Download Retarding Field Energy Analyzer Measurements of Ion Velocity

Retarding Field Energy Analyzer Measurements of Ion Velocity Distributions in a
Helicon Plasma Source
Zane Harvey, Alex Hansen, William S. Przybysz, and Earl E. Scime Department of Physics, West Virginia University
Abstract
RFEA Theory and Analysis
A four grid retarding field energy analyzer (RFEA), with a fifth grounded entrance grid, has been
constructed based on published design criteria [Charles et al., Phys. Plasmas 7, 5232 (2000).]. A
fast amplifier is used to sum the current collected by the suppressor grid and the collector current.
Measurements of the ion velocity distribution function (ivdf) as a function of neutral pressure and
magnetic field mirror ratio in the HELIX plasma source will be presented. The ivdf measurements
will also be compared to laser induced fluorescence measurements made at the same location in
the expansion region of the plasma source.
The principle operation of a retarding field analyzer is to select or reject either positive ions or negative electrons from the plasma using electrostatic fields. These fields
are created by applying variable voltages between parallel fine mesh screens through which the particles travel. Particles with sufficient energy to overcome the
retarding fields are collected on a flat plate and measured as a current. As the retarding field is increased the collected current decreases until all the particles are
rejected. The derivative of the collector current Ic as a function of the retarding potential (also called the discriminating voltage Vd) is often interpreted as the particle
energy distribution simply shifted by the voltage difference between the front grid of the RFEA and the plasma, i.e., the plasma potential. This interpretation is not
entirely correct as bulk drifts of particles lead to an increased width of the distribution as measured in energy space. For a d rifting Maxwellian ion population, the
measured RFEA current as a function of discriminator voltage, Φ D, is given by
Grid Voltages
eΦD − Eb
)
2
Tb 

+ Eb π erfc 

(
eΦD − Eb

Tb  
 

)
Where n b = beam density; Eb = beam drift energy, and Tb = beam temperature. Note
the importance of the beam energy to the total current measured by the
RFEA. The derivative of this expression, often described as the “energy distribution function” when applied to experimental measurements is given by
+100V
Vd
− (
dI (Φ D )
1
= − nbe
e 
d ΦD
2mπ Tb
0 – 60V
Sweep
Vs
Vc
Insulating
Pocket
Copper
Spacers
 
− (
 nb  Tb e 
 
e2
2 mπ
I (Φ D ) =
)
eΦ D − Eb
2
Tb 

∆Φ D = 4 Tb Eb
which has a full width at 1/e of the peak of
Note that the distribution width depends strongly on the beam energy and does not represent the true temperature of the ion distribution.
Vr
-100V
Repeller
Suppressor
Discriminator
Stable Double Layer Occurs at Higher RF Frequencies
Collector
0.2
f R F = 9.5 MHz
0.1
N
5
N
5
even after 100’s of
averages, the RFEA
signal still noisy.
0
5
RFEA Current (arb)
N
5
RFEA Current
5
The amplifier used with the RFEA is a switched gain
DC amplifier with gains of 2, 11, 101, 1001, and a
bandwidth of approximately 10kHz. The amplifier is
powered from a single 24V DC floating plug-pack
power supply with a ground reference established
internally at 12V positive from the negative supply,
giving +/- 12V supply to the amplifier. The output of
the amplifier is buffered to enable driving a 50 ohm
load. Detector probe current develops a voltage
across a 10k resistor which is then amplified.
Secondary emission collected by the suppressor grid
is subtracted from the collected current measurement.
The design schematics were obtained from ANU and
built by researchers at WVU.
-0.1
-0.2
-0.3
-0.4
0.6
f R F = 13.56 MHz
0.5
RF Power = 700W
B HELIX = 800 G
B LEIA= 14 G
PHELIX = 1.3 mTorr
0.4
0.3
0.2
0.1
~ Vplasma
10
15
20
25
~ 12 eV
0
30
35
40
45
-0.1
50
Discriminator Voltage (V)
Vplasma
10
15
20
25
beam
30
35
40
45
50
As shown in the adjacent
poster by Przybysz, when the
source is operated at 9.5 MHz
instead of 13.56 MHz (which
typically yields better
performance), large
instabilities arise. At 13.56
MHz, a clear ion beam is
observed and appears to have
an energy approximately 12
eV larger than the background
ions (which appear at 25 eV
after acceleration to the probe
from the plasma).
Discriminator Voltage (V)
5
N
VHUV
X
HOH
FW
5
Comparison of Derivative and Fitting Methods to Obtain IEDF/IVDF
5
-0.06
-0.07
f R F = 9.5 MHz
-0.05
-0.05
dI /dV
dI /dV
-0.04
Experimental Geometry
The left figure is the derivative of the
collected current versus discriminator
voltage for the 9.5 MHz case. On the
right is dI /dV for the 13.56 MHz case.
With the 13.56 MHz data for
reference, it is possible to identify a
beam at approximately 37 V in the 9.5
MHz case. However, the noise in the
measurement is considerable. In the
13.56 MHz data, the accelerated
background ion population at ~ 28 eV
and beam at a total energy of ~ 40 eV
are evident. In this analysis, the
beam appears to be larger than the
background ion population.
f R F = 13.56 MHz
-0.06
-0.03
-0.04
-0.03
-0.02
-0.02
-0.01
-0.01
0
0
0.01
RFEA
10
15
20
25
30
35
40
45
50
10
15
20
Discriminator Voltage (V)
25
30
35
40
45
50
Discriminator Voltage (V)
0.6
Fit
Current (arb)
0.4
0.3
0.014
0.177
28.5
0.013
0.059
39.5
1.2 10-2
-0.06
0.2
8 10 -3
-0.04
-3
-0.02
4 10
0.1
dI/ dV
Amp 1
T1
E1
Amp2
T2
E2
F(V) from Fit
0.5
Langmuir range
0
10
9150
6100
3050
200
160
80
120
Position (cm)
50
0 10
0
0
10
15
20
25
30
35
40
Discriminator Voltage (V)
45
50
The total ion distribution that best fits the measured collector
current (shown in green) matches the essential features of the
derivative of the collected current versus discriminator voltage.
The relative amplitudes of the two populations given by the fit
result is quite different than what was indicated by the simplis tic
derivative method.
Both the “derivative” and “beam-fitting” analysis methods shown above ignore key aspects of the RFEA
measurement process. First, the acceleration of a drifting Maxwellian population in a spatially localized
electric field (the sheath in front of the probe) yields a clearly non-Maxwellian ion distribution– a result of
“compression” in velocity space. Second, only the half of the background ion population moving towards
the RFEA should actually make it into the RFEA aperture.
0.01
0.6
0.5
0 m/s
0.02
Current (A)
Current (A)
45
Comparison of RFEA IVDF and LIF IVDF Measurements
0
f R F = 9.5 MHz
RF Power = 700W
BHELIX = 800 G
BLEIA= 14 G
PHELIX = 1.3 mTorr
PLEIA = 0.1 mTorr
Flow = 8 SCCM
Gas feed @ end of source
25
30
35
40
Discrimator Voltage (V)
The measured collector current is well fit by a twopopulation pair of Maxwellian distributions, each as
described by the expression above. The fit yields a plasma
potential of 28.5 V and a total beam energy (after
accelerated through the plasma potential) of 39.5 eV.
Based on this analysis, the populations are nearly
equal in magnitude and have very low ion
temperatures.
12200
0.02
0.01
20
Φ plasma
f R F = 13.56 MHz
RF Power = 700W
BHELIX = 800 G
BLEIA= 14 G
PHELIX = 1.3 mTorr
PLEIA = 0.1 mTorr
Flow = 8 SCCM
Gas feed @ end of source
Therefore, the effect of the acceleration of the background and beam ion populations through the plasma
potential must be considered before comparison with LIF measurements. Since velocity space
compression due to acceleration is difficult to see in the above schematic, consider two argon ions, one
traveling at 0m/s and one at 6,926 m/s (10 eV). If they both experience a 20 V accelerating potential,their
finals speeds will be 9,795 m/s (20 eV) and 11.997 m/s (30 eV). So the velocity difference between these
two ions has shrunk to ~ 2,200 m/s .
RFEA Current
Ion Velocity (m/s)
Previous laser-induced-fluorescence (LIF)
measurements of the parallel ivdf in the
HELIX-LEIA system have demonstrated the
existence of an accelerated population of
ions co-existing with a background ion
population at rest (typical LIF observations
are shown to the right). The RFEA probe is
situated approximately 25 cm ( z = 226 cm)
further downstream than the leftmost data in
the LIF figure. An rf-compensated, planar
Langmuir probe provides measurements of
N e, Te, and plasma potential from z = 195 to
285 cm.
15
0.4
0.3
0.2
0.1
RFEA
ΦP = 26 V
Tp = 2.5 eV
E p = 0.5 eV
Tb = 0.2 eV
E b = 13.5 eV ( ∆V = 6,500 m/s)
Np /Nb = 7.4
0
5
The expression below describes the expected current for two drif ting Maxwellian populations ( a “plasma”
and “beam” population) that have been accelerated into the RFEA by the plasma potential between the
RFEA and the plasma. Note that only half of the plasma density is assumed to make it into the RFEA.
10
15
20
25
30
35
Discriminator Voltage (V)
-40
-20
0
Bias Voltage (V)
20
40
-60
For Φ D = Φ P
-40
-20
0
20
Bias Voltage (V)
Summary:
• For plasma parameters shown to produce an ion beam in laser-induced-fluorescence (LIF) measurements, RFEA measurements
confirm the presence of an ion beam population in the expansion region of HELIX
• Conventional RFEA theory and analysis has been modified to inclu de the effects of the additional acceleration in the RFEA
probe sheath of a drifting Maxwellian population. The new model accounts for the velocity space “compression” that results
from acceleration in the sheath and for the collection of only half of a background, nearly stationary, ion plasma.
•
One surprising result was the observation that the double layer is more stable and produces a “cleaner” ion beam when the
source is operated at higher RF driving frequencies.
{Te
P
  np 
(
    TP e
e2   2  


2mπ  
− (Φe −D

 nb  Tb e
 

−

40
I (Φ D ) =
} {Te
+ EP π erfc  E P TP  + nb
e Φ D − e ΦP −E
Φ
e P− E
P
) T b 
2
b
) TP
2



b
+ EP π erfc 

(
+ Ebπ erfc 

(
+ E b π erfc  E b
eΦ D − eΦ P − E
eΦD − e ΦP − Eb
)
P

Tb  

}
 
T P  + 
  



Tb  




)
The best fit of the above expression to the RFEA measurement is shown in the top figure at the right.
The two ion populations that are obtained from the fit are shown at the lower right as function of velocity
in units of laser frequency for comparison with LIF measurements obtained at a similar axial location in
LEIA. Note how this analysis method dramatically reduces the amplitude of the “beam” relative to the
background plasma – a result of correctly accounting for the greater impact on measured current of an
ion beam. The higher temperature background population obtained from the RFEA measurements
suggests that the ions are heated in the RF sheath as they fall into the RFEA probe.
IVDF from LIF (arb)
-60
0
−( Eb Tb )
50
LIF
Tp = 0.9 eV
Tb = 0.4 eV
∆V= 6400 m/s
Np /Nb = 9
0.8
0.12
0.08
0.6
0.4
0.04
0.2
0.00
0
5
10
Frequency (GHz)
15
Top Figure. RFEA measurement (green) and fit
(blue) based on expression given at left. Bottom
Figure. The two ion distributions obtained from the
fir to the RFEA data (red) and a LIF measurement of
the ivdf at the same axial location (green).
IVDF from RFEA Model
0
−(EP TP )
45
1
For Φ D < Φ P
e 2  np 
I (Φ D ) =
2mπ  2 
40