Capacitively Coupled Plasmas
Modeling for Impedance Matching
Motivation
E
B
ALINE  A LINear Experiment
RF Power
3axis
Probe
BField
E field
Localized
Asymmetric
Melting
Impurity release
Limit discharge times
Connected to RF processes
ExB drifts
Measure E?
"Hot Spots"
Inefficient power coupling
Power reflections
Impedance Matching
Matching Network
Zeq = R
T
ALINE's
R , X
Parallelplate reactor
PLASMA
Sheath
D
D
a
b
Density
ions
electrons
Equivalent ε !
Sheath impedance
E
field
x=0
x=s (t)
a
DC
2nd Harmonic
Efficient power transfer
No power reflections
Particle Balance Te
Particles
created
in bulk
Particles
lost in
the walls
=
Energy
absorbed
=
Energy
lost
Bulk Plasma
Ohmic
Sheath edge
Stochastic
e

Energy gained
Incident Flux
units
Aeff/A
Geometry
Physics DEs
Boundary conditions
Mesh
Run!
e

Fluid driftdiffusion (Max VDF)
X, X*, X
"Electrostatics"  Poisson's law
For each specie: He, He ,He
*
+
mass fraction
MaxwellStefan
Diffusivity
Flux vector
"Electrostatics"
"walls"
V=0
V=V cos(ωt)
e  reflection
X, X*, X  reaction

+
Benchmarking
GEC reactor (NIST)
GEC Argon Z and Global Model Z
Voltage
Experiments in ALINE
Plasma
Parameters
Lab
Single
Probe
COMSOL
2D
Global
~Asymmetric
"Rough"
Approximation
Electrical Impedance
Without plasma
Conclusions
A
B
C
Problem is in the
"cloud"
still
s
Analytical
Software
Package
Parallelplate reactor success
n, Te, Z in He, Ar
Asymmetric needs more work
Solve ODEs?
High Pressure PP success
He flying colors
2D n, Te, Z in He, Ar
Extend pressure?
Smaller mesh?
Takes 2 days!!
Pedro A. Molina Cabrera
Msc. Candidate
Dr. Eric Faudot
Assistant Professor  Supervisor
RF plasma > Capacitively coupled?
Start without B field
ICRH 10100MHz
RF Antenna inplasma
Wave
propagation
Inductively
Coupled?
Microwave
Heated
Z of ALINE  Asymmetric CCP?
I need a
matching box
What is the Z
of ALINE?
d
Only need
n, ν(Te)
Finite Element Method
Plasma Module  2011
+
MaxwellStefan diffusion
o
Capacitively
Coupled?
Energy Balance  n
p
E
fields
Ion/Electron
Density over
RF period
Higher
pressure
Ar
He
n
GEC
Benchmarking
GEC Cell
Global
COMSOL
Ar
Z
He
ALINE
Ar
He
Global
COMSOL
Ar
He
Asym
2D
GEC
Experimental
density in Ar
Analytical
"Global"
COMSOL
x,
.
Microwave
Diagnostics
Experimental
density in He
GEC
Global
Exp 24MHz
x
Exp 32MHz
Ar
Ar
* High P only
*
*
x5
x3
x5
x2
No data
found
x5
FAILS!
**
** 2 days to converge
COMSOL
Global
Analytical
"Global"
COMSOL
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CCP modeling for Impedance Matching
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