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Use of Langmuir probesin strong RF plasmas
Francis F. Chen, UCLA
KAIST, Daejeon, S. Korea, April 2011
Commercial probe systems
Shown here is the Hiden ESPION probe. I use the older Hiden ESP probe software, but I make my own probes.
I presume you are familiar with the PlasMart probe.
The Chen B probe
To reject RF pickup, resonant chokes (inductors) and a good auxiliary electrode are needed.
The choke must be >200 k
This is a good choke. High Z is good for low density. High frequency can use lower Z. It is sometimes possible
to adjust the RF frequency to match the choke.
0
200
400
600
800
1000
10 15 20 25 30f (MHz)
Z (
k)
Probe 61110
2Rp = .005" = .0127 cm,L = 1.2 cm, R = 12.7
How RF distorts the I-V characteristic
The RF shifts Vp back and forth. Since the I-V curve is nonlinear, the average current does not reproduce the curve.
This shows what the uncompensated I-V curve would look as the RF pickup voltage is varied.
Why the auxiliary electrode is needed
Probe tip
Cs1 causes the choke to lose part of the oscillation of the probe. The large,floating auxiliary electrode (Zx) strongly drives the choke to oscillate with the plasma’s RF fluctuations.
The orbital-motion-limited theory
Large probe, dense plasma, thin sheath
½sat p sI neA c
Small probe, weak plasma, thick sheath
Langmuir’s Orbital-Motion-Limited (OML) theory
Langmuir’s simple OML formula
1/ 22 p
i sat pi
eVI I A ne
M
OML is valid only when the sheath is so thick that there is no “absorption radius”.
However, it works better than other theories even when it should not be applicable.
Both Hiden and PlasmArt use this simple formula.
To use this formula, probe tips should be as thin as possible to minimize Rp/D.
The simple OML formula
1/ 22 p
i sat pi
eVI I A ne
M
The ion saturation current Isat is independent of Te and
can be used easily to measure density n. Isat varies as the square root of Vp. This is a characteristic
of ion orbiting when there is no absorption radius. However, the linear I2 – Vp relation is followed even when
the Rp/D is not so large!
Ap is the probe tip area, Mi the ion mass, and Vp the probe
potential relative to the plasma potential.
A typical I2 – Vp curve for n < 1012 cm-3
0.0
0.5
1.0
1.5
2.0
2.5
3.0
-100 -80 -60 -40 -20 0 20Vp (volts)
I2 (
mA
)2
Ii (data)
Ii (OML)
1/2/ 2i p iI A ne KT M F
½ ½1erf ( ) erfc( )F e
/ 0p ieV KT
2 2/ 1, /( 1) , /(1 )pR s .
How did Langmuir get such a simple formula?
This is what he started with for Maxwellian ions:
s is an assumed sheath radius at which ions start with their thermal velocities
½ ½2( ) erfc( )F e
½½ 2
1 3 1erfc( ) 1 ...
2 4( )
e
½ ½ ½ ½½
2 1 1 2( ) 2
( )F e e
1/ 2 1/ 21/ 22 2
2p pi
i p pi i
eV eVKTI A ne A ne
M KT M
Then he made some dubious approximations
The ion temperature cancels out!
Attempt to use the exact OML formula
0
50
100
150
200
250
-100 -80 -60 -40 -20 0 20V
I2 (
mA
)2
Ii squared
Ii(OML)
Exact
At high density, the curve does not fit a straight line. Using the exact OML formula gives too much curvature even if the sheath radius is adjusted to give the best fit.
It is still unknown why the I2-V curve is so close to linear.
The semilog electron curve 1
0
1
2
3
4
5
-100 -80 -60 -40 -20 0 20V
I2 (
mA
)2
Ii squared
Ii(OML)
File 110313_62
27.12 MHz400W
1.2 mTorr
n= 5.8E11
First, we have to fit the ions so that we can subtract them
The semilog electron curve 2
Now we make the semilog electron curve
0.01
0.1
1
10
-5 0 5 10 15 20 25 30 35V
I (m
A)
Ie
Ie(fit)
Ie (0)
File 110313_62
27.12 MHz400W
1.2 mTorr
Te=7.19 eV
Vs=50.3V
Note that the right amount of ion current added back is essential
False indication of electron beams
0
10
20
30
40
50
-100 -80 -60 -40 -20 0 20V
I2 (
mA
)2
Ii squared
Ii(OML)
File 110314_12
27.12 MHz400W
15 mTorr
n= 15.2E11
0.01
0.1
1
10
100
-5 0 5 10 15 20 25V
I (m
A)
Ie
Ie(fit)
Ie (0)
File 110314_12
27.12 MHz400W
15 mTorr
Te=3.29 eV
Vs=28.8 V
0
10
20
30
40
50
-100 -80 -60 -40 -20 0 20V
I2 (m
A)2
Ii squared
Ii(OML)
File 110314_12
27.12 MHz400W
15 mTorr
n= 15.9E11
0.01
0.1
1
10
100
-5 0 5 10 15 20 25V
I (m
A)
Ie
Ie(fit)
Ie (0)
File 110314_12
27.12 MHz400W
15 mTorr
Te=2.75 eV
Vs=26.5 V
Apparatus for helicon thruster
PERMANENT MAGNET
GAS FEED
HEIGHT ADJUSTMENT
LANGMUIR PROBE
PERMANENT MAGNET
GAS FEED
HEIGHT ADJUSTMENT
LANGMUIR PROBE
1 magnet, 65 gauss 2 magnets, 280 gauss max (lower)
Very thin vertical probe
Effect of auxiliary electrode 1: no electrode
-0.008
-0.006
-0.004
-0.002
0.000
0.002
0.004
0.006
0.008
0.010
0.012
-100 -80 -6 0 -40 -20 0 20V
I (A
)
0
10
20
30
40
50
60
-100 -80 -60 -40 -20 0 20V
I2 (m
A)2
Ii squared
Ii(OML)
0.01
0.1
1
10
100
-30 -25 -20 -15 -10 -5 0 5 10 15 20
V
I (m
A)
Ie
Ie(fit)
Ie (2)
0.01
0.1
1
10
100
-30 -25 -20 -15 -10 -5 0 5 10 15 20
V
I (m
A)
Ie
Ie(fit)
Ie (2)
The I-V curve looks more rounded. The I2-V curve is linear, but goes down fast.
N = 15.8E11
Te = 3.65 eV
Te = 10.4 eV
Effect of auxiliary electrode 2: with electrode
-0.020
0.000
0.020
0.040
0.060
0.080
0.100
0.120
-100 -80 -60 -40 -20 0 20V
I (A
)
0
10
20
30
40
50
60
-100 -80 -60 -40 -20 0 20V
I2 (m
A)2
Ii squared
Ii(OML)
0.01
0.1
1
10
100
-10 -5 0 5 10 15 20 25 30
V
I (m
A)
Ie
Ie(fit)
Ie (2)
I-V curve more normal.
n = 16.8E11
Te = 3.01 eV
The temperature is more normal, but the high-Te part still exists. Need a larger auxiliary electrode.
1000 W with a 5-mil probe
0
50
100
150
-100 -80 -60 -40 -20 0 20V
I2 (
mA
)2
Ii squared
Ii(OML)
File 110314_39
27.12 MHz1000W
15 mTorr
n= 27.4E11
0.01
0.1
1
10
100
0 5 10 15 20 25V
I (m
A)
Ie
Ie(fit)
Ie (0)
File 110314_39
27.12 MHz1000W
15 mTorr
Te=2.66 eV
Vs=31.1 V
The thinnest probe (125 m diam) gives I2-V curves that bend at high density.
There is no theory that predicts the curve shape.
This probe will glow in the discharge unless the sweep time is minimized.
We can use a thick probe and thin-sheath theory, but the discharge will be disturbed by the probe current.
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