200 7. 5. 2

2007. 5. 2

Low-Pressure Capacitive RF DischargesLow-Pressure Capacitive RF Discharges

Hyun-Chul Kim*

* [email protected]

Plasma Processing (EECE654)

Substitute Lecture

Many slides in this lecture are based onProf. Lieberman’s Presentation Material(http://www.eecs.berkeley.edu/~lieber/#talks).

Plasma Reactors for Plasma ProcessingPlasma Reactors for Plasma Processing

Plasma Processing for Semiconductor Device Fabrication

• Integrated Circuit Cross Section• Integrated Circuit Cross Section

There are up to 10 layers, mostly interconnects (metal + dielectric).

Typical Processing Discharges

• Capacitive Discharges (L&L Chap. 11)

• Capacitive Discharges (L&L Chap. 11)

• Wave-Heated Discharges (L&L Chap. 13)

• Wave-Heated Discharges (L&L Chap. 13)

• Inductive Discharges (L&L Chap. 12)

• Inductive Discharges (L&L Chap. 12)

ions, radicals, electrons, photons

Evolution of Etching Discharges

1st Generation1st Generation

2nd Generation2nd Generation

Evolution of Etching Discharges (Cont’d)

3rd Generation3rd Generation

Hardware Simplicity Low cost Robust uniformity over large area Control of dissociation (F-atoms)

High plasma density Independent control of the ion/radical fluxes (through the source power) and the ion-bombarding energy (through the substrate electrode power)

• Capacitive Discharges• Capacitive Discharges • Inductive Discharges• Inductive Discharges

Inductive vs. Capacitive RF Discharges

++

+

+

+ +–

–

–

– –

– –+

+–+

~

Sheath

Sheath

)cos( tJ ll

~ )cos( tJ hh

Dual-Frequency CCP Reactor

Bulk Plasma

Substrate

Low density Low etch rate No independent control of ion flux and bombardment energy

Dual-Frequency (DF) CCP

MHz 2 MHz, 27 i.e. lh ff

• Drawbacks of single-frequency (SF) capacitively coupled plasma (CCP)

• Drawbacks of single-frequency (SF) capacitively coupled plasma (CCP)

→ Critical application for dielectric etch

ions

Electron Heating MechanismsElectron Heating Mechanisms

Discharge Sustainment

Electron generation mechanisms

• Electron-impact ionization in the volume - ionization collisions between electrons and the background gas

- -+

-

probabilistic event

• Another emission mechanisms: thermionic emission, photo emission, field emission, explosive emission, and so on.

• Secondary electron emission (SEE) on a surface - particle (ions, electrons) impact to a material

-

probabilistic event

++

thie ,

(eV) ethi.

+

Energy Transfer from External Energy Source to Plasma

[Ref] Y.P. Raizer, Gas Discharge Physics, Springer-Verlag, Berlin (1991)

(a) Inductively Coupled (or H-Type) Plasma

– Sustained by the solenoidal (directed along the plasma boundary) electric field

induced by a time-varying magnetic field

– Electrodeless

(b, c) Capacitively Coupled (or E-Type) Plasma

– Sustained by longitudinal (directed perpendicular to the boundary) electric field

– (b) Voltage applied to electrodes in contact with plasma

– (c) Electrodes insulated from plasma (electrodeless)

Electron Heating Mechanisms

Ohmic Heating (collisional heating) – capacitive, inductive discharges• Heating by energy gain from the electric field between collisions

with neutrals• Dominant in the bulk at high pressure

Stochastic Heating (collisionless heating) – capacitive, inductive

discharges• Heating by interaction with oscillating sheaths• Dominant in the sheath at low pressure

Resonant Wave-Particle Interaction Heating - electron cyclotron

resonance and helicon discharges

How is the field energy converted to electron thermal energy?

Ohmic Heating in RF E-fields The motion of an electron in Oscillating Fields ( )

• Free oscillations (the motion of a single electron without collisions)

0 vEe

00 const ,)sin( EtEE

00

0 )cos()sin( vE

vEv tm

etem

-

E

• In the presence of collisions : breaking the phase-coherent motion

mEmmm

Eee

)(2 22

20

2

vE

mmtem vEv )sin(0-

E

An electron has a coherent velocity of motion that lags the phase of the electric field force by 90°. → No electron heating on the average.

An electron has a coherent velocity of motion that lags the phase of the electric field force by 90°. → No electron heating on the average.

Electron collisions with other particles destroy the phase coherence of the motion (phase randomization), leading to a net transfer of power. The field does work on overcoming the friction due to collisions of the electron.

Electron collisions with other particles destroy the phase coherence of the motion (phase randomization), leading to a net transfer of power. The field does work on overcoming the friction due to collisions of the electron.

Stochastic Heating (Collisionless Heating)

A spatially nonuniform electric field by itself might lead to electron

heating, even in the absence of interparticle collision, provided that the

electrons have thermal velocities sufficient to sample the field

inhomogeneity.

A spatially nonuniform electric field by itself might lead to electron

heating, even in the absence of interparticle collision, provided that the

electrons have thermal velocities sufficient to sample the field

inhomogeneity.

- In the nonlocal regime, the time-varying field seen by an individual thermal electron is nonperiodic. The electron loses phase coherence with the field, resulting in stochastic interaction with the field and collisionless heating.

Stochastic heating mechanism in CCPs - Fermi acceleration* “Hard wall” model for stochastic heating (after Godyak) - An electron’s interaction with sheath potential barrier is approximated as a test particle colliding elastically with a moving wall.

Stochastic heating mechanism in CCPs - Fermi acceleration* “Hard wall” model for stochastic heating (after Godyak) - An electron’s interaction with sheath potential barrier is approximated as a test particle colliding elastically with a moving wall.

• Stochastic heating in Capacitive discharges• Stochastic heating in Capacitive discharges

* M.A. Lieberman and V.A. Godyak, IEEE Trans. Plasma Sci. 26, 955 (1998)

Fermi Acceleration

Stochastic Heating for Homogeneous Model

)cos(v)(v 0 tt ss

v

v

)(v ts

, H

Stochastic Heating for Inhomogeneous Model

[Ref] E. Kawamura et al., Phys. Plasmas 13, 053506 (2006)

H

Experimental Evidence for Stochastic Heating

Analytic Model for Capacitive Discharges

Analytic Model for Capacitive Discharges

L&L Chap. 11.1

++

+

+

+ +–

–

–

– –

– –+

+–+

~

Sheath

Sheath

)cos(0 tV

• 1D RF Voltage-Driven System

• 1D RF Voltage-Driven System

Bulk Plasma

Substrate

X direction

Potential

Density of : Electron and Ion

Animation from Fluid Simulation Result

ei nn

const),( ntrni

0en

Chap. 11.1 Homogeneous Model

)( , 0

)( , 0

tsx

tsxen

x

E

a

a

t

txEJtJ drf

),()( 0

)sin(0 tsssa

Matrix sheath

This is “unrealistic” model but gives a considerable insight into the qualitative behavior of “real” capacitive discharges.

This is “unrealistic” model but gives a considerable insight into the qualitative behavior of “real” capacitive discharges.

)cos()( 1 tJtJ rf

Chap. 11. 1 Homogeneous Model

Chap. 11. 1 Homogeneous Model

Chap. 11. 1 Homogeneous Model

• Spatial potential distribution as a function of rf phase

• Spatial potential distribution as a function of rf phase

Chap. 11. 1 Homogeneous Model

Analysis of Discharge Equilibrium Analysis of Discharge Equilibrium

Production due to ionization = Loss to the walls

Power in = Power out

Juude

mP ecBeme

2/1

)()2(

J

ue

udmn

ecB

em

2/1

3 )(

)2(

2

1

VV8

3

2

028

3

f

JuP B

i

Summary Summary

Chap. 11. 1 Inhomogeneous Model

Child Law sheath

Nonlocal Electron KineticsNonlocal Electron Kinetics

Local or NonLocal Election Kinetics

))(,(),v2

1( 2 rEWfrmWf

• EEDF in the local regime ( ) : Equilibrium with the local electric field

• EEDF in the local regime ( ) : Equilibrium with the local electric field

L

At high pressures, the EEDF at a given point depends only on local conditions at that point.

At high pressures, the EEDF at a given point depends only on local conditions at that point.

At low pressures, the EEDF as a function of total energy does not explicitly depends on the spatial position.

At low pressures, the EEDF as a function of total energy does not explicitly depends on the spatial position.

Distance

Ionization rate

Power

Distance

Ionization rate

Power• EEDF in the nonlocal regime ( ) : Non-equilibrium with the local electric field : Spatially uniform distribution of total energy of electrons

• EEDF in the nonlocal regime ( ) : Non-equilibrium with the local electric field : Spatially uniform distribution of total energy of electrons

L

))((),( reWfrWf

• Nonlocal electron kinetics is taken into account in 1. Kinetic Theory (L&L Chap. 18) (but not in Fluid Theory) 2. Particle Simulation

• Nonlocal electron kinetics is taken into account in 1. Kinetic Theory (L&L Chap. 18) (but not in Fluid Theory) 2. Particle Simulation

The slow electrons with are trapped inside the bulk by the potential

well formed by the ambipolar potential. The accessible volume of the electrons depends on their energies. The EDF of trapped electrons is a function of the total energy only and does

not depend explicitly on the coordinates. The whole available discharge volume

contributes to the EDF formation. The fast electrons with can reach the sheath where the rf field

is large and thus much more effectively heated.

The slow electrons with are trapped inside the bulk by the potential

well formed by the ambipolar potential. The accessible volume of the electrons depends on their energies. The EDF of trapped electrons is a function of the total energy only and does

not depend explicitly on the coordinates. The whole available discharge volume

contributes to the EDF formation. The fast electrons with can reach the sheath where the rf field

is large and thus much more effectively heated.

[Ref] V.I. Kolobov et al., IEEE Trans. Plasma Sci., 23, 503 (1995)

Sheath Bulk• Nonlocal concept was Bernstein and Holstein (1950’s) and has been much developed by Tsendin.

we

we

Nonlocal Electron Kinetics in CCPs (I)

cm 2 d

2d

Local:2

Nonlocal:2

d

d

In the typical condition of low-pressure rf discharges, EEDF is in nonlocal regime.

In the typical condition of low-pressure rf discharges, EEDF is in nonlocal regime.

cm) 2 (i.e.Length Plasma :

Pressure Gas Neutral :

Path FreeMean Electron :

Length RelaxationEnergy :

d

pe

Nonlocal Electron Kinetics in CCPs (II)

Ref: V.A. Godyak et al., Phys. Rev. Lett. 65, 996 (1990) I.D. Kaganovich et al., IEEE Trans. Plasma Sci., 20, 66 (1992) U. Buddemeier, Appl. Phys. Lett. 67, 191 (1995)

• Comparison of measured and calculated EDFs for argon at 68.4 mTorr

• Calculation of 1D spatially averaged kinetic model

(nonlocal approximation)– hom. field: spatially homogeneous rf field

without sheath heating (only Ramsauer effect)– = 0 : spatially inhomogeneous rf field without stochastic heating

– > 0 : spatially inhomogeneous rf field with stochastic heating

The concave EDFs can be due to a combination of various effects – the sheath heating, the spatially inhomogenous field, and the Ramsauer effect.

The concave EDFs can be due to a combination of various effects – the sheath heating, the spatially inhomogenous field, and the Ramsauer effect.

• Investigation of EEDF shape

• Investigation of EEDF shape

As the spatial inhomogeneity of the rf field increases, high-energy electrons are more heated than low-energy electrons and hence EEDF becomes bi-Maxwellian.

As the spatial inhomogeneity of the rf field increases, high-energy electrons are more heated than low-energy electrons and hence EEDF becomes bi-Maxwellian.

Nonlocal Electron Kinetics in CCPs (III)

Measured atx = 0.0 (solid), 7.5, 13.4, 19.6, 22.5 mm

Measure atx = 0.0 (solid), 13.4, 25, 28.7 mm

p = 0.03 Torr p = 0.3 Torr

[Ref] V.A. Godyak et al., Appl. Phys. Lett. 63, 3138 (1993)

cm 0.3cm 20 dldh cm 5.0cm 8.2 dl

• Investigation of spatial profile of Te from EEDF measurement

• Investigation of spatial profile of Te from EEDF measurement

The spatially resolved EDF of kinetic energy is found by a simple truncation from the EDF of total energy.

The spatially resolved EDF of kinetic energy is found by a simple truncation from the EDF of total energy.

Nonlocal Electron Kinetics in CCPs (IV)

Transition in Capacitively Coupled Plasma

V.A. Godyak et al., “Abnormally low electron energy and heating mode transition in a low-pressure argon RF discharge at 13.56 MHz”, Phys. Rev. Lett. 65, 996 (1990).

Godyak’s interpretation: Low-energy group at low pressures is attributed to the combined effect of the stochastic heating and the Ramsauer minimum of argon.

Godyak’s interpretation: Low-energy group at low pressures is attributed to the combined effect of the stochastic heating and the Ramsauer minimum of argon.

Kaganovich’s interpretation*: the strongly inhomogeneous rf field together with the effects of nonlocality can lead to strong low-energy group, even without accounting for the stochastic heating. (local at high pres. → nonlocal at low pres.)

Kaganovich’s interpretation*: the strongly inhomogeneous rf field together with the effects of nonlocality can lead to strong low-energy group, even without accounting for the stochastic heating. (local at high pres. → nonlocal at low pres.)

* I.D. Kaganovich and L.D. Tsendin, IEEE Trans. Plasma Sci. 20, 66 (1992).

Pressure (Torr)

Plasma Conductivity

Ohm’s Law in local regime (where fluid theory is based)

)()()( xExxJ e

)()(

2

jm

enx

e

ee

).),((both on dependent are )',(: men

dd

df

jm

enx

m

ee

0

5.12

)(3

2)(

)'(

2

jm

en

en

e

for constme

• Classical Definition of Conductivity (Maxwellian EEDF)

• Conductivity for a non-Maxwellian EEDF given by kinetic theory

)( mm

: Collision Freq. for Momentum Transfer

Nonlocal Conductivity

L

x

xe xdxExxGxdxExxG

e

m

m

nexJ )(),()(),(

22)(

0

2

Current Density in the non-local limit for a non-Maxwellian EEDF(Kinetic Theory)

)()(

2

xEjm

en

effeff

e

).,(by replaced is )',(: effeffen

Under the nonlocality condition, generalized ohm’s law with two effective frequencies can be considered.

Under the nonlocality condition, generalized ohm’s law with two effective frequencies can be considered.

effenm general,In

effwww '1. Shape of EEDF (non-Maxwellian) or Dependence of Collision Freq. on Energy

2. Non-Locality or Collisionless Heating

1 2

Plasma Properties

)cos(

))()(Re()( *

rmsrmsEJ

xExJxP

JE

eff

eff

)tan(

2

)cos()1

Re(

en

m

J

E

J

E

e

eff

• Plasma Resistivity, Plasma Reactance, and Power Density

2

)sin()1

Im(

en

m

J

E

J

E

e

eff

Various Frequencies in SF/DF CCPs

• At the discharge center• At the discharge center

Benchmark of PIC Simulation in CCPs

Our PIC/MCC Simulation Result

Our PIC/MCC simulation result agrees well with Dr. Godyak’s experimental result(Godyak et al, Phys. Rev. Lett. 65, 996 (1990)).

Our PIC/MCC simulation result agrees well with Dr. Godyak’s experimental result(Godyak et al, Phys. Rev. Lett. 65, 996 (1990)).

[Refs] H.C Kim et al., Jpn. J. Appl. Phys. 44, 1957 (2005);

H.C. Kim et al., J. Phys. D: Appl. Phys. 38, R283 (2005)

PIC vs. Fluid Models (I)

In PIC simulation result, as the gas pressure decreases, electrons are localized in the discharge center. Meanwhile, no change in the spatial profile of electron density is found in fluid simulation since the nonlocal electron kinetics is not incorporated in swarm distribution. The larger plasma potential in fluid simulation result can lead to the overestimation of ion energy on the substrate.

In PIC simulation result, as the gas pressure decreases, electrons are localized in the discharge center. Meanwhile, no change in the spatial profile of electron density is found in fluid simulation since the nonlocal electron kinetics is not incorporated in swarm distribution. The larger plasma potential in fluid simulation result can lead to the overestimation of ion energy on the substrate.

In PIC simulation result, as the gas pressure decreases, the spatial profile of electron temperature changes significantly. (It is associated with the change of the EEDF shape from Druyvesteyn to bi-Maxwellian type under nonlocal conditions.*) In fluid simulations, the spatial profile of electron temperature does not change much since the shape of swarm EEDF is not so sensitive to the reduced field.

In PIC simulation result, as the gas pressure decreases, the spatial profile of electron temperature changes significantly. (It is associated with the change of the EEDF shape from Druyvesteyn to bi-Maxwellian type under nonlocal conditions.*) In fluid simulations, the spatial profile of electron temperature does not change much since the shape of swarm EEDF is not so sensitive to the reduced field.

* V.A. Godyak and R.B. Piejak, Appl. Phys. Lett. 63, 3137 (1993).

PIC vs. Fluid Models (II)

In PIC simulation results, as the gas pressure decreases, the electron power deposition in the bulk changes from positive to negative value. In fluid simulations, as the gas pressure decreases, the Ohmic heating decreases but the transition from positive to negative power deposition is not observed.

In PIC simulation results, as the gas pressure decreases, the electron power deposition in the bulk changes from positive to negative value. In fluid simulations, as the gas pressure decreases, the Ohmic heating decreases but the transition from positive to negative power deposition is not observed.

PIC vs. Fluid Models (III)

Summary for PIC vs. Fluid Models

PIC simulations have been compared with fluid simulations

under the gas pressures of 100 mTorr and 50 mTorr.

For two different pressures, the significant difference in the

spatial profiles of electron density and electron temperature as well

as EEDF transition and negative power deposition was found in

PIC simulations but not in fluid simulations.

These discrepancies mean that fluid model is not sufficiently

reliable in low-pressure capacitive rf discharges where the effect of

the nonlocal electron kinetics is considerable.