capacitive discharges driven by combined dc/rf sourceslieber/liebermandcrfgec07crop.… · •...

University of California, Berkeley PLASMA

CAPACITIVE DISCHARGES DRIVEN BYCOMBINED DC/RF SOURCES

Emi Kawamura, M.A. Lieberman, and A.J. Lichtenberg

Department of Electrical Engineering and Computer SciencesUniversity of California

Berkeley, CA 94720

E.A. Hudson

Lam Research CorporationFremont, CA 94538

Download this talk:

http://www.eecs.berkeley.edu/∼lieber

LiebermanDublin07 1


MOTIVATIONS FOR ADDING DC SOURCE

• “Tune” discharge particle and energy balance(⇒ Te ↓, ne ↑, radial uniformity)

• “Tune” secondary electron bombardment of substrate(etch selectivities, charging damage)

OUTLINE

• Structure of DC/RF sheaths — theory

• Equal area diode discharges — theory and 1D PIC simulations

• Asymmetric diode discharges — theory and 1D PIC simulations

• Secondary electrons — timescales and energy deposition

• Triode discharges — theory and 2D PIC simulations

LiebermanDublin07 2


STRUCTURE OF A DC/RF SHEATH

Vdc

Vrf

–

+

~ ss0 s1

V1V0

V0~

V1~

Bulkplasma

+–+–

ADCpart

RFpart

ni

ne(t)z

n

Ji– DC voltage V = V 0 + V 1

RF voltage Ṽ = Ṽ0 + Ṽ1

• New result for Child law for collisionless ions:

J̄i =4

9ǫ0

(2e

M

)1/2 (V 1/2 − 13V

1/2

1 )(V1/2

+ 23V

1/2

1 )2

s2

• New result for Child law for collisional ion sheath also obtained

LiebermanDublin07 3


EQUAL AREA DIODE DISCHARGE

• Comparison of theory with 1D particle-in-cell (PIC) simulations

Vdc

Vrf

–

+

~ ss0 s1

V1V0

V0~

V1~

Bulkplasma

++ ––+–

DC/RF sheath RFsheath

A

V1~

V1 A

s1

0 0.5 1 1.5 2

V /V

0

0.1

0.2

0.3

0.4

0.5

V /V

45

100

60 45

10060

45

15

45

60

100

4MHz, γ = 0.24MHz, no sec.

13MHz, no sec.

Collisionless

Collisional, β 0

Collisional, β = 0.1

a1

rf

∼

dc rf

i

(Symbols: PIC with argon pressure in mTorr;

lines: theory; β ∝ λD/λi = collisionality;

γi = secondary emission coefficient)

• Excellent agreement of PIC with collisional Child law

LiebermanDublin07 4


DENSITY AND VOLTAGE AT CONSTANT Prf(60 mTorr, 6 cm gap, 4 MHz, 0.017 W/cm2, Vdc = 350 V)

0 0.01 0.02 0.03 0.04 0.05 0.06

x (m)

0

2e+15

4e+15

6e+15

n (m

)

..

rf (γ =0)dc + rf (γ = 0)rf (γ =0.2)dc + rf (γ =0.2)

(a)

i

i

rf sheath "b" dc/rf sheath "a"

sb

nb

i

i

e-3

−

0 0.01 0.02 0.03 0.04 0.05 0.06

x (m)

-200

0

200

400

600

V (V

)

rf (γ = 0)dc + rf (γ = 0)rf (γ =0.2)dc + rf (γ =0.2)

i

i

rf sheath "b" dc/rf sheath "a"

i

i

(b)

_p

AddDC

γi Vrf (V) V b (V) Eceff (V)

Rf only 0 1064 436 64Dc+rf 0 1277 398 60Rf only 0.2 805 330 53Dc+rf 0.2 980 283 46

(V b = plasma potential; Eceff =collisional energy loss/electron-ion pair)

• Plasma potential V b and sheath width sb independent of Vdc• Secondary electrons increase discharge efficiency• Vdc reduces bulk plasma thickness

LiebermanDublin07 5


ASYMMETRIC DIODE RESULTS

• Excellent agreement between1D (cylindrical) PIC andcollisional CL theory

Vdc

Vrf

–

+

~ sasa0 sa1

sb

Va1Va0

Va0~

Va1~

Vb~

Bulkplasma

++ ––+– Vb

DC/RF sheath RFsheath

Aa Ab

• Introduce rf voltage asymmetry ratio αab = Ṽa1/Ṽb

-0.5 0 0.5 1 1.5 2

V /V

0

0.2

0.4

0.6

0.8

1

V /

V

15(0.093)

45(2.2)

45(0.46) 45(0.48)

45(0.48)

45(0.15)

45(0.15)

45(0.1)

45(0.13)

50(0.34)

45(0.14)

50(0.38)

ab

4MHz, γ = 0.232MHz, no sec.

6.78MHz, no sec.

0.1

α =10

0.15

0.3

0.5

1.02.0

brf

dc rf

i

∼

(a)

-0.5 0 0.5 1 1.5 2

V /V

0

0.2

0.4

0.6

0.8

1

s /

s 0.1

α =10

0.15

0.3

0.51.0

2.0

15(0.093)

45(2.2)

45(0.46)

45(0.48)

45(0.48)45(0.15)

45(0.15)

45(0.1)45(0.13)

50(0.34)

45(0.14)

50(0.38)

ab 4MHz, γ = 0.232MHz, no sec.

6.78MHz, no sec.

a1

a

dc rf

i

(b)

Numbers near each symbol: mTorr (αab)

LiebermanDublin07 6


SECONDARY ELECTRON LOSS PROCESSES

• Surface losses to substrate and walls:

— Transit time across gap τfr = d/vh at low pressures

— Diffusion time τdiff = d2/2Dh at higher pressures (Dh = λhv̄h/3)

— Trapping time τtrap = δ/f (favorable configuration of rf voltagescan trap secondaries for a fraction δ of the rf period 1/f)

τlh = (τ2fr + τ

2diff + τ

2trap)

1/2 = ν−1lh

• Volume losses: secondary electrons lose energy and join the thermalpopulation

τ∗izh =Eh

νizhEch(Eh, νizh are secondary energy and ionization frequency;

Ech ≈ 20 V is secondary collisional energy loss/e-i pair created)

• Total loss frequency is νh = νlh + ν∗

izh

If ν∗izh ≫ νlh, secondary electrons efficiently produce e-i pairsIf νlh ≫ ν

∗

izh, secondary electrons efficiently bombard the substrateLiebermanDublin07 7


ENERGY DEPOSITION REGIONS

10-2

10-1

100

101

102

d/λ

10-3

10-2

10-1

100

101

fd/v

= 70 V, δ = 0.5

h

h

τ = τ

τ =

τ

τ =

τ

τ =

τ

τ =

τ

fr

τ = τ

trap

trap

izh*

trap

diff

dif

ffr

dif

f

fr

*

*

izh

εh

izh

No energydeposition

Trapped anduntrapped

energydeposition

Trappeddepositionuntrapped

diffusion

Trap

ped

depo

sitio

n

untra

pped

flow

(τ , τ , τ < τ )fr trapdiff izh* (τ > τ )diff

*izh

(τ > τ )trap izh*

τ > τ τ > τ diff frfr diff

τ , τ < τ izhfr diff *

Example

pressure

freq

uenc

y

• Most interesting regions are where trapped and untrapped electronsbehave differently

LiebermanDublin07 8


TRIODE DC/RF DISCHARGE

• Substrate can have a dielectric layer which cannot draw dc current

A triode configuration is necessary

Vdc Vrf

–

+

~sasa0 sa1

sb

Va1Va0

Va0~

Va1~

Vb~

Bulkplasma

++ ––+– Vb

DC/RF sheathRF

sheath

Aa Ab

sg Vg~

+

–Vg

Ag

Substrate

DCcurrent

• A global model incorporating the collisional dc/rf sheath is used todetermine the voltages, currents, and sheath widths

LiebermanDublin07 9


TRIODE RF PLASMA POTENTIAL Ṽb VERSUS Vdc

• Collisional theory results for triode

0.01 0.1 1 10

V /V

0

0.2

0.4

0.6

0.8

V /

V

A /A =0.5, A /A =0.5A /A =1.0, A /A =0.5A /A =0.5, A /A =1.0

dc rf

brf

∼

a c b c

ca b c

a c b c

• Example (red solid line):

DC electrode area = ground electrode area = 12× RF electrode area

For Vdc → 0, equal area diode and Ṽb/Vrf = 0.5

For Vdc → ∞, asymmetric diode and Ṽb/Vrf = 0.86.LiebermanDublin07 10


2D PIC SIMULATION BASE CASE

• p = 30 mTorr, Prf = 2.2 W, γi = 0.2 at all surfaces

• Secondaries in “trapped deposition, untrapped diffusion” regime

1.6

cm

CB

ArPlasma

30 mT

3 cm

9 cm

Vrf13.56 MHz

345 V

14

cm

1.6

cm

CB

+

_

ArPlasma

30 mT

3 cm9

cm

VrfVdc

200 V

13.56 MHz

285 V

14

cm

1.6

cm

1.6

cm

RF only DC/RF triode

x

y

LiebermanDublin07 11


UNIFORMITY IS MODIFIED BY Vdc

0 0.02

0.04 0.06

0.08 0.1

0.12

y (m) 0

0.01

0.02

0.03

x (m)

0

2e+15

4e+15

6e+15

8e+15

0 0.02

0.04 0.06

0.08 0.1

0.12

y (m) 0

0.01

0.02

0.03

x (m)

0

2e+15

4e+15

6e+15

8e+15

0 0.02

0.04 0.06

0.08 0.1

0.12

y (m) 0

0.01

0.02

0.03

x (m)

0

2e+11

4e+11

6e+11

8e+11

1e+12

1.2e+12

0 0.02

0.04 0.06

0.08 0.1

0.12

y (m) 0

0.01

0.02

0.03

x (m)

0

2e+11

4e+11

6e+11

8e+11

1e+12

1.2e+12

1.4e+12

Dc/rfRf only

Plasma

density

(m-3)

Secondary

density

(m-3)

• Thinner bulk plasma near midplane (y = 0.06 m) for DC/RF case

⇒ center-low plasma density profile



BALLISTIC SECONDARY ELECTRONS CREATED BY Vdc

0 0.02

0.04 0.06

0.08 0.1

0.12y (m) 100

200 300

400

ε (V)

0

1e+11

2e+11

3e+11

4e+11

0 0.02

0.04 0.06

0.08 0.1

0.12y (m) 100

200 300

400

ε (V)

0

2e+11

4e+11

6e+11

0 0.02

0.04 0.06

0.08 0.1

0.12y (m) 0.4

0.8 1.2

1.6

θ (rad.)

0

1e+11

2e+11

3e+11

4e+11

5e+11

6e+11

0 0.02

0.04 0.06

0.08 0.1

0.12y (m) 0.4

0.8 1.2

1.6

θ (rad.)

0

1e+12

2e+12

3e+12

4e+12

Dc/rf

ballistic

highenergy

Rf only

Secondary

energy

distribution

(arb units)

Secondary

angular

distribution

(arb units)

• Secondary electrons are ballistic and have high energies for DC/RFcase



PLASMA DENSITY PROFILES VERSUS PRESSURE

0 0.02

0.04 0.06

0.08 0.1

0.12

y (m) 0

0.01

0.02

0.03

x (m)

0

2e+15

4e+15

6e+15

8e+15

0 0.02

0.04 0.06

0.08 0.1

0.12

y (m) 0

0.01

0.02

0.03

x (m)

0

2e+15

4e+15

6e+15

8e+15

Dc/rfRf only

30 mTorr

0 0.02

0.04 0.06

0.08 0.1

0.12

y (m) 0

0.01

0.02

0.03

x (m)

0

2e+15

4e+15

6e+15

8e+15

1e+16

0 0.02

0.04 0.06

0.08 0.1

0.12

y (m) 0

0.01

0.02

0.03

x (m)

0

2e+15

4e+15

6e+15

8e+15

1e+16

1.2e+16

1.4e+16

1.6e+16

45 mTorr

• Effects of Vdc on profile:Thinner bulk plasma ⇒ center-low profileIncreased secondary ionization ⇒ center-high profile



CONCLUSIONS

• Collisionless and collisional DC/RF Child laws determined

• DC voltage can control the discharge asymmetry

• DC voltage increases secondary electron ionization

• DC voltage reduces bulk plasma thickness

• DC voltage promotes the formation of ballistic electrons

• DC voltage modifies the plasma density profile

Download this talk:

http://www.eecs.berkeley.edu/∼lieber

Ref: E. Kawamura, M.A. Lieberman, and A.J. Lichtenberg, “Capacitive DischargesDriven by Combined DC/RF Sources”, J. Vac. Sci. Technol. A, 25, 1456–74,Sept. 2007


capacitive discharges driven by combined dc/rf sourceslieber/liebermandcrfgec07crop.… · •...

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