Transcript Slide 1

Cylindrical probes are best
high bias
Plane probes have undefined
collection area.
low bias
If the sheath area stayed the
same, the Bohm current
would give the ion density.
A guard ring would help.
A cylindrical probe needs
only a centering spacer.
A spherical probe is hard
to make, though the theory
is easier.
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In RF plasmas, the probe is more complicated!
ChenB probe tip detail
3
.250 x .188 x 5/8
.001 Nickel
.030 Tungsten
1
.094 x .063 x 1 1/8
.005 Tungsten rod
4
.060 OD vacuum slip joints
2
.050 x .020 x 3/8
Spot weld
Solder
6
.125 x .040 x 1/4
5
double hole
(1)
(2)
(3)
(4)
Coors #65682
Coors #65650
Coors #65658
Ceramaseal #11288-02-X
Vacuum epoxy
.998 Alumina
Alumina or pyrex
Copper
Tungsten
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Parts of a probe’s I–V curve
Vf = floating potential
Vs = space (plasma) potential
Isat = ion saturation current
Iesat = electron saturation current
I here is actually –I (the electron
current collected by the probe
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The electron characteristic
0.10
0.08
Iesat
Knee
I (A)
0.06
0.04
Exponential
0.02
0.00
-0.02
0
5
10
15
V
20
25
30
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The transition region (semilog plot)
100.0
Ie, w/o ions
Ie (fit)
Ie, raw
I (mA)
10.0
1.0
0.1
0
5
Vp
10
15
20
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The exponential plot gives KTe
(if the electrons are Maxwellian)
I e  I es e
e(V p Vs ) / KTe )
I es eAne v / 4
æöKTe
ene A ç÷
èø2p m
1/ 2
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Ion saturation current
0.020
0.015
This gives the plasma density the best.
However, the theory to use is complicated.
I (A)
0.010
0.005
0.000
-0.005
-100
-80
-60
-40
-20
0
20
V
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Thin sheaths: can use Bohm current
Sheath edge
Probe tip
Ii = necs
I B   neAcs , cs  ( KTe / M )
½
  0.5, but is larger for thicker sheaths
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Floating potential (I = 0)
½
Isat  I B  ½neAcs , cs  ( KTe / M )
Ie  Ies exp[e(Vp  Vs )/ KTe )]
Set Isat = Ie. Then Vp = Vf, and
KTe æ 2M ö
V f  Vs 
ln ç
÷
2e è p m ø
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Electron saturation usually does not occur
0.10
Reasons:
0.08
sheath expansion
collisions
magnetic fields
Iesat
Knee
I (A)
0.06
Ideal for plane
0.04
Exponential
0.02
0.00
-0.02
0
5
10
15
V
20
25
30
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Extrapolation to find “knee” and Vs
4E-03
Vs?
Electron current
3E-03
2E-03
1E-03
0E+00
-1E-03
-10
0
10
20
Probe voltage
30
40
50
60
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Vs at end of exponential part
0.08
dIe/dVp = 0 or
2
0.06
2
d Ie/dVp = 0
Ie (A)
0.04
0.02
0.00
-0.02
-10
-5
0
5
Vp
10
15
20
25
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Ideal minimum of dI/dV
2
0
-2
dI / dV
-4
-6
-8
-10
-12
-14
0
5
10
V
15
20
25
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Finally, we can get Vs from Vf
KTe æ 2M ö
V f  Vs 
ln ç
÷
2e è p m ø
Vf and KTe are more
easily measured.
6
5
However, for
cylindrical probes,
the normalized Vf is
reduced when the
sheath is thick.
Vf /KT e
4
3
2
1
0
0.1
1
Rp / l D
10
100
1000
F.F. Chen and D. Arnush, Phys.
Plasmas 8, 5051 (2001).
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Two ways to connect a probe
v
Cs
PROBE
Resistor on the ground side does
not see high frequencies because
of the stray capacitance of the
power supply.
R
Floating
milliammeter
PROBE
Resistor on the hot side requires a
voltage detector that has low
capacitance to ground. A small
milliammeter can be used, or a
optical coupling to a circuit at
ground potential.
R
v
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RF Compensation: the problem
B
e
e
e
e
As electrons oscillate in the RF field, they hit the walls and
cause the space potential to oscillate at the RF frequency. In
a magnetic field, Vs is ~constant along field lines, so the
potential oscillations extend throughout the discharge.
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E le ctro n current
Effect of Vs osc. on the probe curve
-20
-10
0
10
20
30
Vp -Vs
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The I-V curve is distorted by the RF
0.5
T e = 3 eV
Helium
0.4
Electron C urrent
V rf V)
0
0.3
5
10
0.2
15
0.1
0.0
-0.1
-20
-15
-10
-5
eV/KT e
0
5
10
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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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Effect of auxiliary electrode
The chokes have enough impedance when the floating
potential is as positive as it can get.
The Chen B probe
ChenB probe tip detail
3
.250 x .188 x 5/8
.001 Nickel
.030 Tungsten
1
.094 x .063 x 1 1/8
.005 Tungsten rod
4
.060 OD vacuum slip joints
2
.050 x .020 x 3/8
Spot weld
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
.998 Alumina
Alumina or pyrex
Copper
Tungsten
Epoxy
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.
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Sample probes (3)
A commercial probe with replaceable tip
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Sample probes (1)
A carbon probe tip has less secondary emission
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Example of choke impedance curve
1000
Probe 70103
900
2a = .010" = .0254 cm, L = 0.95 cm, R = 12.6 è
800
700
Z (k è )
600
500
400
300
200
100
0
10
15
MHz
20
25
30
The self-resonant impedance should be above ~200KW at the RF frequency,
depending on density. Chokes have to be individually selected.
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Equivalent circuit for RF compensation
The dynamic sheath capacitance Csh has been calculated in
F.F. Chen, Time-varying impedance of the sheath on a probe in an RF plasma,
Plasma Sources Sci. Technol. 15, 773 (2006)
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Electron distribution functions
If the velocity distribution is isotropic, it can be found by
double differentiation of the I-V curve of any convex probe.


n   4p c f (c)dc   g (c)dc
0
2
0
d2 j
2e
g (c)  8 2 , where   (V p  Vs )
m
d
(A one-dimensional distribution to a flat probe requires only one differentiation)
This applies only to the transition region (before any saturation effects) and
only if the ion current is carefully subtracted.
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Examples of non-Maxwellian distributions
EEDF by Godyak
A bi-Maxwellian distribution
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Example of a fast electron beam
The raw data
After subtracting the ion current
After subtracting both the
ions and the Maxwellian
electrons
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Cautions about probe EEDFs
• Commercial probes produce smooth EEDF curves by
double differentiations after extensive filtering of the data.
• In RF plasmas, the transition region is greatly altered by
oscillations in the space potential, giving it the wrong shape.
• If RF compensation is used, the I-V curve is shifted by
changes in the floating potential. This cancels the detection
of non-Maxwellian electrons!
F.F. Chen, DC Probe Detection of Phased EEDFs in RF Discharges,
Plasma Phys. Control. Fusion 39, 1533 (1997)
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Summary of ion collection theories (1)
Langmuir’s Orbital Motion Limited (OML) theory
Integrating over a Maxwellian
distribution yields
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Langmuir’s Orbital Motion Limited (OML) theory (2)
For s >> a and small Ti, the formula becomes very simple:
I2 varies linearly with Vp (a parabola).
This requires thin probes and low densities (large lD).
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Langmuir’s Orbital Motion Limited (OML) theory (3)
4
Ii squared
Ii(OML)
2
2
I (mA)
2
3
1
0
-100
-80
-60
-40
Vp
-20
0
20
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Summary of ion collection theories (2)
The Allen-Boyd-Reynolds (ABR) theory
SHEATH
PROBE
The sheath is too thin for OML but too thick for vB method.
Must solve for V(r).
The easy way is to ignore angular momentum.
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Allen, Boyd, Reynolds theory: no orbital motion
d æ d ö
1/ 2



J



e
0
ç
÷
d è d ø
This equation for cylinders was
given by Chen (JNEC 7, 47 (65)
with numerical solutions.
Absorption radius
Allen, J.E., Boyd, R.L.F., and Reynolds, P.
1957 Proc. Phys. Soc. (London) B70, 297
ABR curves for cylinders, Ti = 0
p = Rp/lD, p = Vp/KTe
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Summary of ion collection theories (3)
The Bernstein-Rabinowitz-Laframboise (BRL) theory
The problem is to solve Poisson’s equation for V(r)
with the ion density depending on their orbits.
Those that miss the probe contribute to ni twice.
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The Bernstein-Rabinowitz-Laframboise (BRL) theory (2)
The ions have a monoenergetic, isotropic distribution at infinity. Here b is Ei/KTe.
The integration over a Maxwellian ion distribution is extremely difficult but
has been done by Laframboise.
F.F. Chen, Electric Probes, in "Plasma Diagnostic Techniques", ed. by R.H. Huddlestone
and S.L. Leonard (Academic Press, New York), Chap. 4, pp. 113-200 (1965)
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The Bernstein-Rabinowitz-Laframboise (BRL) theory (3)
Example of Laframboise curves: ion current vs. voltage for various Rp/lD
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Summary of ion collection theories (4)
Improvements to the Bohm-current method
0 .0 3
B R L the o ry
 p = 20
L ine a r fit
Te = 3 e V , n = 4 x 1 0
B o hm c urre nt
12
cm
-3
I (m A)
Vf
Vs
0 .0 0
I   neApvB
 = 0 .7 4
-0 .0 3
-1 6 0
-1 4 0
-1 2 0
-1 0 0
-8 0
V
-6 0
-4 0
-2 0
0
20
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Variation of  with p
2.0
Evaluated at Vf - 25KTe
Extrapolated to Vf

1.5
1.0
0.5
0.0
0
10
20
 p  R p / lD ,

30
40
50
2
lD
  0 KTe / ne2
I B   neAcs , cs  ( KTe / M )½ ,   0.5
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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Parametrization of Laframboise curves
10
1


4
(A
1
1
B 4
)
(C
Rp/lD
D 4
)
0
1
2
I / Io
2. 5
3
1
Fit
4
5
10
50
1 00
0
0
1

10
100
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The fitting formulas
BRL
ABR
F.F. Chen, Langmuir probe analysis for highdensity plasmas, Phys. Plasmas 8, 3029 (2001)
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Comparison of various theories (1)
6
BRL
mWave
BRL*ABR
ABR
4
Density (10
11
-3
cm )
5
3
2
1
0
200
300
400
500
600
Prf
700
800
900
1000
The geometric mean between BRL and ABR gives approximately the right density!
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Comparison of various theories (2)
4
Data
OML, n = 3.45E11
ABR, n = 1.76E11
I2 (mA)2
3
BRL, n = 5.15E11
2
1
0
-100
-80
-60
-40
V
-20
0
20
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Comparison of various theories (3)
Density increases from
(a) to (d)
ABR gives more current
and lower computed
density because orbiting
is neglected.
BRL gives too small a
current and too high a
density because of
collisions.
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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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Including collisions makes the I - V curve
linear and gives the right density
Z. Sternovsky, S. Robertson, and M. Lampe, Phys. Plasmas 10, 300 (2003).\
However, this has to be computed case by case.
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The floating potential method for measuring ion density
cs
Vf
d
s
2
d  (2 f )3 / 4 lD  1.018 f 3 / 4lD
3
(Child-Langmuir law)
Unexpected success of the C-L (Vf) method
6
Ne(MW)
Ni(CL)
Ni(ABR)
Ne,sat
n (1011cm-3 )
5
4
10 mTorr
3
2
1
0
300
450
600
Pr f (W)
750
900
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
2.5E-04
0.0009
Amps
2.0E-04
1.5E-04
-I (A)
Mk2,
short
tube, 100W
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
Probe electron current can pull Vs up
if the chamber is not grounded
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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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
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25
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
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
Recent data in Medusa 2 (compact)
Probe outside, near wall
0.30
10.0
Ii squared
Ii(OML)
0.25
Ie
Ie(fit)
Ie (2)
1.0
I (mA)
0.15
2
I (mA)
2
0.20
0.1
0.10
0.0
0.05
0.00
-100
0.0
-80
-60
-40
V
-20
n = 0.81  1011 cm-3
0
20
-6
-1
4
V
Te = 1.37 eV
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9
Recent data in Medusa 2 (compact)
Probe under 1 tube, 7” below, 3kW, 15 mTorr
3.5
Ii squared
Ii(OML)
3.0
2
1.5
I (mA)
2.0
2
2.5
1.0
0.5
n = 3.12  1011 cm-3
0.0
-100
-80
-60
-40
-20
0
V
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Recent data in Medusa 2 (compact)
100.0
Ie
Ie(fit)
Ie (2)
I (mA)
10.0
1.0
Te (bulk) = 1.79 eV
0.1
0.0
-20
-15
-10
-5
V
0
5
10
Probe under 1 tube, 7” below,
3kW, 15 mTorr
10.00
Ie
Ie(fit)
Ie (2)
I (mA)
1.00
Te (beam) = 5.65 eV
0.10
0.01
0.00
-20
-15
-10
-5
V
0
5
10
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Other important probes not covered here
• Double probes (for ungrounded plasmas)
• Hot probes (to get space potential)
• Insulated probes (to overcome probe coating)
• Surface plasma wave probes (to overcome coating)
Conclusion
There are many difficulties in using this simple
diagnostic in partially ionized RF plasmas, especially
magnetized ones, but the problems are understood and
can be overcome. One has to be careful in analyzing
probe curves!
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Conclusion
There are many difficulties in using this simple
diagnostic in partially ionized RF plasmas,
especially magnetized ones, but the problems are
understood and can be overcome. One has to be
careful in analyzing probe curves!
UCLA