez

Er

Collisionless heating in the DF sheath

S(t)

0n0

ns

Enhancement!

Collisionless heating in the DF sheath

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 thesheath size such that the high frequency produces heating over alarger 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)

r

z

Field line E

E0

r

z

Field line E Field line B

E0 B1

First order

The capacitor at high frequency(Feynman “Lectures on Physics”, chapter 23-2)

r

z

Field line E Field line B

E0 B1E1

First order

The capacitor at high frequency(Feynman “Lectures on Physics”, chapter 23-2)

r

z

Field line E Field line B

E0 B1E1

-0,4 -0,2 0,0 0,2 0,40,0

0,2

0,4

0,6

0,8

1,0

E0+E1 (100 MHz)

E (u

.a.)

r (m)

E0

• Standing wave profile

• The electric field is not radially uniform

The capacitor at high frequency(Feynman “Lectures on Physics”, chapter 23-2)

Electromagnetic regime: λ ∼ R and δ ∼ d

~

z

r0

R

Solve Maxwell’s equations for given s and ne (not self-consistent):

• λ ∼ R : Standing wave effect (Ez)• δ ∼ d : Skin effect (Er)• Edge effects

Hφ

Ez

Er

M.A. Lieberman et al., Plasma Sources Sci. Technol. 11 (2002) 283L. Sansonnens et al., Plasma Sources Sci. Technol. 15 (2006) 302

Fields are not radially uniform

Transmission line model

z

0 r

dr

TL elements depends on:• Local voltage and/or current (Vrf, Irf)• Electron density, ne• Sheath size, sm

Use:• Child law• Particle balance• Power balance

Self-consistent solutions for:• Vrf (r) and Irf (r)• ne(r)• sm(r)

C’R’cap

2R’i

L’R’ind

dr

P. Chabert et al., Physics of Plasmas 11 (2004) 1775P. 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

64 planar probesCartography of the ion flux

3 RFEARetarding Field Energy Analyser

Ion energy uniformity

Standing wave effect (1/2)

13.56 MHzJi max = 0.07 mA.cm-2

50 W, 200 mTorr (local heating)Ji/Jimax

Ji/Jimax

Ji/Jimax

60 MHzJi max = 0.15 mA.cm-2

81.36 MHzJi max = 0.17 mA.cm-2

A. Perret et al., Appl. Phys. Lett 83 ( 2003) 243

-20 -10 0 10 200,00

0,02

0,04

0,06

0,08

0,10

0,12

0,14

0,16

0,18 Experiments

J i(m

A.c

m-2)

X (cm)

TL Theory

81.36 MHz200 mTorr (local heating)50 W

Standing wave effect (2/2)

P. Chabert et al., Physics of Plasmas 11 (2004) 1775

Worsening factor

Fairly insensitive to the gas composition

Experiments

Skin effect, inductive heating

A. Perret et al., Appl. Phys. Lett 83 ( 2003) 243

TL Theory

Spatial E to H transitionsE mode at the centre, H mode at the edge

0 500 1000 1500 20000.0

0.5

1.0

1.5

2.0

Pin

d/Pca

p

V0 (V)

200 MHz

Global E to H transitions at low pressure

( ) eeeeeee nTKnPkTndtd )(

23

−=⎟⎠⎞

⎜⎝⎛

Uniform temperature plasma

Ploss : Inelastic collisions and energy flux at the wall E

H

Electrode radius = 0.15

1. Principles and equivalent circuit2. E to H transitions3. Instabilities at the E-H transition when electronegative

gases are being used

Inductive discharges (the issue of instabilities)

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

e

pp ne

mc

02μω

δ ==

Inertial skin depth (low-pressure)

Resistive skin depth (high pressure)

0

2μωσ

δp

p =

H~

E~ zk

cmp 31−≈δ

Dielectricwindow

Coil

Decaying wave

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

ne

Pabs

Inductive (H)

Capacitive (E)H~

E~ zk

E

Ground

Increasing RF current leads to E → H transition

E→H Transitions

ne

Power

Pressure

Power

Inductive (H)

Capacitive (E)

Ploss

1rfI

12 rfrf II >

Instabilities at the transition…

0 5 10 15 20 25 300

50

100

150

200

250

300

Instabilities

Stable Inductive (H)

Stable Capacitive (E)

Effe

ctiv

e po

wer

(W)

Pressure (mTorr)

Experiment in CF4

…If electronegative gas is used !

2 4 6 8 10 12 14 160,0

0,2

0,4

Inte

nsity

(a. u

.)

Time (ms)

Light fluctuations

Global model of the instability

e

e

nnn +=

Γ+Γ=Γ

−+

−+

( )

i

e

T

Teee

iBi

eVn

eVn

Tunl

/

/

4141

2.015.1

Φ−−−−

Φ−

++

=Γ

=Γ

+=Γ

λ

Particle balance :

Power balance :

( ) −−−−=⎟⎠⎞

⎜⎝⎛ nKnKnPkTn

dtd

eeeabsee23

What is the formof this term ?

Loss term

VAKnnKnnKnn

dtdn

eattgegizgee Γ−−+= − det

*

VAKnnKnnKnn

dtdn

grecattge −−+−− Γ−−−= det

*

Typical model result

• Problems !• Experiment: 10 kHz• Model: 1.2 kHz• Model window is smaller• Model densities are

smaller

• More about this later…

SF6 For appropriate Icoil

0 1 2 3 40,01

0,1

1

10

n-n+

ne

Den

sitie

s (1

010 c

m-3)

Time (ms)

1. The wave mode and E-H-W transitions2. Instabilities, Double-layers3. Space propulsion using Double-layers?

Some aspects of helicon discharges

Experimental set-up (ANU-like)

Gas inlet

Pump

Pyrex tube

Double saddle antenna

Grid

Z (cm)

0

26

36

5456

Movable probesOr analyzer

Diff

usio

n ch

.S

ourc

e ch

ambe

r

B field

E → H → W Transitions (1)

• 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

0 400 800 1200 1600 20000

1

2

3

4

5

6

7

8SF6

Régime hélicon (W)Régimeinductif (H)

Transition H W

Transition E H

Rég

ime

capa

citif

(E)

Pres

sion

(mTo

rr)

Puissance rf (W)

E → H → W Transitions (2)

ns

PPloss

PAbsorbed

Equilibrium

P Ploss

PAbsorbed (Irf > Imin)(Irf < Imin)

ns

Eq.

Inductive H

Capacitive E

1

P

ns

2

3

E → H → W transitions

Lost power :

Absorbed power :( ) eecBeloss KnEEAunP ≈+=

StocOhmabs PPP +=

0ms 5ms 10ms0

1

2

3

4

5

6

7

z = 14 cm

z = 26 cm

z = 18 cm

z = 22 cm

I+ s

atur

atio

n (a

.u.)

Time

Instabilities with EN gases

0 5 10 15 20 250

200400600800

10001200140016001800

Pow

er (W

)

Pressure (mTorr)

Downstream instability

Source instability

E-H relaxation oscillationsChabert et al. Plasma Sources 10 478 (2001)Corr et al. Plasma Sources 12 265 (2003)

Downstream instability; looks similar to previous workTuszewski et al. Phys. Plasmas 10 539

0ms 1ms 2ms0

1

2

3

4

5

6

7

z = 16 cm

z = 20 cm

z = 23 cm

I+ s

atur

atio

n (a

.u.)

Time

z = 26 cm

0 5 10 15 20 25 300

5

10

15

20

25

30

Z (cm)

<Vp>

Diffusion chamber Sourcechamber

DOUBLE LAYER

18 cm

1mT, 600W, SF6:Ar (1:1) mixture Z axis

0 cm

26 cm

HIGHVp

LOWVp

18 cm+

+

+

+++

-- - -

- ---

-

In addition to downstream instabilities: Double-layers

t/Tinsta

Z (m

m)

Plasma Potential

0.5 1 1.5 2

50

100

150

200

250

300

350

400

450

500

10

15

20

25

30

35

Electronegative; Low Te

Ele

ctro

posi

tive

Hig

h Te

Plasma potential dynamics

26% SF6, Pressure = 1 mT, Power = 600 W Frequency = 850 Hz

Vp(z,t)

Propagating double layers

Propagating speed = 150 m/s

Static double layers

0 10 20 30 40 50 601015

1016

1017

E

lect

ron

dens

ity (m

-3)

Z (cm)

Diffusionchamber

source

0 10 20 30 40 50 600

1

2

3

4

5

6

Elec

tron

tem

pera

ture

(eV)

Z (cm)

Diffusionchamber source

4% SF68% SF6

4% SF68% SF6

0 7 13 % SF6

No DL Stable DL Propagating DL

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

• The Helicon Double Layer Thruster (HDLT) uses highly diverging B field to generate the DL

Charles and Boswell (2003) Appl. Phys. Lett. 82 1356Charles, 2005 Phys. Plamsas (2005) 12 044508

Xe Xe+ beam

DL

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