wave and electrostatic coupling in 2-frequency capacitively coupled plasmas

WAVE AND ELECTROSTATIC COUPLINGIN 2-FREQUENCY

CAPACITIVELY COUPLED PLASMAS UTILIZING A FULL MAXWELL SOLVER*

Yang Yanga) and Mark J. Kushnerb)

a)Department of Electrical and Computer Engineering Iowa State University, Ames, IA 50011, USA

[email protected]

b)Department of Electrical Engineering and Computer ScienceUniversity of Michigan, Ann Arbor, MI 48109, USA

[email protected]

http://uigelz.eecs.umich.edu

October 2008

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* Work supported by Semiconductor Research Corp., Applied Materials and Tokyo Electron Ltd.

AGENDA

Wave effects in 2-frequency capacitively coupled plasma (2f-CCP) sources

Description of the model

Base cases: Ar/CF4 = 90/10, HF = 10-150 MHz

Scaling with:

Fraction of CF4

HF power

Concluding remarks

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University of MichiganInstitute for Plasma Science

and Engineering

WAVE EFFECTS IN HF-CCP SOURCES

Wave effects (i.e., propagation, constructive and destructive interference) in CCPs become important with increasing frequency and wafer size.

Wave effects can significantly affect the spatial distribution of power deposition and reactive fluxes.

G. A. Hebner et al, Plasma Sources Sci. Technol., 15, 879(2006)YY_MJK_AVS2008_03


and Engineering

Relative contributions of wave and electrostatic edge effects determine the plasma distribution.

Plasma uniformity will be a function of frequency, mixture, power…

Results from a computational investigation of coupling of wave and electrostatic effects in two-frequency CCPs will be discussed :

Plasma properties

Radial variation of ion energy and angular distributions (IEADs) onto wafer

GOALS OF THE INVESTIGATION

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and Engineering

Full-wave Maxwell solvers are challenging due to coupling between electromagnetic (EM) and sheath forming electrostatic (ES) fields.

EM fields are generated by rf sources and plasma currents while ES fields originate from charges.

We separately solve for EM and ES fields and sum the fields for plasma transport.

Boundary conditions (BCs):

EM field: Determined by rf sources.

ES field: Determined by blocking capacitor (DC bias) or applied DC voltages.

mEE

METHODOLOGY OF THE MAXWELL SOLVER

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and Engineering

t

H

r

E

z

E zr

0

t

EJ

z

H rrr

0

t

EJ

r

rH

rz

rz

0

1

Launch rf fields where power is fed into the reactor.

For cylindrical geometry, TM mode gives Er , Ez and H .

Solve EM fields using FDTD techniques with Crank-Nicholson scheme on a staggered mesh:

Mesh is sub-divided for numerical stability.

ji ,

1,1 ji

ji ,1jiEr ,

jiEr ,1

jiEz , jiEz ,1jiB ,

1, ji

FIRST PART: EM SOLUTION

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Solve Poisson’s equation semi-implicitly:

Boundary conditions on metal: self generated dc bias by plasma or applied dc voltage.

Implementation of this solver:

Specify the location that power is fed into the reactor.

Addressing multiple frequencies in time domain for arbitrary geometry.

First order BCs for artificial or nonreflecting boundaries (i.e., pump ports, dielectric windows).

t

dt

tttdttt

,)(

SECOND PART: ES SOLUTION

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HYBRID PLASMA EQUIPMENT MODEL (HPEM)

Electron Energy Transport Module: Electron Monte Carlo Simulation

provides EEDs of bulk electrons Separate MCS used for secondary,

sheath accelerated electrons Fluid Kinetics Module:

Heavy particle and electron continuity, momentum, energy

Maxwell’s Equation Plasma Chemistry Monte Carlo Module:

IEADs onto wafer

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E, N

Fluid Kinetics ModuleFluid equations

(continuity, momentum,

energy)Maxwell

Equations

Te,S,μ

Electron Energy Transport

Module

Plasma Chemistry Monte Carlo

Module University of MichiganInstitute for Plasma Science

and Engineering

REACTOR GEOMETRY

2D, cylindrically symmetric.

Ar/CF4, 50 mTorr, 400 sccm

Base conditions

Ar/CF4 =90/10

HF upper electrode: 10-150 MHz, 300 W

LF lower electrode: 10 MHz, 300 W

Specify power, adjust voltage.

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Main species in Ar/CF4

mixture

Ar, Ar*, Ar+

CF4, CF3, CF2, CF, C2F4, C2F6, F, F2

CF3+, CF2

+, CF+, F+

e, CF3-, F-


and Engineering

Center Edge

IEADs INCIDENT ON WAFER: 10/150 MHz

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Total Ion CF3+

Center Center Edge Edge

IEADs are separately collected over center&edge of wafer.

From center to edge, IEADs downshifted in energy, broadened in angle.

Ar/CF4=90/10, 50 mTorr, 400 sccm HF: 150 MHz/300 W LF: 10 MHz/300 W


and Engineering

Center Edge


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Total Ion CF3+



IEADs undergo less change from center to edge than 10/150 MHz.


and Engineering

Center Edge


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Total Ion CF3+



Less radial change compare to 10/150 MHz case.

Why radial uniformity of IEADs changes with HF ?

Many factors may account for variation: sheath thickness, sheath potential, mixing of ions …


and Engineering

ELECTRON DENSITY: Ar/CF4 = 90/10

Changing HF results in different [e] profile, thereby giving different radial distribution of sheath thickness, potential...

[e] profile is determined by wave and electrostatic coupling.

HF = 150 MHz, Max = 1.1 x 1011 cm-3

HF = 50 MHz, Max = 5.9 x 1010 cm-3

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Ar/CF4=90/10 50 mTorr, 400 sccm

HF: 10-150 MHz/300 W LF: 10 MHz/300 W

AXIAL EM FIELD IN HF SHEATH HF = 50 MHz, Max = 410 V/cm

HF = 150 MHz, Max = 355 V/cm

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|Ezm| = Magnitude of axial EM field’s first harmonic at HF.

No electrostatic component in Ezm: purely electromagnetic.

150 MHz: center peaked due to constructive interference of plasma shortened wavelengths.

50 MHz: Small edge peak.

Ar/CF4=90/10, 50 mTorr, 400 sccm HF: 10-150 MHz/300 W LF: 10 MHz/300 W


and Engineering

AXIAL E-FIELD IN HF AND LF SHEATH: 10/150 MHz

|EZ| in LF(10 MHz) Sheath, Max = 1700 V/cm

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Significant change of |Ez| across HF sheath as evidence of traveling wave.

HF source also modulates E-field in LF sheath.


and Engineering

|EZ| in HF (150 MHz) Sheath, Max = 1500 V/cm


HF: 150 MHz/300 W LF: 10 MHz/300 W

ANIMATION SLIDE-GIF

LF CYCLE AVERAGEDAXIAL E-FIELD IN HF AND LF SHEATH: 10/150 MHz

|EZ| in LF(10 MHz) Sheath, Max = 750 V/cm

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Significant change of |Ez| across HF sheath as evidence of constructive interference.


and Engineering

|EZ| in HF (150 MHz) Sheath, Max = 450 V/cm


HF: 150 MHz/300 W LF: 10 MHz/300 W

SPATIAL DISTRIBUTION OF NEGATIVE IONS

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Finite wavelength effect at 150 MHz populates energetic electrons in the reactor center.

More favorable to attachment processes (threshold energies 3 eV) than ionization (threshold energies 11 eV).

[CF3- + F-] increases in the center.

[CF3- + F-]

HF: 10-150 MHz/300 W LF: 10 MHz/300 W University of Michigan

Institute for Plasma Scienceand Engineering

HF = 150 MHz, Max = 1.2 x 1011 cm-3

SPATIAL DISTRIBUTION OF POSITIVE IONS

University of MichiganOptical and Discharge Physics

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Difference in radial profiles for different ions. Different sheath transiting time due to differences in mass and

sheath thickness. Eventually translates to radial non-uniformity of IEADs.

CF3+ Ar+

HF: 10-150 MHz/300 W LF: 10 MHz/300 W

ELECTRON IMPACT IONIZATION SOURCE FUNCTION


HF = 10 MHz, Max = 2.1 x 1015 cm-3s-1

HF = 50 MHz, Max = 6.3 x 1015 cm-3s-1

HF = 100 MHz, Max = 4.2 x 1015 cm-3s-1

HF = 150 MHz, Max = 3.8 x 1016 cm-3s-1

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Source from bulk and secondary electrons.

50 MHz: bulk ionization from Ohmic heating, edge peaked due to electrostatic field enhancement..

150 MHz: ionization dominated by sheath accelerated electrons (stochastic heating).

100 MHz: has both features, but edge effect dominates.


HF: 10-150 MHz/300 W LF: 10 MHz/300 W

ION FLUXES INCIDENT ON WAFER

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Uniformity of incident ion fluxes and their IEADs are both determined by plasma spatial distribution.

Relative uniform fluxes and IEADs at 100 MHz.

CF3+ Flux

HF: 10-150 MHz/300 W LF: 10 MHz/300 W University of Michigan


Total Ion Flux

Center Edge

IEADs INCIDENT ON WAFER: Ar/CF4 = 80/20

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Total Ion CF3+

Inner Inner Outer Outer

Less radial variation across the wafer.

More radial uniformity of sheath thickness and potential counts.

Implicates adding CF4 improves plasma uniformity.



and Engineering

SCALING WITH FRACTION OF CF4 IN Ar/CF4: 10/150 MHz

Pure Ar, Max = 3.8 x 1011 cm-3

10% CF4, Max = 1.1 x 1011 cm-3

20% CF4, Max = 4.8 x 1010 cm-3

30% CF4, Max = 4.4 x 1010 cm-3

50 mTorr, 400 sccm HF: 150 MHz/300 W LF: 10 MHz/300 W

With increasing fraction of CF4:

[e] decreases thereby decreasing conductivity.

Weakens constructive interference of EM fields by increasing wavelength.

Maximum of [e] shifts towards the HF electrode edge.

Skin depth also increases. Increasing penetration of EM

fields. More uniform [e] profile

results.

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ION FLUXES INCIDENT ON WAFER: 10/150 MHz

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50 mTorr, 400 sccm

Uniform [e] profile at 20% CF4 results in

Radial uniformity of incident ion fluxes. Uniform radial profile of IEADs.

CF3+ Flux Total Ion Flux

HF: 150 MHz/300 W LF: 10 MHz/300 W University of Michigan


SCALING TO HF POWER: 10/150 MHz

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Increasing HF power reduces plasma uniformity. Finite wavelength effect preferentially produces negative ions in

the center. With increasing [e], wave penetration is less affected in the radial

direction due to the HF sheath, so [e] peak only moves 2 cm from 300 W to 1000 W.


HF: 50-150 MHz LF: 10 MHz/300 W


and Engineering

1000 W, [CF3- + F-]

[e]

IMPACT OF HF POWER ON ION FLUXES ONTO WAFER

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Non-uniformity of ion fluxes onto the wafer also increases with increasing HF power.


HF: 50-150 MHz LF: 10 MHz/300 W


and Engineering

Total Ions Flux

Center Edge

TOTAL ION IEADs INCIDENT ON WAFER


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300 W Center Center Edge Outer

More uniform IEADs at higher HF power.

With increasing HF power (increasing [e]), LF voltage decreases to keep LF power constant.

Diminishes radial variation of IEADs.

Ar/CF4=90/10, 50 mTorr, 400 sccm HF: 150 MHz LF: 10 MHz/300 W

1000 W

CONCLUDING REMARKS

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A full Maxwell solver separately solving for EM and ES fields was developed and incorporated into the HPEM.

For 2f-CCPs sustained in Ar/CF4=90/10 mixture,

HF determines wave and electrostatic coupling which, in turn, determines plasma spatial distribution.

Non-uniform IEADs across the wafer at HF =150 MHz due to plasma non-uniformity.

Increasing fraction of CF4 to 20% results in more uniform plasma profile and IEADs incident on wafer.

At HF = 150 MHz, increasing HF power increases plasma non-uniformity.


and Engineering

wave and electrostatic coupling in 2-frequency capacitively coupled plasmas

Documents

plasma transport

plasma distribution

plasma sources

em fields

plasma currents

plasma uniformity

electrostatic effects

es fields