Transcript No Slide Title

Starting point: Langmuir’s OML theory
p
Vo
a
Rp
1/ 2
2  | eV p | 
I 
 Ap ne


Ti  0
  M 
No integration necessary; very simple formula for ion current.
This requires very small Rp / lD, so that there is no absorption
radius.
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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
4
Data
OML, n = 3.45E11
ABR, n = 1.76E11
BRL, n = 5.15E11
2
2
I (mA)
2
3
1
0
-100
-80
-60
-40
V
-20
0
20
They fit the OML theory, which is not applicable!
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Each theory yields a different density
Here
  Rp / lD
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The real density is close to the
geometric mean!
6
-3
cm )
5
Density (10
11
4
BRL
mWave
BRL*ABR
ABR
3
2
1
0
200
400
600
800
1000
Prf (W)
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Reason: collisions destroy orbiting
An orbiting ion loses its angular momentum in a chargeexchange 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 verified
Sternovsky, Robertson, and Lampe, Phys. Plasmas 10, 300 (2003).
Sternovsky, Robertson, and Lampe, J. Appl. Phys. 94, 1374 (2003).
Rp/lD = 0.05
Rp/lD = 0.26
Rp/lD = 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 /
lD: 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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Electron current
Introduction: RF distortion of I-V trace - 1
-20
-10
0
10
20
30
Vp - Vs
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Solution: RF compensation circuit*
Epoxy seal
0.239"
0.094"
coax
compensation electrode
10 pF capacitor
* 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)
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Self-resonance of choke chains
400
250
350
200
300
k
150
100
k
250
50
200
0
1.0
1.5
2.0
MHz
150
2.5
3.0
100
50
0
1.0
1.5
2.0
2.5
MHz
3.0
3.5
To get high impedance, self-resonance of chokes must be
used. Chokes must be individually chosen because of
manufacturing variations.
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4.0
A large compensation electrode helps
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What is the sheath capacitance as Vs oscillates?
0.06
V
V0
C-L
sheath
h<0
h>0
Debye
sheath
Ideal OML curve
Ie (A)
0.04
s
p
Vs
0.02
Vp
0.00
-20
-15
-10
-5
Vp
0
5
10
15
20
A small RF oscillation will bring the probe from the Child-Langmuir
sheath to the Debye sheath to electron saturation
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Sheath capacitance: exact vs. C-L
40
35
Exact
Approx.
C-L
Csh (pF/cm 2 )
30
25
Floating
potential
20
15
10
5
0
0
1
2
3
4
h
5
6
7
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
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8
Variation of Csh during an RF cycle
40
Exact
w. cutoff
Vrf = 10 V
35
2
Csh (pF/cm )
30
25
Large probe, which
draws enough current
to affect Vs.
No RF
20
15
10
5
0
0
90
180
270
360
450
wt (degrees)
540
630
720
These curves will give
rise to harmonics!
40
Exact
w. cutoff
Vrf = 10 V
35
A normal small probe,
which goes into
electron saturation.
2
Csh (pF/cm )
30
25
No RF
20
15
Cylindrical effects will
smooth over the dip.
10
5
0
0
90
180
270
360
450
wt (degrees)
540
630
720
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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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Peculiar I-V curves: not caused by RF
3.0E-04
0.0014
0.0009
-I (A)
2.5E-04
Mk2, short tube, 100W
Amps
2.0E-04
1.5E-04
Ideal OML
curve
0.0004
-0.0001
-100
-80
-60
-40
-20
0
20
40
60
80
100
Vp
15 mTorr
3 mTorr
1.0E-04
5.0E-05
0.0E+00
-5.0E-05
-20
0
20
40
Volts
60
80
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100
Potential pulling by probe
0.0032
19
Ie(A)
Vf
0.0028
0.0024
17
15
0.0016
11
0.0012
9
0.0008
7
0.0004
5
0.0000
3
-0.0004
1
Ie (A)
13
-50
-40
-30
-20
-10
0
Vp (V)
10
20
30
40
50
Curves taken with two probes, slowly, point by point
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Vf (V)
0.0020
Apparatus: anodized walls, floating top plate
5.4
antenna
10.5
probe
21
35.5
Ceramic shaft
PUMP
1.9 MHz, 60-100W, 3-10 mTorr Ar
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Direct verification of potential pulling
0.0003
Vp
Amps
0.0002
0.0001
-0.0001
EPN I-V curves as Vp on ChenA is varied
-50V
0V
10V
20V
30V
40V
50V
-0.0002
-0.0003
-100
-75
-50
Volts
-25
0
25
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Correcting for Vf shift gives better I-V curve
3.5E-03
3.0E-03
Manual, Vf corrected
Manual, uncorrected
Hiden MKIU
2.5E-03
Amps
2.0E-03
1.5E-03
1.0E-03
5.0E-04
0.0E+00
-5.0E-04
-50
-40
-30
-20
-10
0
Volts
10
20
30
40
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50
Slow drift of probe currents: ions
0.0015
0.0013
0.0007
10 mA scale
1 mA, scan 1
1 mA, scan 2
1 mA, scans 3&4
0.0005
1mA curves drift, then settle
to agree with 10mA curve
0.0011
Amps
0.0009
0.0003
0.0001
-0.0001
-0.0003
-0.0005
-100
-50
Volts
0
50
A scan takes 2-3 sec (200 points), and ~3 sec between scans.
The time constant is very long.
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Slow drift of probe currents: electrons
4.5E-04
4.0E-04
3.5E-04
Amps
3.0E-04
2.5E-04
100W, 15mTorr
0129_02a
0129_02b
0129_02c
0129_02d
0129_02e
2.0E-04
1.5E-04
1.0E-04
5.0E-05
0.0E+00
-5.0E-05
-100
-80
-60
-40
-20
0
Volts
20
40
60
80
100
The drift direction depends on the parking voltage between scans.
The drift can continue for >10 sec.
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Reason: the walls are charged through the probe
• 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 = R0Aw/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.
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Insertion of grounding plate close to probe
Antenna
Not used
10.50
Port 2
21.00
Port 1
`
Grounding plate
Permanent
magnets on
surface
36.00
Pump
Port 2
EPN in Z-drive
Grounding plate
Port 1
1/4" probe in Wilson seal
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Grounding plate reduces change in Vf
16
Watts/mTorr/Ground plate
100/9.7/IN
100/9.7/OUT
Vf (V)
12
High pressure (9.7 mTorr)
8
4
0
-50
-30
-10
Vp (V)
10
30
50
12
Watts/mTorr/Ground plate
10
160/2.7/OUT
160/2.7/IN
Vf (V)
8
Low pressure (2.7 mTorr)
6
4
2
0
-50
-40
-30
-20
-10
0
Vp (V)
10
20
30
40
50
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But the I-V curves are about the same
0.0345
Watts/mTorr/Ground plate
0.0295
160/2.7/IN
160/2.7/OUT
100/9.7/IN
100/9.7/OUT
Amps
0.0245
0.0195
0.0145
0.0095
0.0045
-0.0005
-50
-30
-10
10
30
Volts
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50
Compare with ideal OML curve
0.0005
0.0445
0.0395
0.0004
Ideal OML
Corrected data
Raw data
0.0003
0.0345
0.0295
Amps
0.0002
Amps
Ideal OML
Corrected data
Raw data
0.0001
0.0245
0.0195
0.0000
0.0145
-0.0001
0.0095
-0.0002
0.0045
-0.0003
-0.0005
-50
-40
-30
Volts
-20
-10
The ion part fits well.
0
10
-30
-20
-10
0
Volts 10
20
30
40
50
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.
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Applying +100V to probe suddenly
SOURCE
+
e
+
e
+ +
+
+
+ + +
e ee
e
e
+
e
+
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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With a grounding plane, how can a probe affect Vs?
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.
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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 no grounding plate, how long does it take
for the ions to redistribute themselves?
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
n
D 
n 
2 

 D2n  2  r 2   D  n '' n ' 
t
r 

r  r r 
where D = Da, the ambipolar diffusion coefficient. The solution is
2a
n(r , t )  n0
 r

 j 2 2 
(1) j
 j r 
sin 
 exp   2 Dt 
j
 a 
 a

j 1

The time constant for the lowest radial mode j = 1 is then
  a 2 /  2 Da  0.17 m sec
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Time to change from uniform to peaked profile
1.2
1.0
t (msec)
0.8
n/n 0
0.01
0.05
0.6
0.10
0.15
0.4
0.20
0.30
0.2
0.40
0.50
0.0
0
3
6
9
r (cm)
12
15
18
Thus, the time required for the ions to adjust to a
new equilibrium is only about 1 msec or less.
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A measured radial density profile
1.0
0.8
n / no
0.6
0.4
Length of probe tip
0.2
0.0
0
5
r (cm)
10
15
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Conclusion: timing is critical
• 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.
Even a DC, point-by-point measured I-V curve
may not be correct.
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Too fast a scan: sheath not in equilibrium
5E-04
4E-04
Mk2-MKIU
Test of effect of dwell
100W, 15mTorr
Dwell 10/10
Reverse scan
Forward scan
Amps
3E-04
2E-04
1E-04
0E+00
-1E-04
-100
-80
-60
-40
-20
0
Volts
20
40
60
80
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100
Hence we must use a dc reference electrode.
ChenB probe with reference electrode
3
.250 x .188 x 1/4
.375 x .250 x 18
3
7
.250 x .188 x 5/8
.001 Nickel
.030 Tungsten
1
.094 x .063 x 1 1/8
.219 x .156 x 22
4
.060 OD vacuum slip joints
2
.050 x .020 x 3/8
.005 Tungsten rod
Compensation electrode
Spot weld
HERE
Reference electrode
Soft solder
6
Vacuum epoxy
.998 Alumina
ChenB
probe with reference electrode
Alumina or pyrex
3
.250 x .188 x 1/4
.375 x .250 x 18
3
Copper
.001 Nickel
.030 Tungsten
1
.094 x .063 x 1 1/8
.005 Tungsten rod
7
.250 x .188 x 5/8
Tungsten
4
.060 OD vacuum slip joints
.219 x .156 x 22
8
2
.050 x .020 x 3/8
Epoxy
Compensation electrode
Nickel
Spot weld
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.
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
.125 x .040 x 1/4
5
double hole
Coors #65682
Coors #65650
Coors #65658
Ceramaseal #11288-02-X
Coors #65673
K.J. Lesker #KL-320K
Coors #65660
Coors 65657 or pyrex tube
For large chokes, must use #65658,
specially ordered to fit into #65660
Reference electrode
Soft solder
6
.125 x .040 x 1/4
5
double hole
(1)
(2)
(3)
(4)
(5)
(6)
Coors #65682
Coors #65650
Coors #65658
Ceramaseal #11288-02-X
Coors #65673
K.J. Lesker #KL-320K
Vacuum epoxy
New, as of 1/1/2005
.998 Alumina
Alumina or pyrex
Copper
Tungsten
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8