Transcript Top Ten List

Abstract
•
Langmuir probes in low-density RF plasmas
sometimes show peculiar I-V characteristics with
no electron saturation. This is due to the space
potential Vs changing with probe potential. This
occurs on an ion time scale, but it also means
that the ion flux to the walls is impeded by an
unknown mechanism. To avoid this, the curve
must be swept faster than Vs can change. A
mysterious ion feature is also observed.
The speed at which data are taken matters!
Apparatus
5.4
antenna
10.5
probe
21
35.5
PUMP
1.9 MHz, 60-100W, 3-10 mTorr Ar
Probes (1)
Epoxy seal
0.239"
0.094"
compensation electrode
10 pF capacitor
coax
Probes (2)
Choke chain impedances
400
350
300
k
250
200
150
100
50
0
1.0
1.5
2.0
2.5
3.0
MHz
3.5
4.0
4.5
5.0
Two samples of the Hiden
chokes for 2 MHz.
The
straight line is the Z of a nonresonant 1 mH choke. Both
probes
have
also
a
compensation electrode to
drive the probe tip.
300
ChenA choke chain
250
Impedance of the Chen A
probe. Chokes to resonate
at 2w could not be found.
k
200
150
100
50
0
1
2
3
MHz
4
5
6
Example of anomalous I - V curve
0.0004
Electron current (A)
0.0003
0.0002
0.0001
0.0000
-0.0001
-100
-75
-50
-25
0
Probe voltage (V)
25
50
75
100
There is no exponential part, and Ie does not saturate.
Measurement of Vf
Port 2
EPN in Z-drive
Port 1
1/4" probe in Wilson seal
Grounding plate
Antenna
Not used
To measure changes in
floating potential Vf, we
used a second probe
close to the first. Though
the
chamber
was
10K
grounded, a grounding
plate could be0.1
inserted
1 M to
mF
put the ground closer.
10.50
Port 2
21.00
Port 1
`
Grounding plate
36.00
Pump
9 M
Permanent
magnets on
surface
10X probe
1 M
Measurement of I-V curves
mA
DVM
DC
Hiden electronics
Although many systems could be
used, the simplest, error-free,
method was to read off mA
directly from a small DVM, taking
date point-by-point.
We also swept the I-V curves
automatically with either the
Hiden ESP Mk2 or the newer
ESPion units. All combinations of
three probe types and three
measurement systems were tried.
Change of Vf with Vp
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
Vf (V)
0.0020
50
This shows that Vf (right scale) rides up with probe voltage Vp.
By adjusting the right-hand scale, the red curve can be made
to resemble the probe characteristic.
Corrected I-V curve
3.5E-03
3.0E-03
Manual, Vf corrected
2.5E-03
Manual, uncorrected
Hiden MKIU
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
50
By correcting for the shift if Vs (as found from Vf), one obtains a more
reasonable curve. Saturation cannot be reached. The red curve is taken
with a fast sweep, which suffers from only part of the Vs shift.
Exact OML equation
I  Ap ejr F ,
F
½
 KT 
jr  n 

 2 m 
s
erf(½ )  e erfc(   )½ , where
a
q (V p  Vs )
s2

,  2

2
KT
s a
The exact Tonks-Langmuir Orbital
Motion Limited probe theory.
Note that a sheath thickness s
has to be assumed.
This form has to be used for
electron saturation.
1/ 2
IONS:
for ions, a very good
approximation independent of KTe
can be made.
ELECTRONS: This is for the
transition (exponential) region.
 (Vs  V p ) 
Ii (mA)  7.06n11Ap 

AtomicNo
.


½
Ie  2.68  1014 nApTeV
e
(V p Vs ) / TeV
Comparison with experiment
4E-04
3E-04
First, the density is
found by fitting the ion
current.
-I (A)
2E-04
1E-04
0E+00
-1E-04
-2E-04
-3E-04
-100
-80
-60
-40
-20
0
20
Vp
0.015
0.013
The Vf -corrected data
then give a short
transition region from
which KTe can be
obtained.
-I (A)
0.011
0.009
0.007
0.005
0.003
0.001
-0.001
-20
-15
-10
-5
0
Vp
5
10
15
20
Electron saturation
0.0445
s / Rp
0.0395
30
10
5
Data
Raw data
0.0345
Amps
0.0295
0.0245
0.0195
0.0145
0.0095
0.0045
-0.0005
-30
-20
-10
0 Volts 10
20
30
40
50
Even the corrected data cannot reproduce electron saturation. This is
probably due to inadequate RF compensation. Note that the OML
theory is independent of s / Rp as long as it is > 5 or 10.
Why does Vp 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.
The numbers don't work out
Area of chamber walls = 4400 cm2
Bohm current density: Ii = 0.5 neAwcs ( n = 2 x 1010 cm3, KTe = 1.6 eV)
Ion current to walls: Ii(wall) = 1.5A. But suppose n there is 0 for now.
Ion current to grounding plate (25 cm2) 8.5 mA
By quasineutrality,
this is also equal to the electron current to the plate.
Electron saturation current at +100V: 3.2 mA (calc.), 25 mA (measured)
Difference is due to sheath expansion (s /a  8).
Thus, Ii to the plate cannot balance Ie to the probe, even if no electrons are
lost to the wall.
BUT: 1) Why are there no ions lost at the chamber wall?
2) Why is Vs changing well before Vp = +100V?
There seems to be a transport barrier at the grounded walls.
Speed of ion response
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 is (for a nearly spherical chamber)
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
Change of density profile
1.2
In theory, a probe drawing a
large Ie can cause n(r) to be
peaked after about 1 msec.
1.0
t (msec)
0.8
0.05
0.6
0.10
0.15
0.4
Below are two measurements
of the density profile, but not
necessarily connected with
this effect.
0.20
0.30
0.2
0.40
0.50
0.0
0
3
6
9
r (cm)
12
15
18
1.0
1.2
1.0
0.8
Length of probe tip
0.8
0.6
n / no
n / n0
n/n 0
0.01
0.6
0.4
0.4
Length of probe tip
Note that the center is 3.4 cm off from the visual center (dashed
line). This shift is not due to the grounding plate, which was
removed in this run.
0.2
0.2
0.0
0.0
-5
0
5
r (cm)
10
15
0
5
r (cm)
10
15
Effect of grounding plate
0.0245
0.0245
Corrected
Hi-p OUT
0.0195
0.0145
Amps
Amps
0.0145
0.0095
0.0095
0.0045
0.0045
-0.0005
-0.0005
-50
-30
-10
Volts
10
30
50
-50
0.0345
-30
-10
Volts
10
30
50
0.0345
0.0295
Corrected
Lo-p OUT
0.0295
0.0245
Corrected
Lo-p IN
0.0245
0.0195
Amps
Amps
Corrected
Hi-p IN
0.0195
0.0145
0.0095
0.0195
0.0145
0.0095
0.0045
0.0045
-0.0005
-50
-30
-10
10
Volts
30
50
-0.0005
-50
-30
-10
10
Volts
30
50
Explanation of test of potential pulling effect
OUT means that the grounding plate is out, and the chamber
wall is the nearest ground.
IN means that the grounding plate is in, and is a ground plane
only 3 cm away from the probe.
It is seen that the difference between the raw curves and those
corrected for potential pulling is smaller with a better ground, as
expected.
Hi-p means 10 mTorr; Lo-p means 3 mTorr.
It is seen that at lower pressure, there is better contact with
ground, as expected, since the ion diffusion is faster.
Conclusions
•
•
•
•
•
Electron saturation is not possible because Vs rides up
with Vp.
When Ie to the probe exceeds Ii to the wall, the potential
and density profiles change to drive ions faster to the wall.
It takes about 1 msec for the profiles to change. A better
I-V curve can be obtained if it is swept in a shorter time.
This should not happen unless ion current to ground is
somehow blocked.
This effect causes the peculiar I-V curves in lo-n ICPs,
but it does not affect the values of n and Te obtained.
An anomalous ion feature
0.0012
A very large ion bump often
occurs at large negative Vp.
0.0010
0.0008
Amps
0.0006
These curves were taken using
the Hiden ESP Mark2 system.
0.0004
0.0002
0.0000
-0.0002
-0.0004
-100
-80
-60
Volts
-40
-20
0
20
This feature changes on the 510 sec time scale between
scans, and it depends on the
termination resistance R. R is
250  on the 10 mA scale and
2500  on the 1 mA scale. The
steady state agrees with the 10mA curve.
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 veritable mystery!
0.0012
0.0012
0.0010
0.0009
0420_06a
0420_06b
0420_06c
0420_06d
Vp =10
0.0006
0.0006
Amps
Amps
0.0008
Vp = 0
10 mA scale
1 mA scale
0.0004
0.0003
0.0002
0.0000
0.0000
-0.0002
-100
-50
Volts
0
50
-0.0003
-100
-50
Volts
0
50
0.0012
Vp = 20
0.0009
The anomalous ion feature
depends on the voltage Vp on
another probe nearby. But...
the slow change in time can
only be caused by probe
contamination.
0420_07a
0420_07b
0420_07c
0420_07d
Amps
0.0006
0.0003
0.0000
-0.0003
-100
-50
Volts
0
50
Both probes have insulating shafts, and the nearest ground is at the walls