Fundamentals of Plasma Physics IIIppst-2007.physik.uni-greifswald.de/fundamentals_3.pdf · • The transition zone between bulk plasma and a surface, the SHEATH, is fundamental in

Institute for Experimental and Applied Physics

Group Plasma Technology

Fundamentals of Plasma Physics IIIH. Kersten

Summer School on Plasma Physics, BNPTGreifswald, 11.09.2007

IEAP University of Kiel

outline

3.1. Gas discharge plasmas

electric breakdown in gasesTownsend mechanismmicro discharges / streamersPaschen’s law

3.2. Stationary gas discharges

Townsend dischargeglow dischargestructures of a glow dischargehollow cathode effect, magnetron effectarc discharge

3.3. Plasma surface interaction

stationary plasma boundary sheathChild-Langmuir lawBohm criterion

mechanical compression• gas is heated by shock waves (ballistic compression)electromagnetic compression• gas heating for short duration by high-current pulse discharges to very high temperatures• special form of electromagnetic compression at Pinch effect where a rapidly increasingmagnetic field compresses the plasma

plasma generation by electric fields

• plasmas are mostly generated by electrical discharges• in principle, a gas becomes ionized by an electric field (ignition) and a self-sustainingmechanism stabilizes the plasma at a certain current• time regime (frequency) of the field, gas pressure and electrode material are of greatimportance

plasma generation by waves / radiation

• for ionization of a gas also waves or particle beams can be used• e.g. microwave radiation, electron beams, laser, radioactive radiation

3.1. Gas Discharge Plasmas

plasma generation(energy supply)

heating/compression

particle beam/external source

electric field

electromagneticfield

electromagneticwaves

glow discharge- positive column- low-pressure lamps- cathode sputtering- hollow cathode

arc discharge- high-pressure lamps- plasma welding

corona dischargedielectric barrier discharge (DBE)

- plasma display panel (PDP)capacitively coupled

plasma (CCP)

inductively coupledplasma (ICP)

- plasma torchmagnetron dischargeplasma focus

electron beam plasmaplasma jetmagnetohydrodynamicgenerator (MHD)

microvwave plasma- electron cyclotronresonance (ECR)

surface wave plasmahelicon wave plasma


atmospheric pressure dischargelow pressure rf discharge in argon

low pressure dc glow discharge in neon (positive column)



plasma application:for example for illumination

recipe(input)

pV, P

fgenerator

B

neutralsnn Tn

j+ jnE+ En

nn

electrons ne Te

ionsn+ n-T+ T-

substrate

chemical processing,deposition

products

physical processing,deposition

energy conversion : field, plasma, surface

plasmaspecies


P inelasticcollisions

optical emission

reactivespecies

new ions andelectrons

thermalizationof field energythrough elastic

collisions:hot electrons

Te↑

electrons gain energy

fromelectric field

~ eλe|E|

electrons and their collisions carry and distribute the energyfrom the matchbox to process gas (neutrals, ions) to the substrate

particle interaction: charge carriers in plasma

non-thermal plasmas


differentreactivespecieselectron

density ne

electron collision

rate νvoltage Ufree mean

path λ+

etch rate

selectivity

homogeneity

power loss (heat)

power

power loss (heat)

loss

plasma

Fundamental

energy conversion : field, plasma, surface


plasma application:for example semiconductor etching

collision processes innon-isothermal plasmas

electron-electroninteraction

heavyparticlereactions

no change ofparticlenumber

change ofparticlenumber

⇒e- + A 2e- + A+

e- + A+ 2e- + A++

e-+ A2 2e- + A + A+

⇒

⇒

e- + A + B A- + Be- + A2 A + A-

⇒⇒

ionization

attachment

dissociatione- + AB e- + A + Be- + AB e- + A+ + B-

elastic collisione- + A e- + A

electron collisions withheavy particles

excitatione- + A e- + A*e- + A* e- + A**(source of radiation:A* A + hv)

e- + A* e- + A⇒

deexcitation

recombinatione- + A+ A + hve- + A2

+ A + A⇒⇒

⇒

⇒

⇒

⇒

⇒⇒

collsion processes : generation

of charge carriers


collsion processes : generation of charge carriers


channels of ionization ( α)

• Direct electron impact ionization

• Ionization from excited levels

• Penning Ionization

** 2iKM e M e− + −+ ⎯⎯→ +

2iKM e M e− + −+ ⎯⎯→ +

* pKAr M M Ar e+ −+ ⎯⎯→ + +

dominant at high energy

dominant at low energy





Ar

ionization energyexcitation energy

ionization via ionization via excited states and excited states and

Penning effectPenning effect

ionization via ionization via impact impact

ionizationionization



energy and momentum conservationcollision of an electron ( and ) and an atom ( and )

(ma >> me , va << ve)

elastic collision

ionizing collision

neon

neon

neon

exciting collision

ex

aaa

ee

aa

ee uv

mv

mv

mv

m++=+ 2222 '

2'

222

'' aaeeaaee vmvmvmvm +=+

io

aaa

eee

aa

ee uv

mvv

mv

mv

m+++=+ 22222 '

2)"'(

222

')"'( aaeeeaaeevmvvmvmvm ++=+

2222 '2

'222 a

ae

ea

ae

e vm

vm

vm

vm

+=+

'' aaeeaaee vmvmvmvm +=+

em evr

aam vr

typical total cross section :)2

( 2e

e vm

uQ =




collsion processes : losses of charge carriers


multiplication of charge carriers


drift

EmeEv

eed

τμ 0==

Townsend‘s coefficient


Pieter van Musschenbroek (1692-1761)Leiden jar‘s


Streamers

FunkenentladungElektrischer Durchschlag

in Luft: E ~ 30 kV/cm


streamers

presence of at least one dielectric in the discharge space

3.1. Gas Discharge Plasmasmicro discharges : DBD

• thin cylindrical weakly ionized plasma columns, ∅ ≈ 200 μm• electron densities: 1014 … 1015 cm-3

• duration: 1 .. 10 ns• non-equilibrium plasmas (Te >> Tgas) ⇒ well suited for initiation of

plasma-chemical reactions

Microdischarges of short duration


micro discharges : DBD

electric breakdown


multiplication of charge carriers


ignition of discharge

Paschen‘s law


Paschen‘s law


surfacegas

breakdown voltage depends on pressure, distance and gas

Paschen‘s law


Johann W. Hittorf (1824-1914)

3.2. Stationary Gas Discharges

Townsend discharge



glow discharge


glow discharge


glow discharge


hollow cathode discharge

• cylindric cathode,

ring shaped anode

(at positive potential)

• merging of of glow edge

• „ideal plasma“: only negative glow

• oscillation of electrons increase of

ionization and dissociation

• hollow cathode effect

E

x

E

r


micro hollow cathode discharge

glow discharge


principle of dc cathode sputtering,diode system

a gas flowb pumpc cathoded targete anodef deposited layerg cathode fallh positive columnI screening, shield

diode system (E)

magnetron system (E X B)

influence of magnetic field


magnetron discharge

capacitively-coupled plasma

~ rf

ωpi ωωpe

rf domainMHz GHz

13.56 MHz

• Capacitive discharges are used in etching and deposition

• Radiofrequency domain is such that electrons follow the rf field wile ions follow time-averaged field

• Ionization degree is small (<0.001)

• Gas pressure is low (a few Pa); collisionless heating is often dominant

rf discharge


rf discharge : CCP, ICP


rf discharge : CCP, ICP


PPR

symmetric, asymmetric

plasma jet

rf discharge : CCP


• plasma excitation by an electric fieldgenerated by the transformer principle

• changing magnetic field of the conductorinduces an electric field in which the electronsare accelerated

• high plasma density

rf discharge : ICP


arc discharge


plasma welding and cutting

arc discharge


Coulomb-dominated

plasmas

„reactive“neutral-

dominatedplasmas

focus

torch

highpressure

lampsMHD

hollow cathode

pseudo sparksECR

heliconelectron beam arcs

ICP

arcs

DBE

PDP

corona

Magnetron

microwavesurfacewaveCCP

low-pressure lamps

positive column

dc cathode sputtering

1012 1014 1016 1018

0.01 1 100 10k pressure p0 (Pa)

gas density N0 (cm-3)

plasma sources at different gas and charge carrier densitiesnon-idealplasmas

thermal plasmas

108

1010

1012

1014

1016

1018

char

geca

rrier

dens

ities

n e, i(

cm-3

)

electron energydistribution:

non-maxwellian

ideal weaklyionized,

non-isothermalplasmas

n e, i= N 0


3.3. Plasma Surface Interaction

role of charge carriers in plasma :

• occurrence of electrical conductivity• screening of electric fields• occurrence of oscillations and waves, and corresponding instabilities• interaction with magnetic fields• formation of characteristic boundary sheaths due to contact with walls

characteristic dimensions / time constants :

Debye length λD is the shielding length for the long range Coulombinteraction. It is the distance over which thermal motion causessignificant deviations from quasi-neutrality

The plasma frequency ωP is critical for the propagation of electromagnetic waves in plasmas (supply of energy).

3.3. Plasma Surface Interactionplasma bulk

plasma in contact with floating wall:

floating potential Vfl

µe >> µi

sheath formation:

sheath potential:

wall charges up until ion flux equals electron flux⇒

or for additional Vs, then : Vbias = Vs - Vpl

evnevn eejje

iij ===

4 4

)/)((exp TVVnn eflplie ke −−=

)/ln(2 mmkTVVV

eie

plflbias−=−=

gas flow

Plasma potential Vpl

plasma

pump out

V

3.3. Plasma Surface Interactionplasma boundary sheath

potential and charge carrier density for a typical glow discharge


plasma boundary sheath

Rp Rstoc

collisionless power dissipation in the sheath






Uev2

m 2e ⋅=⋅+e-

h n

E

Rudolf SeeligerUniversität Greifswald1918 -1955

Gehrcke-Seeliger-Demo.exe








plasma boundary sheath : Child-Langmuir

• electrons are repelledion matrix sheath

• ions are attractedexpanding sheath

• energetic ions arrive at substrate• stationary sheath position may be reached if

ω pl,e−1 = ε0 me e2 ne( )1 2

ω pl,i−1 = ε0 mi e2 ni( )1 2

ion current in plasmaspace-charge limited current

(Child current for given voltage and actual sheath thickness)

=

Negative voltage pulse applied:



• The transition zone between bulk plasma and a surface, the the SHEATH, is fundamental in plasmaSHEATH, is fundamental in plasma--surface interaction, plasmasurface interaction, plasma--assisted deposition of films, and ion extraction in ion sources.assisted deposition of films, and ion extraction in ion sources.

• Child Law (1911):

• Can be interpreted as – limited current density, j, for given distance, d, or–– adjusting sheathadjusting sheath thickness for given current density and

voltage.

2

230

212

94

dmQej wall

ii

φε⎟⎟⎠

⎞⎜⎜⎝

⎛=



( )

2c c

2Ebeje

2e

j e

jn and e-

j e

jnth wi

21

002

01

00

e0

e

0

02

2

00

i

0

ii

0

e

0

ee

0

02

2

Vc

Ec

dxdE

emj

bj

dxdE

mVe

jdx

Vd

mVevEbv

nnedxdE

dxVd

ii

e

e

i

i

i

ieeie

+=

==−=

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

+−=

====−=−=

εεε

ε

ε

( ) ( ) ( ) ( ) ( )

2

21

21

2122

)(

)(

21

21

)(

)(

2

21

21

221

21

2

dxdV

42xE

E

42

221 2

21

⎟⎠⎞

⎜⎝⎛

↑↑

⎟⎠⎞

⎜⎝⎛ −+−=−

↑

⎥⎦

⎤⎢⎣

⎡+=

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+=

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛+=

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛

∫ ∫∫

ccc

x

d

xV

dV

xE

dE

dVxVcdxcdE

VdcdxcdxdVd

VdcdxcdxdVdV

dxdcc

dxdV

dxd

c cc

≈ 0E(x) ... )E(d :E

V(x)... ) V(d:V

x ... d :x

c

c

c

X 0 dc

V(dc)

E(dc)

integration limits ?


( ) ( ) ( ) 4221

221

21 ⎟⎠⎞

⎜⎝⎛ +⎟

⎠⎞

⎜⎝⎛+−=⇒ cc dExVcdxc

dxdV

0j mm j 121e

i

ei ≈⇒<<⇒>> ccc

( ) ( )

( ) ( )

( ) 0dV

4

4

2

21

c

21

221

2

21

221

2

≈

↑

⎟⎠⎞

⎜⎝⎛ +⎟

⎠⎞

⎜⎝⎛=

⎟⎠⎞

⎜⎝⎛ +⎟

⎠⎞

⎜⎝⎛≈

c

c

c

d

dxdExVcdV

dExVcdxdV

if sheath determined by positive space charges, then :

( )( )

iicc

ccc

V

d

mje

Vd

Vc

ddccV

dxcxV

dVdxxVcdVc

c

0023

2

23

2

224

3

0

0

241

41

2

294

1942

34

2 2

ε=

=⇒−=

=≈ ∫ ∫

294 0

202

3

2

ii

cc m

ej

Vd ε=

( )

( )sh

ci

mpfc

dd

xVme

dPap

~d 29

4j

10

c2

23

21

00⎟⎟⎠

⎞⎜⎜⎝

⎛=

≥↔≤

ε

λ


V0 = Vc

S = dc




trench-to-sheath size is crucial for conformal treatment



not to scale


plasma boundary sheath : magnetron

Argon, 0.005mbar, 10W 30W 50W

Argon, 50W 0.005mbar 0.01mbar

... andepends on discharge power and pressure


10Pa 3Pa

2 4 6 8 10 120

2

4

6

8

10

12

14

16

18

20

H2 0.25μm H2 1μm He 0.25μm He 1μm Ne 0.25μm Ne 1μm O2 0.25μm O2 1μm N2 0.25μm N2 1μm Ar 0.25μm Ar 1μm

h [m

m]

p [Pa]


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

sb(t)

sa(t)

EzEz

3.3. Plasma Surface Interactionplasma boundary sheath : Bohm

( )Sdxx sh === ... 0

sheath

no ionization in the sheath

continuity equation of ions:

conservation of energy:

vi(x) between 0 and dsh:

Boltzmann :

Poisson-equation :

( ) ( ) ( ) ( )0,0 iiii vnxvxn =

( ) 0 x 210;

21

02 =+= plii VekTvm ( )

i

plipli m

VevVekT 0

0

20 =⇒<<

( ) ( )( )i

pli m

xVVexv

−= 02 ( ) ( )( )

( ) ( ) ( )xVVV

nxn

mVe

nm

xVVexn

pl

plii

i

pli

i

pli

−=

=−

0

2)0(

2 00

( ) ( )[ ] ( )( )

( )

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−⎟

⎟⎠

⎞⎜⎜⎝

⎛

−−=⇒−−= ekT

xVe

pl

pleei e

xVVVne

dxVdxnxne

dxVd 02

1

0

02

2

0

02

2 0εε

( ) ( )( )e

okT

xVe

ee enxn 0=

plasma boundary sheath : Bohm

( ) ( ) ( ) ( )

⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

⎥⎥⎦

⎤

⎢⎢⎣

⎡−+

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−⎟

⎟⎠

⎞⎜⎜⎝

⎛−= 111202 0

0

21

0

02 ekTxVe

e

plpl

e eekT

VxVVnexE

ε

( )

( ) ( ) ??? e and xV 2

1e and 81

2111

0

2x22

1

epl kTxVVfor

xxxxx

<<<<

++≈−−≈−

( ) ( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( ) ( )

( ) ( ) ( )

⇒≥

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

−≈

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

++−−≈

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎟⎟⎠

⎞⎜⎜⎝

⎛−+++⎟

⎟⎠

⎞⎜⎜⎝

⎛−−−≈

ple

ple

e

epl

e

ee

e

plplpl

e

VhTe

VkTexVnexE

kTxVexV

VxVxVnexE

TkxVe

kTxVe

ekT

VxV

VxVVnexE

21

210

2410

12

1181

211202

0

0

0

202

20

2

0

02

22

2200

02

2

0

02

ε

ε

ε

with

in order to have a real solution, it must

Bohm criterion

0 21 epl kTVe ≥

plasma boundary sheath : Bohm

p = 2.4Pa

p = 0.5Pa

ion energy [eV]

inte

nsity

[cps

]

0 50 100 150 200 250 300

Ar, p=5Pa, Vrf=520Vpp

ArH+

Inte

nsity

(a.

u.)

Ion Energy (eV)ion energy [eV]

inte

nsity

[a.u

.]

Ar, p = 5Pa, Vrf= 520Vpp

Vpl

VS

VshIEDF


0 5 10 15 20 25 30

0,000

0,001

0,002

0,003

0,004

0,005

0,006

0,007

Ar, 0.7Pa

300W 200W 100W 50W

sign

al [A

/Vcm

2 ]

ion energy [eV]

0 5 10 15 20 25 30 35 40

0,000

0,002

0,004

0,006

0,008

0,010

0,012

0,014

Ar, 300W

sign

al [A

/Vcm

2 ]

ion energy [eV]

0.35Pa

0.7Pa

2Pa

4.7Pa

7Pa

IEDF : dependence on powerintensity

IEDF : dependence on pressureintensity, mean energy


chemistry in bulk plasma provides etch speciesphysics provides ions and e- chemical

etching

desorption of etch products

physical sputtering

etchspecies etch rate

selectivity

homogeneityphysics in space charge sheaths

activation energy

ionic current

ion energyand current

3.3. Plasma Surface Interactionplasma boundary sheath : etching

References

Documents

Fundamentals of Plasma Physics IIIppst-2007.physik.uni-greifswald.de/fundamentals_3.pdf · • The transition zone between bulk plasma and a surface, the SHEATH, is fundamental in