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Starting point: Langmuir’s OML theory. No integration necessary; very simple formula for ion current. This requires very small R p / l D , so that there is no absorption radius. UCLA. Post-Langmuir probe theories - 1. Sheath, but no orbiting. UCLA. Post-Langmuir probe theories - 2. UCLA. - PowerPoint PPT Presentation
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Starting point: Langmuir’s OML theoryp
a
Vo
Rp
1/ 2
0
| |2i
ppT
eVI A ne
M
No integration necessary; very simple formula for ion current.
This requires very small Rp / D, so that there is no absorption radius.
UCLA
Post-Langmuir probe theories - 1
Sheath, but no orbiting
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Post-Langmuir probe theories - 2
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Post-Langmuir probe theories - 3
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Post-Langmuir probe theories - 4
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Probes in fully ionized plasmas
Experimental verification in Q-machine - 1
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Experimental verification in Q-machine - 2
Such nice exponentials were never seen again!
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Experimental verification in Q-machine - 3
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Problems in partially ionized, RF plasmas
• Ion currents are not as predicted
• Electron currents are distorted by RF
• The dc plasma potential is not fixed
Getting good probe data is much more difficult!
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Ion currents in an ICP discharge
0
1
2
3
4
-100 -80 -60 -40 -20 0 20V
I2 (
mA
)2
Data
OML, n = 3.45E11
ABR, n = 1.76E11
BRL, n = 5.15E11
They fit the OML theory, which is not applicable!
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Each theory yields a different density
Here
Rp / D
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The real density is close to thegeometric mean!
0
1
2
3
4
5
6
200 400 600 800 1000Prf (W)
De
nsity
(1
01
1 c
m-3
)
BRL
mWave
BRL*ABR
ABR
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Reason: collisions destroy orbiting
An orbiting ion loses its angular momentum in a charge-exchange collision and is accelerated directly to probe. Thus, the collected current is larger than predicted, and the apparent
density is higher than it actually is.
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This collisional effect has been verifiedSternovsky, Robertson, and Lampe, Phys. Plasmas 10, 300 (2003).Sternovsky, Robertson, and Lampe, J. Appl. Phys. 94, 1374 (2003).
Rp/D = 0.05 Rp/D = 0.26 Rp/D = 0.49
The extra ion current due to collisions is calculated and added to the OML current. The result agrees with measurements only for very low density (< 108 cm-3).
The theory is incomplete because the loss of orbiting ions is not accounted for. Also, there is no easy computer program.
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Summary: how to measure density with Isat
High density, large probe: use Bohm current as if plane probe. Ii does not really saturate, so must extrapolate to floating potential.
Intermediate Rp / D: Use BRL and ABR theories and take the geometric mean.
Small probe, low density: Use OML theory and correct for collisions.
Upshot: Design very thin probes so that OML applies. There will still be corrections needed for collisions.
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Problems in partially ionized, RF plasmas
• Ion currents are not as predicted
• Electron currents are distorted by RF
• The dc plasma potential is not fixed
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-20 -10 0 10 20 30Vp - Vs
Ele
ctro
n cu
rre
nt
Introduction: RF distortion of I-V trace - 1
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* V.A. Godyak, R.B. Piejak, and B.M. Alexandrovich, Plasma Sources Sci. Technol. 1, 36 (19920. I.D. Sudit and F.F. Chen, RF compensated probes for high-density discharges, Plasma Sources Sci. Technol. 3, 162 (1994)
Solution: RF compensation circuit*
0.239"0.094"Epoxy seal
10 pF capacitor
compensation electrode
coax
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Self-resonance of choke chains
0
50
100
150
200
250
300
350
400
1.0 1.5 2.0 2.5 3.0 3.5 4.0MHz
k
To get high impedance, self-resonance of chokes must be used. Chokes must be individually chosen because of
manufacturing variations.
0
50
100
150
200
250
1.0 1.5 2.0 2.5 3.0MHz
k
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A large compensation electrode helps
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What is the sheath capacitance as Vs oscillates?
A small RF oscillation will bring the probe from the Child-Langmuir sheath to the Debye sheath to electron saturation
0.00
0.02
0.04
0.06
-20 -15 -10 -5 0 5 10 15 20Vp
I e (
A)
Vs
Vp
h > 0 h < 0
Ideal OML curve
s p
Debye sheath
V0 V C-L
sheath
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Sheath capacitance: exact vs. C-L
0
5
10
15
20
25
30
35
40
0 1 2 3 4 5 6 7 8h
Csh
(pF
/cm
2)Exact
Approx.
C-L
Floating potential
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This is an extension of the work by Godyak: V.A. Godyak and N. Sternberg, Phys. Rev. A 42, 2299 (1990)
V.A. Godyak and N. Sternberg, Proc. 20th ICPIG, Barga, Italy, 1991, p. 661
Variation of Csh during an RF cycle
0
5
10
15
20
25
30
35
40
0 90 180 270 360 450 540 630 720wt (degrees)
Csh
(pF
/cm
2)
Exact
w. cutoff
No RF
Vrf = 10 V
0
5
10
15
20
25
30
35
40
0 90 180 270 360 450 540 630 720wt (degrees)
Csh
(pF
/cm
2)
Exact
w. cutoff
No RF
Vrf = 10 V
Large probe, which draws enough current to affect Vs.
A normal small probe, which goes into electron saturation.
Cylindrical effects will smooth over the dip.
These curves will give rise to harmonics!
UCLA
Problems in partially ionized, RF plasmas
• Ion currents are not as predicted
• Electron currents are distorted by RF
• The dc plasma potential is not fixed
UCLA
UCLA
-5.0E-05
0.0E+00
5.0E-05
1.0E-04
1.5E-04
2.0E-04
2.5E-04
3.0E-04
-20 0 20 40 60 80 100Volts
Am
ps
15 mTorr
3 mTorr
Mk2, short tube, 100W
-0.0001
0.0004
0.0009
0.0014
-100 -80 -60 -40 -20 0 20 40 60 80 100Vp
-I (
A)
Ideal OML curve
Peculiar I-V curves: not caused by RF
Potential pulling by probe
-0.0004
0.0000
0.0004
0.0008
0.0012
0.0016
0.0020
0.0024
0.0028
0.0032
-50 -40 -30 -20 -10 0 10 20 30 40 50Vp (V)
Ie (
A)
1
3
5
7
9
11
13
15
17
19
Vf (V
)
Ie(A)
Vf
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Curves taken with two probes, slowly, point by point
Apparatus: anodized walls, floating top plate
PUMP
antenna
probe21
35.5
10.5
5.4
1.9 MHz, 60-100W, 3-10 mTorr Ar
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Ceramic shaft
Direct verification of potential pulling
-0.0003
-0.0002
-0.0001
0.0001
0.0002
0.0003
-100 -75 -50 -25 0 25Volts
Am
ps
-50V
0V
10V
20V
30V
40V
50V
Vp EPN I-V curves as Vp on ChenA is varied
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Correcting for Vf shift gives better I-V curve
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-5.0E-04
0.0E+00
5.0E-04
1.0E-03
1.5E-03
2.0E-03
2.5E-03
3.0E-03
3.5E-03
-50 -40 -30 -20 -10 0 10 20 30 40 50Volts
Am
ps
Manual, Vf corrected
Manual, uncorrected
Hiden MKIU
Slow drift of probe currents: ions
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-0.0005
-0.0003
-0.0001
0.0001
0.0003
0.0005
0.0007
0.0009
0.0011
0.0013
0.0015
-100 -50 0 50Volts
Am
ps
10 mA scale
1 mA, scan 1
1 mA, scan 2
1 mA, scans 3&41mA curves drift, then settle to agree with 10mA curve
A scan takes 2-3 sec (200 points), and ~3 sec between scans.The time constant is very long.
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-5.0E-05
0.0E+00
5.0E-05
1.0E-04
1.5E-04
2.0E-04
2.5E-04
3.0E-04
3.5E-04
4.0E-04
4.5E-04
-100 -80 -60 -40 -20 0 20 40 60 80 100Volts
Am
ps
0129_02a
0129_02b
0129_02c
0129_02d
0129_02e
100W, 15mTorr
Slow drift of probe currents: electrons
The drift direction depends on the parking voltage between scans.The drift can continue for >10 sec.
Reason: the walls are charged through the probe
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• The only connection to ground is through the probe.
• The plasma potential has to follow Vp.
• Hence the capacitance of the insulating layer has to be charged.
CV = Q = I*t, t = CV/ I
C = R0Aw/d, Aw = 0.44 m, R ~ 3, d ~ 1 m
C ~ 10 F, V ~ 100 V, Ie ~ 2 mA
t ~ 0.5 sec
This is the right order of magnitude.
Slower drifts may be due to small leaks in the insulation.
Insertion of grounding plate close to probe
`
36.00
21.00
10.50
Port 2Port 1
Pump
Grounding plate
Antenna Not used
Permanentmagnets on
surface
Grounding plate
Port 2EPN in Z-drive
Port 11/4" probe in Wilson seal
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Grounding plate reduces change in Vf
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0
4
8
12
16
-50 -30 -10 10 30 50Vp (V)
Vf
(V)
100/9.7/IN
100/9.7/OUT
Watts/mTorr/Ground plate
0
2
4
6
8
10
12
-50 -40 -30 -20 -10 0 10 20 30 40 50Vp (V)
Vf
(V)
160/2.7/OUT
160/2.7/IN
Watts/mTorr/Ground plate
High pressure (9.7 mTorr)
Low pressure (2.7 mTorr)
But the I-V curves are about the same
-0.0005
0.0045
0.0095
0.0145
0.0195
0.0245
0.0295
0.0345
-50 -30 -10 10 30 50Volts
Am
ps
160/2.7/IN
160/2.7/OUT
100/9.7/IN
100/9.7/OUT
Watts/mTorr/Ground plate
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Compare with ideal OML curve
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-0.0005
0.0045
0.0095
0.0145
0.0195
0.0245
0.0295
0.0345
0.0395
0.0445
-30 -20 -10 0 10 20 30 40 50Volts
Am
ps
Ideal OML
Corrected data
Raw data
-0.0003
-0.0002
-0.0001
0.0000
0.0001
0.0002
0.0003
0.0004
0.0005
-50 -40 -30 -20 -10 0 10Volts
Am
ps
Ideal OML
Corrected data
Raw data
The ion part fits well.The electron part, after correcting for the Vf shift, fits the exponential region better, but still fails at saturation.
The remaining discrepancy must be due to inadequate RF compensation.
Applying +100V to probe suddenly
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e+
+e
ee
+
+
+ ++
+++
+
WA
LL
SOURCE
ee
ee Vs ~ Vs0
There is an initial transient, but a normal electron sheath at electron saturation should come to equilibrium in
several ion plasma periods (<< 1 msec).
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Normally, the probe current Ie is balanced by a slight adjustment of the electron current to the walls, Iew, via a small change in sheath drop.
Since Iew = Iiw, Vs should not change detectably if Ie << Iiw.
With a grounding plane, how can a probe affect Vs?
Let’s work out the numbers
Bohm current density: Ii = 0.5 neAwcs ( n = 2 x 1010 cm3, KTe = 1.6 eV)
Ion current to grounding plate (25 cm2) 8.5 mA
Electron saturation current at +100V = 25 mA (measured) (Same order of magnitude, within variations.)
Thus, at high Vp, ion loss is too small to balance electron loss.
BUT: Vs changes well before Ie reaches 25 mA
The ion flux to ground may be less than Bohm.
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If the probe draws excess electrons at the center, an ambipolar field will develop to drive ions faster to the wall. The density profile n(r) will change from essentially uniform to peaked.
The diffusion equation for a nearly spherical chamber is
2 22
2'' '
n D nD n r D n n
t r r rr
where D = Da, the ambipolar diffusion coefficient. The solution is
2 2
0 21
2 ( 1)( , ) sin exp
j
j
a j r jn r t n Dt
r j a a
The time constant for the lowest radial mode j = 1 is then
2 2/ 0.17 msecaa D
If no grounding plate, how long does it take for the ions to redistribute themselves?
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Time to change from uniform to peaked profile
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0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 3 6 9 12 15 18r (cm)
n/n 0
0.01
0.05
0.10
0.15
0.20
0.30
0.40
0.50
t (msec)
Thus, the time required for the ions to adjust to a new equilibrium is only about 1 msec or less.
A measured radial density profile
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0.0
0.2
0.4
0.6
0.8
1.0
0 5 10 15r (cm)
n / n
o
Length of probe tip
• The dwell time must be long enough for the sheath to come into equilibrium. This is several ion plasma periods (>100 nsec).
• The total sweep time must be << 1 msec, or the plasma potential will change.
• With very slow sweeps, Vs will change and must be monitored.
Conclusion: timing is critical
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Even a DC, point-by-point measured I-V curve may not be correct.
Too fast a scan: sheath not in equilibrium
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-1E-04
0E+00
1E-04
2E-04
3E-04
4E-04
5E-04
-100 -80 -60 -40 -20 0 20 40 60 80 100
Volts
Am
ps
Reverse scan
Forward scan
100W, 15mTorrDwell 10/10
Mk2-MKIU Test of effect of dwell
.998 Alumina
Alumina or pyrex
Copper
Tungsten
Epoxy
.005 Tungsten rod
.094 x .063 x 1 1/81
.050 x .020 x 3/82
.001 Nickel.030 Tungsten
.250 x .188 x 5/83
.060 OD vacuum slip joints4
Spot weld
Soft solder Vacuum epoxy6 .125 x .040 x 1/4 double hole5
(1) Coors #65682(2) Coors #65650(3) Coors #65658(4) Ceramaseal #11288-02-X(5) Coors #65673(6) K.J. Lesker #KL-320K(7) Coors #65660(8) Coors 65657 or pyrex tube For large chokes, must use #65658, specially ordered to fit into #65660
ChenB probe with reference electrode
Nickel
Auxiliary electrode: Nickel foil is wrapped around ceramic tube and spotwelded along length. Tabs are then cut, and the rest wrapped tightly to cylinder. A small tab is left for spotwelding to .030 tungsten rod.
Compensation electrode
Reference electrode
.375 x .250 x 187
.219 x .156 x 228
.250 x .188 x 1/43
New, as of 1/1/2005
.998 Alumina
Alumina or pyrex
Copper
Tungsten
Epoxy
.005 Tungsten rod
.094 x .063 x 1 1/81
.050 x .020 x 3/82
.001 Nickel.030 Tungsten
.250 x .188 x 5/83
.060 OD vacuum slip joints4
Spot weld
Soft solder Vacuum epoxy6 .125 x .040 x 1/4 double hole5
(1) Coors #65682(2) Coors #65650(3) Coors #65658(4) Ceramaseal #11288-02-X(5) Coors #65673(6) K.J. Lesker #KL-320K(7) Coors #65660(8) Coors 65657 or pyrex tube For large chokes, must use #65658, specially ordered to fit into #65660
ChenB probe with reference electrode
Nickel
Auxiliary electrode: Nickel foil is wrapped around ceramic tube and spotwelded along length. Tabs are then cut, and the rest wrapped tightly to cylinder. A small tab is left for spotwelding to .030 tungsten rod.
Compensation electrode
Reference electrode
.375 x .250 x 187
.219 x .156 x 228
.250 x .188 x 1/43
New, as of 1/1/2005
Hence we must use a dc reference electrode.
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HERE
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