simulations of helicon discharges using a two dimensional hybrid plasma … · 1999-09-20 · in...

UNIVERSITY OF ILLINOISOPTICAL AND DISCHARGE PHYSICSUCLA99_1

SIMULATIONS OF HELICON DISCHARGES USING A TWO

DIMENSIONAL HYBRID PLASMA EQUIPMENT MODEL*University of California - Los Angeles

September 21, 1999

Ronald L. Kinder and Mark J. KushnerUniversity of Illinois, Urbana-Champaign

e-mail : [email protected] [email protected]

web site : http://uigelz.ece.uiuc.edu

*Work Supported by SRC, AFOSR/DARPA,Applied Materials, and LAM Research

UNIVERSITY OF ILLINOISOPTICAL AND DISCHARGE PHYSICSLAM99_2

AGENDA

• Foreword: Plasma Processing

• Hybrid Plasma Equipment Model (HPEM)

• Cold Plasma Tensor and Collisionless Heating

• Helicon Behavior in a Solenoidal Field

• Low Field Inductive to Cyclotron Mode Transition

• High Field Inductive-Helicon Mode

• Helicon Tool Design

• Conclusions and Future Work

NATIONAL TECHNOLOGY ROADMAP FOR SEMICONDUCTORS


• In the early 1980’s, Gordon Moore (Intel) observed that the complexity and performance of microelectronics chips double every year and a half.

• The NTRS sets goals for the microelectronics fabrication industry for future generations of devices.

• Feature size will continue to shrink with more transistors per chip while...

INCREASED COMPLEXITY REQUIRES NEW SOLUTIONS


The levels of interconnect wiring will increase to 8-9 over the next decadeproducing unacceptable signal propagation delays. Innovative solutions such ascopper wiring and low-k dielectrics are being implemented.

•

PLASMA ARE ESSENTIAL FOR ECONOMICALLYFABRICATING FINE FEATURES IN MICROELECTRONICS

UNIVERSITY OF ILLINOISOPTICAL AND DISCHARGE PHYSICSUCLAL99_5

In plasma processing, ions are accelerated nearly vertically into the wafer, therebyactivating etch and via filling processes which produce straight walled, anisotropicfeatures.

IONSNEUTRALS

MASK

SiO2

Si

Ref: “Principles of Plasma Discharges and

Materials Processing, Michael A. Liebermanand Allan J. Lichtenberg, p.2, 1994

•

NEED FOR PLASMA PROCESSING EQUIPMENT MODELS


An increasing fraction of the cost for building a major fabrication facility is onprocessing equipment.

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HYBRID PLASMA EQUIPMENT MODEL (HPEM)


• The Computational Optical and Discharge Physics Group (CODPG) developscomputer aided design tools of plasma equipment and process.

HPEM USING WAVE HEATED DISCHARGES


In order to encompass a larger range of plasma processing reactors, the HPEMhas been enhanced to enable simulation of wave heated discharges.

CONVENTIONAL WAVE HEATED

CAPACITIVELYCOUPLED

INDUCTIVELYCOUPLED

ELECTRONCYCLOTRONRESONANCE

HELICON

PLASMASOURCES

•


MOTIVATION FOR USE HELICON DISCHARGES

Due to their high ionization efficiency, high flux density and their ability to depositpower within the volume of the plasma, helicon reactors are being developed fordownstream etching and deposition.

The power coupling of the antenna radiation to the plasma is of concern due toissues related to process uniformity.

Furthermore, operation of helicon discharges at low magnetic fields (5 -20 G) isnot only economically attractive, but lower fields provide greater ion fluxuniformity to the substrate.

To investigate these issues, we have improved the electromagnetics module ofthe HPEM to resolve the helicon structure of a m = 0 mode.

Results for process relevant gas mixtures are examined and the dependence onmagnetic field strength, field configuration, and power are discussed.

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COLD PLASMA CONDUCTIVITY TENSOR

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•

Algorithms were developed to enable investigations of helicon plasma tools usingHPEM-2D. A full tensor conductivity was added to the Electromagnetics Module(EMM) which enables one to calculate 3-d components of the inductively coupledelectric field based on 2-d applied magnetostatic fields.

− ∇ ⋅1µ

∇E

= − iωσ ⋅ E − iωJ ext + ω 2εE

σo = q2ne

m e νm

α = me

qνm + iω ( ) where, and,

The plasma current in the wave equation is addressed by a cold plasma tensorconductivity.

σ = σo

me νm

qα1

α2 + B2

α2 + B r2 αBz +B rBθ −αBθ + B rBz

−αBz + BrB θ α2 + Bθ2 αB r + BθBz

αBθ +B rBz −αB r + BθBz α2 + Bz2

MAGNETIC FIELD (G)

1.5

1.0

0.5

0.020 30 40 50100 60 70


COLLISIONLESS HEATING - LANDAU DAMPING

• There is considerable evidence that collisional absorption is too weak to account forenergy deposition at low pressures (< 10 mTorr Ar). Chen (1991) estimated the effectivecollisional frequency for Landau damping of the helicon mode shown below.

In the low electron density and high magnetic field regimes, Landau damping significantlyaffects the power deposition efficiency. Furthermore in the electron cyclotron mode ofoperation, Landau damping shift or remove resonant heating.

1.5

1.0

0.5

0.02 3 4 5

ELECTRON DENSITY/MAGNETIC FIELD

( x 1010 cm-3 G-1)

10

Model(x 0.1)

( )23LD exp2 ξωξπν −=

thυ

ωξ

2k

z

=

•

Average wo/Landau

Average w/Landau

Downstream wo/Landau

Downstream w/Landau

Ar, 10 mTorr, 1 kW, 50 sccm•


SIMULATION OF SOLENOIDAL GEOMETRY

• Since Helicon sources are more complex than other plasma sources, we have conductedpreliminary studies in a solenoidal geometry similar to that used by Chen et at.

However, since simulation were two dimensional in nature, we begun studies with theuse of a two coil antenna which produces an m = 0.

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RightHelical

Antenna

to 27.12MHz

amplifier

4.7 cm ODquartz tube

End CoilsMagnetic Field Coils

Gas Feed

End Coils

Nagoya Type III Antenna

Two Ring Antenna

15 mTorr Ar, RF power of 2kW at 27.12 MHz, 0-1.2 kG•

LOW FIELD INDUCTIVE TO HELICON TRANSITION - AZIMUTHAL

UCLA99_15

UNIVERSITY OF ILLINOISOPTICAL AND DISCHARGE PHYSICS

• At a critically low magnetic field, the azimuthal electric field remains inductively coupledand a radially propagating wave dominates.

As magnetic fields is increased, standing wave patterns arise in radial direction and theelectric field begins to propagate in the axial direction.

Ar, 10 mTorr, 1 kW, 50 sccm•(V / cm)15 0.15

Radians6.283 0

Eθ PhaseB = 40 G

Eθ Phase Eθ Phase Eθ Phase Eθ PhaseB = 80 G B = 150 GB = 20 GB = 10 G

•

RADIUS (cm)0 1010

40

Coils

Glass

Substrate

Solenoid

LOW FIELD INDUCTIVE TO HELICON TRANSITION - RADIAL

UCLA99_16


• Effects similar to those for the azimuthal electric field can be seen in the distribution andpropagation of the radial electric field.

Initially propagation is dominantly in the the radial direction, showing the existence of ahighly damped wave.

Ar, 10 mTorr, 1 kW, 50 sccm•(V / cm)5 0.05

Radians6.283 0

B = 40 G B = 80 G B = 150 GB = 20 GB = 10 G

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Er Phase Er Phase Er Phase Er PhaseEr Phase

LOW FIELD INDUCTIVE TO HELICON TRANSITION - AXIAL

ULA99_17


• The axial electric field distribution has a greater dependence on radial static magneticfield gradients than magnetic field magnitudes.

In the magnetic field spectrum shown, the propagation of the axial electric fields is in theradial direction and does not significantly contribute to the power deposition.

Ar, 10 mTorr, 1 kW, 50 sccm•

B = 40 G B = 80 G B = 150 GB = 20 GB = 10 G

•

(V / cm)0.03 0.003

Radians6.283 0

Ez Phase Ez Phase Ez Phase Ez PhaseEz Phase

LOW FIELD INDUCTIVE TO HELICON TRANSITION - POWER

UCLA99_18


• At low magnetic fields power deposition is inductively coupled and occurs near the coils.

As nodal structure develops in the azimuthal and radial fields, the skin depth of thepower deposition is increased to within the volume of the plasma.

Ar, 10 mTorr, 1 kW, 50 sccm•(W / cm3)6 0.06

(cm-3)7E+12 7E+10

Power ElectronDensity

B = 40 G B = 80 G B = 150 GB = 20 GB = 10 G

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Power ElectronDensity Power

ElectronDensity Power


ElectronDensity

GEOMETRIC DEPENDENCE OF WAVE STRUCTURE - AZIMUTHAL

UCLA99_19UNIVERSITY OF ILLINOIS

OPTICAL AND DISCHARGE PHYSICS

R = 2.5 cm

B = 80 G B = 150 GB = 40 GB = 20 G

R = 8.5 cm

(V / cm)15 0.15

Radians6.283 0

Eθ Phase Eθ Phase Eθ Phase Eθ Phase

*Not to scale.

GEOMETRIC DEPENDENCE OF WAVE STRUCTURE - RADIAL



R = 2.5 cm

B = 80 G B = 150 GB = 40 GB = 20 G

R = 8.5 cm

5 0.05

Radians6.283 0

Er Phase Phase Phase Phase

(V / cm)

Er Er Er

GEOMETRIC DEPENDENCE OF WAVE STRUCTURE - POWER



R = 2.5 cm

B = 80 G B = 150 GB = 40 GB = 20 G

R = 8.5 cm

(W / cm3)6 0.06

1E+12 1E+10(cm-3)

Power [e] Density Power [e] Density Power [e] Density Power [e] Density

LOW FIELD DENSITY PEAK IN THE DOWNSTREAM

UCLA99_23

Previous indications taken with a Nagoya Type III antennas in uniform magneticfields, by Chen and Chevalier, in the low magnetic field regime show a small peak inthe electron density in the downstream region.

A similar result is observed in simulations conducted with varying tube radius.


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100 1000100

MAGNETIC FIELD (G)

Ar, 5 mTorr, 1 kW, 50 sccm

2

1

r = 2.5 cmr = 4.0 cmr = 6.0 cmr = 8.5 cm

0

1.0

0.2

0.4

0.6

0.8

0MAGNETIC FIELD (G)

20 40 60 80 100 120

r = 4 cmr = 2 cm

Experimental Results by Chen and Chevalier

Ref: Chen, F.F. ad Chevalier, G., J. Vac. Sci. Technol. A, 10,

1389 (1992).

Downstream Value at z = 10 cm

LOW FIELD DENSITY PEAK IN THE DOWNSTREAM

UCLA99_24

The position of most efficient power deposition along the magnetic field spectrumdepends on the total momentum transfer collision frequency.

A shift of the ECR position toward higher magnetic fields as the tube radius isdecreased occurs because of the subsequent increase in electron temperature.


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0 10080604020MAGNETIC FIELD (G)

1

0

νm = 107 s-1

νm = 108 s-1

νm = 5 x 108 s-1

νm = 109 s-1

2 10864TUBE RADIUS (cm)

3.5

3.0

3.1

3.2

3.3

3.4DecreasingMagnetic

Field

Reactor Average Values

POWER (W)1500500 750 1000 12502500

0

1

ModelExperiment (Chen et al.)

Ar, 10 mTorr, 200 G, 20 sccm

REACTOR AVERAGE PLASMA DENSITY

UCLA99_25

The transition from inductive coupling to helicon mode appears to occur when the fraction of power deposited through the radial and axial fields dominates.

The improved HPEM has been able to reproduce Inductive to Helicon transitions in the magnetic field spectrum. Differences between the simulation and experimental results are attributed to small variations in geometry and antenna design.


•

•

100 100010MAGNETIC FIELD (G)

r = 2.5 cmr = 4.0 cmr = 6.0 cmr = 8.5 cm

0

5

1

2

3

4

Ar, 10 mTorr, 20 sccm

TRIKON MORITM 200 HELICON PLASMA SOURCE


• A commercial Trikon Technologies, Inc., Pinnacle 8000 helicon source plasmasystem will be used to validate simulation models.

Electromagnet

ProcessChamberWafer

PermanentMagnets

Antenna

APPLICATION OF HPEM TO HELICON TOOL DESIGN

UCLA99_27

Investigations have begun applying theHPEM to helicon tool design.

Preliminary results show that the axialelectric field has a strong dependence ondetails of the magnetic field configuration,and could control the inductive-helicon modetransition.


RF COILS

SOLENOID

WAFERPUMPPORT

SHOWERNOZZLE

MAGNETICBUCKET

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•

Bz

Br

Bθ

Experimental

Simulation - Ar, 10 mTorr, 1kW, 20 sccm•

Experiment - Ar, 10 mTorr, 1kW•


UCLA99_29


20 cm 20 cm00

50 cm

Ar, 10 mTorr, 1kW, 50 sccm•

B = 20 G B = 100 G B = 300G

(V / cm)15 0.15

Radians6.283 0

Eθ Phase Eθ Phase Eθ Phase

At low fields, the electromagnetic propagation is mainly radial, producingstanding wave pattern in the radial direction.

However as the field increases, propagation dominates in the axial direction,shifting standing wave patterns in the direction of propagation.

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UCLA99_30


20 cm 20 cm00

50 cm


B = 20 G B = 100 G B = 300G

(V / cm)5 0.05

Radians6.283 0

Er Phase Phase Phase

Similar effects can be seen in the radial electric field profile and propagation.

Antenna coupling seems to have a significant effect at higher magnetic fields.

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Er Er


UCLA99_31


20 cm 20 cm00

50 cm


B = 20 G B = 100 G B = 300G

(V / cm)5 0.05

Radians6.283 0

Ez Phase Phase Phase

Axial electric field propagation and wave pattern resembles radial electric fields.

As magnetic fields are increased, overall electric field propagation in the axial directiondominates.

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Ez Ez


UCLA99_32


20 cm 20 cm00

50 cm


B = 20 G B = 100 G B = 300G

As the magnetic fields increase, axial propagation dominates depositing power in thedownstream region.

An increase in ion current to the substrate comes at the loss of flux uniformity.

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(W / cm3)1 0.01

(cm-3)4E+12 4E+10

Power ElectronDensity Power


ElectronDensity

CONCLUDING REMARKS

UCLA99_33

Algorithms were developed to enable investigations of helicon plasma tools using HPEM-2D. In the low electron density and high magnetic field regimes, Landau damping significantly affects the power deposition efficiency.

Parametric studies in the low magnetic field range show three well defined regimes:i) enhanced inductively coupled mode.ii) a resonant peak in the power deposition efficiency and plasma density, an effect attributed to off-resonant cyclotron heating.iii) inductively coupled - helicon mode regime.

The transition from inductive coupling to helicon mode appears to occur when the fraction of power deposited through the radial and axial fields dominates.

Studies have begun applying the improved HPEM to tool design. Improvements will be transferred to HPEM-3D.


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simulations of helicon discharges using a two dimensional hybrid plasma … · 1999-09-20 · in...

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