numerical investigation of wave effects in high-frequency capacitively coupled plasmas*
DESCRIPTION
NUMERICAL INVESTIGATION OF WAVE EFFECTS IN HIGH-FREQUENCY CAPACITIVELY COUPLED PLASMAS* Yang Yang and Mark J. Kushner Department of Electrical and Computer Engineering Iowa State University, Ames, IA 50011 [email protected] [email protected] http://uigelz.ece.iastate.edu October 2007. - PowerPoint PPT PresentationTRANSCRIPT
NUMERICAL INVESTIGATION OF WAVE EFFECTS IN HIGH-FREQUENCY
CAPACITIVELY COUPLED PLASMAS*
Yang Yang and Mark J. Kushner
Department of Electrical and Computer Engineering Iowa State University, Ames, IA 50011
[email protected] [email protected]://uigelz.ece.iastate.edu
October 2007
YYANG_AVS2007_01
* Work supported by Semiconductor Research Corp., Applied Materials and NSF.
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AGENDA
Wave effects in hf capacitively coupled plasma (hf-CCP) sources
Description of the model Base Case: 160 MHz, single frequency Scaling of plasma properties with frequency Scaling of dual frequency CCP (dfCCP) properties in Ar/Cl2
Concluding Remarks
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WAVE EFFECTS IN hf-CCP SOURCES
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A. Perret et al, Appl. Phys. Lett. 83, 243(2003)
Wave effects in CPPs impact plasma uniformity at high frequencies: Standing waves due to finite
wavelength tend to produce center peaked plasma.
Skin effects due to high electron density tend to produce edge peaked profile.
Electrostatic edge effects still contribute.
Relative contributions of wave and electrostatic edge effects determine plasma distribution.
Electronegative additives complicate issue by changing relationship between power and plasma density.
Plasma uniformity will be a function of frequency, power, mixture…
In this talk, results from a computational investigation will be discussed: Wave effects on plasma properties in hf-CCPs. Roles of electronegative gases on uniformity.
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GOALS OF THE INVESTIGATION
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HYBRID PLASMA EQUIPMENT MODEL (HPEM)
Electron Energy Transport Module: Electron energy equation with
Boltzmann equation derived transport coefficients.
MCS for secondary, sheath accelerated electrons
Fluid Kinetics Module: Heavy particle and electron
continuity, momentum, energy Maxwell’s Equations in potential
form
Es, N
Fluid Kinetics ModuleFluid equations
(continuity, momentum,
energy)Maxwell
Equations
Te,S,μ
Electron Energy Transport
ModuleBoltzmann equation
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FULL-WAVE MAXWELL SOLVER
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A full-wave Maxwell equation solver has been developed to address finite wavelength wave effects. Vector potential : Coulomb Gauge :
With vector and scalar potential, Maxwell equations are:
tA
ji ,
1, ji 1,1 ji
ji ,1jiAr ,
1, jiAr
jiAz , jiAz ,1
0 AAB
)()(22
2
tJAA
tA
In 2D cylindrical coordinates, , solved on a staggered mesh using sparse matrix techniques.
E field :
,, rz AA
tAE
Scalar potential :
jiB ,
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NUMERICAL REPRESENTATION OF EQUATIONS
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jittt
jirji
ttjirtt
jir
ttjir
tjir
ttjir
trtJ
rA
At
AAA,,2
,
,,.
22
,,, 1)'()(2
jittt
jiztt
jiz
ttjiz
tjiz
ttjiz
tztJA
tAAA
,,,2
2,,, 1)'()(
2
)()(1)( ,, tNqtAAt k
kkmjittttt
ji
l
lllee
m
ttttqtq
tt
t)(
2)()(
)(
Radial vector potential:
Axial vector potential:
Scalar potential:
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TENSOR TRANSPORT COEFFICIENTS
eeeee nDEqn
With azimuthal magnetic field, the electron flux is given by
where and are the tensor mobility and diffusivity.
e eD
and electron momentum transfer collision frequency.
22
22
22
220
)(zzrzr
zrrz
zrrzr
BBBBBBBBBBBBBBBBBBBBB
BAA
qmm
m
Fluxes of heavy particles given by momentum equations.
jiAr ,
1, jiAr
jiAz , jiAz ,1jiB ,
1, jiAz 1,1 jiAz1, jiB
jiAr ,1
1, jiAr
jiAr ,1
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NORMALIZATION OF SPARSE MATRIX
Normalized vector and scalar potentials solved in same matrix.
=
elementsArArelementsAz
ArelementsAr
elementsAz
ArAr ji,
AzAz ji,
ji ,elements
ArE ji,
AzF ji ,
jiG ,00
Arelements
Azelements
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REACTOR GEOMETRY
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2D, cylindrically symmetric. Ar, 50 mTorr, 200 sccm Base case: 160 MHz, 300 W (upper
electrode) Specify power, adjust voltage.
Ar for single frequency. Ar/Cl2 dual frequency
Ar, Ar*, Ar+
Cl2, Cl, Cl* Cl2
+, Cl+, Cl-
e
ELECTRON DENSITY
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[e] peaked at center with Maxwell solution (MS) due to finite wave length effect.
With Poisson solution (PS), a flat [e] profile.
Less power penetrates into bulk plasma with MS.
Ar, 50 mTorr, 200 sccm 160 MHz, 300 W, 48 V
Maxwell Solution
Electrostatic Poisson Solution
)(tAjP
)( jP
ELECTRON HEATING
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Bulk ionization follows electron density as Te is fairly uniform.
With MS, lower Te obtained in the center due to reduced ohmic heating in high electron density region .
Ar, 50 mTorr, 200 sccm 160 MHz, 300 W, 48 V
Maxwell Solution
Electrostatic Poisson Solution
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Maxwell Solution Axial field
Electrostatic Poisson Solution
E
- 170 V/cm – 260 V/cm
Radial fieldE
- 89 V/cm – 24 V/cm
Axial fieldE
- 130 V/cm – 250 V/cm
CYCLE AVERAGEDELECTRIC FIELD
Ar, 50 mTorr, 200 sccm160 MHz, 300 W, 48 V
With MS, the cycle averaged axial electric field is stronger in the center in sheath region.
As such, standing wave effect mainly enhances stochastic heating in the center.
Relative weak radial electric field in the bulk plasma region.
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Maxwell Solution Azimuthal - 0.07 G – 0.07 G
Scalar Potential - 61 V – 54 V
Electrostatic Poisson Solution Potential - 65 V – 45 V
Symmetric B due to out of phase sheath motion.
Magnitude of B is small and not major contributor here.
Similar scalar potential from MS as electrostatic potential from PS.
B Animation Slide POTENTIAL AND
MAGNETIC FIELD
Ar, 50 mTorr, 200 sccm160 MHz, 300 W, 48 V
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Maxwell Solution Azimuthal Max = 0.09 G
Scalar Potential - 14 V – 30 V
Electrostatic Poisson Solution Potential - 19 V – 25 V
B CYCLE AVERAGED
MAGNETIC FIELD
Ar, 50 mTorr, 200 sccm160 MHz, 300 W, 48 V
Symmetric B due to out of phase sheath motion.
Magnitude of B is small and not major contributor here.
Similar scalar potential from MS as electrostatic potential from PS.
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SCALING WITH FREQUENCY
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Maxwell Solution
Ar, 50 mTorr200 sccm300 W
Uniform [e] at 5 MHz for MS, similar to PS.
With increasing frequency, [e] profile undergoes transition from flat at 5 MHz, to edge peaked at intermediate frequencies, to center peaked at 160 MHz.
Wider edge peak with MS at 50 and 100 MHz .
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COMPARISON WITH EXPERIMENT
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[e] close to experiments from 5 to 100 MHz; Better match with MS.
PS radial [e] is not sensitive to frequency.
Ar 50 mTorr 200 sccm
Maxwell Solution
Poisson Solution
Line integrated [e]
G. A. Hebner et al, Plasma Sources Sci. Technol., 15, 879(2006)
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ION FLUX
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Ar 50 mTorr 200 sccm
Maxwell Solution Electron density
Experiment Ion saturation current
G. A. Hebner et al, Plasma Sources Sci. Technol., 15, 879(2006)
MS transitions from uniform to edge peaked to center peaked from 5 MHz to at 160 MHz.
Skin effect and wave effects have different contributions with frequency.
Trends agree with experiment.
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2-FREQUENCY CCP
Ar, 50 mTorr, 200 sccm
Electron density Single frequency at 160 MHz, 300 W
Dual frequency 10/160 MHz, 500/500 W
Ar has center peaked [e] for single frequency (160 MHz/300 W).
dfCCP (PLF=PHF) 10 MHz ionization source has uniform distribution.
Electrons are “seeded” where HF ionization might not occur (near edges) increasing skin effect.
Combined effects dominate over standing wave .
Edge high [e] with a small center peak is produced.
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Ar/Cl2 dual frequency have similar effect of reduced importance of wave effects.
Increasing Cl2 decreases electron density and reduces axial current.
Result is weakening of standing wave effect and skin effect. 50 mTorr, 200 sccm LF: 10 MHz/500 W, HF: 160 MHz/ 500 W
ELECTRONEGATIVE DISCHARGE: Ar/Cl2
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ELECTRONEGATIVE DISCHARGE: Ar/Cl2
Electron density
Ar/Cl2 dual frequency Decreasing
importance of wave-effects produce edge-high electron densities.
50 mTorr, 200 sccm LF: 10 MHz/500 W
HF: 160 MHz/ 500 W
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POWER DEPOSITION
Ar/Cl2 = 80/20, more bulk power deposition due to lower electron density.
Lower [e] produces smaller axial current, smaller Ar, Az and longer wavelength.
Ratio of inductive to capacitive field decreases.
Power deposition
Ratio: inductive to capacitive field
)(tAjP
/tA
50 mTorr, 200 sccm LF: 10 MHz/500 W
HF: 160 MHz/ 500 W
)(tAjP
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CONCLUDING REMARKS A full Maxwell solver was developed and incorporated into HPEM;
to resolve wave effects. Experimental trends of transition of plasma density from flat to
edge peaked to center peaked with increasing frequency are reproduced.
At low powers, azimuthal B is not a large contributor to electromagnetic effects.
Standing wave generally increases sheath fields at center of reactor.
With dual frequency excitation, low frequency provides ionization independent of wave effect. Seeding of electrons reduces severity of high frequency wave effect.
Adding Cl2 reduces wave effects by lengthening wavelength and increasing bulk electron heating.