Voltage, current and electron density measurements in an air radio-frequency plasma
TU/e
EPG
M. Sorokine, D. Hayashi, W.W. Stoffels, G.M.W. Kroesen
Elementary Processes in Gasdischarges
Department of Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
IV
15
5
5
10
15
3924600
4273000
Amplifier
RF
Fig. 2 Experimental setup
5
10
15
20
25
Power, Wtt
Fig. 4
Frequencies of the cavity modes were calculated beforehand. As
it was expected, the two series (3036900 kHz and 3924600 kHz –
the two upper lines), that were believed to correspond to
Transverse Magnetic Waves (TM) - TM110 and TM210 modes,
showed the best agreement between each other. They were also
the best distinguishable in the cavity spectrum observed and had
the most appropriate frequency for the calculated modes. So,
these two modes were chosen for the experiments, presented in
this work.
Fig.8 and 9 show the spatial electric field distribution for TM110
and TM210 [3] within the cylindrical cavity with dimensions
mentioned above.
2
1.8
39246000
25
4
6
Pressure, E-01 Torr
V [1], V
V [2], V
8
V [3], V
10
V [4], V
Fig. 16. Voltage RMS. Fixed Voltage[0] (100
Volts).
k Hz
12
12
10
10
f f 2
FE  0
f  ne 0
f0
(3)
8
6
4
has been calculated. As there is E2 under the integral in the equation
(2), obtained behavior of the value FE needs to be compared to the
one of the E2 obtained from the theory. Taking into account finite
size of a plastic probe (10mm) a following value has been calculated:
FEt ( x) 
1.2
0
1
E
2
2
4
6
8
( y)dy
25
Fig. 14 Electron Density in air discharge. Fixed
Voltage (100 Volts)
10
15
Power, Wtt
20
25
4
0
3.5
3
-25
2.5
-50
ne 0 


(2)
Response, mV
300
200
100
0
Frequency KHz
10
20
30
40
50
60
radius, mm
TM[210] exp
TM[110] Theor
TM[210] Theor
Fig.11. TM110 and TM210 modes in a plane of the antennas.
150
100
50
0
-50 0
2
4
6
8
10
-100
-150
50
Pressure, E-01 Torr
0
Phs [0], degrees
Ph [3], Deg
The lines with dots are the experimental curves, and the thin solid
lines are obtained from the theory.
50
Ph [1], Deg
Ph [4], Deg
Fig. 18 presents impedance changes.
Imp[i]=Voltage[i]RMS/Current[i]RMS
Since the current in the odd harmonics (3f, 5f etc) is low (Fig.
16), no accurate Impedance can be calculated for those
frequencies.
It can be noticed that the Impedance for the third harmonics
(imp[3]) experiences dramatic change with pressure goes
higher then 4 Torr.
100
90
80
70
60
50
40
30
20
10
0
0
Ph [2], Deg
2
Imp [0], Ohms
Fig. 15 Phase shift between harmonics of Voltage and
Current in air discharge. Fixed Voltage (100 Volts)
2.5
0
-25
4
6
Pressure, E-01 Torr
Imp [1], Ohms
Imp [3], Ohms
8
10
Imp [4], Ohms
Fig. 18. Impedance. Fixed Voltage[0] (100Volts).
4000000
It has been noticed that the behaviour of the first harmonics of
current, voltage and power (Fig.16, 17, 18) is pretty much the
same as the behaviour of the electron density.
2
-50
V
1.5
1
0
Fig. 6 Represents spectrum of the cavity.
Fig. 6. Cavity spectrum
0
TM[110] exp
-50
E ( x) 2 d x
3000000
10
25
However, by combining results from several modes some
spatial information can bee obtained.
2000000
200
0
Fig.8. TM110 mode electric field spatial profile. No z
dependence. Only Ez is present.
-50
ne ( x ) E ( x ) 2 d x
cavity
1
0.5
50
2
This method does not provide any spatial resolution as ne0 is
merely a space averaged density weight with the square of the
field strength (E2),
cavity
8
Re P [2], Wtt
250
1.5
0
From the shift f = f – f0 of the resonant frequency f with
respect to its value in vacuum (f0) the microwave field
averaged electron density (neo) is deduced [2]:
( 1)
Re P [1], Wtt
Re P [4], Wtt
2
These graphs strongly resemble those that one would expect
to see in case of simple electrical circuit with direct current
and constant resistance. Though, it is seen that the curves do
not trend to zero, as it would be for a simple resistor.
2fme 0 (2 f )

f 0e2
4
6
Pressure, E-01 Torr
Fig. 17 Real Power RMS. Fixed Voltage[0]
(100Volts).
Also, it was clearly seen from the graphs for the phase difference
between harmonics of current and voltage (Fig.15), that in
mentioned above pressure range the value for the first and,
especially, for the third harmonics experiences dramatic changes.
The idea of monitoring certain processes through the study of the
phase behaviour is not a new one [1] and can be very promising
in commercial production environment.
Phase, degrees
5
2
Re P [0], Wtt
Re P [3], Wtt
3 9 2 4 6 0 0 0 k Hz
It was noticed that by changing the discharge pressure from 0.6 to
0.8 Torr the discharged seemed to come to another state.
x 5
0.2
0
P r e s s u r e, E - 1 T o r r
3 0 3 6 9 0 0 k Hz
(4)
Fig.11 and 12 show both FE and FEt [see equations (3) and (4)] for
the two different planes in cavity.
50
4
10
-50
0.4
6
0
0
0
50
8
2
2
x 5
1.4
Current, Amp
Fig. 13 Electron Density in air discharge. Fixed
pressure O.10 Torr.
For the estimation of electric field value FE
1.6
Power input measurements
Using a Plasma Impedance Monitor (PIM)
device by Scientific Systems we obtain
information on the amplitudes of voltage and
current for the driving frequency and first four
harmonics, as well as on the value of phase
shift between them. Along with that, power
and impedance are calculated. Fig. 3 shows
the principle of the PIM IV Sensor .
k Hz
20
Power, Wtts
20
ne 0
pumping
IV sensor
10
15
P o w e r, Wa t t s
Impedance, Ohms
60
Gas flow
W
Matching box
2
V [0], V
5
3036900
n, E14 m-3
80
40
V
Acquisition unit
0
0
Fig.10. Electric field spatial profile
experiment.
100
The resonance frequency of the cavity, which depends on the
number of free electrons within, is determined by tuning the
microwave generator to maximum transmission.
Microwave
generator
RF Generator
0
Plastic
probe
4358700
120
Microwave technique
A schematic drawing of the measurements is
shown on Fig. 2.
20
20
-50
III. DIAGNOSTICS
40
30
0
140
Fig.5
insulation
60
40
Fig. 7. Preliminary results
0
RF
80
10
0
3036900
0
Fig. 1 Cylindrical microwave cavity
100
20
0
0.6
slits
Antennas’ plane
120
160
0
antenna
n, E14 m-3
10
0.8
antenna
50
Antenna
180
EXPERIMENT
The experiment has been carried out with a
13.56 MHz capacitively coupled air plasma,
confined in an aluminium cylinder cavity with
two symmetrical slits. A schematic drawing of
the plasma chamber is shown on Fig. 1. The
dimensions are: diameter – 120mm, height –
37mm, slit width – 10mm, distance between
antennas – 90mm, the lower power electrode
diameter – 107mm.
20
Power by PIM, Watts
0
II
25
50
Fig.9. TM210 mode electric field spatial profile. No z
dependence. Only Ez is present.
0.5
1
0
0
10
20
30
40
50
60
radius, mm
En experimental study of the electric field in the cavity has also
been carried out. If a piece of plastic is placed within the cavity,
then, according to formula (1), the resonant frequency will
change its magnitude. And, the bigger the field at the position of
the probe, the bigger the frequency shift. Hence, the space profile
of the microwave electric field within the chamber cavity can be
examined. Measurements have been made in two vertical planes,
perpendicular to each other: the plane with slits (slits’ plane), and
the antennas’ plane. A plastic probe was placed at different places
in the cavity. Dimensions of the probe are: 15mm x 15mm x
10mm. For each probe position a resonance frequencies for the
modes have been found and then used in further calculations.
TM[110] exp
TM[210] exp
TM[110] Theor
TM[210] Theor
Fig.12. TM110 and TM210 modes in a plane of the slits.
0.8
0.6
-------------------------------------------------
0.4
[1] Kieran Dobbyn, M.Sc. thesis, “Design and Application of
a Plasma Monitor for RF Plasma Diagnostics.” Dublin City
University, 2000.
0.2
0
0
2
4
6
8
Pressure, E-01 Torr
A good agreement is seen from the graphs, though for the middle of
the cavity the experimental electric field is higher than that obtained
from the theory. Probably this can be explained by other harmonics
contributing to the field in the middle. Also, analysis of the mode
structure up to 5 GHz shows that the TM110 and TM210 modes are the
only ones that can fit the experimental curve.
ACKNOWLEDGEMENT
This work is supported by the European Commission under
contract No. NNE5-1999-0004 H-alpha solar. The research of
W.W. Stoffels has been made possible by a fellowship from
the Royal Netherlands Academy of Arts and Sciences
(KNAW).
1.2
Current, Amps
Microwave methods to measure electron
density are advantageous due to its time
resolution possibilities. Moreover, it is also a
non-intrusive in situ measurement technique.
Fig. 4 and 5 show Current/Power and Voltage/Power graphs
for 0.10 Torr Air discharge.
Voltage, Volts
Power input control is really alluring because
of its simplicity in implementation. In most
experiments the main characteristic for the RF
discharge is its consumed power. Nevertheless,
in most theoretical works, the rf voltage is
taken to be constant, which makes
comparisons between experimental and
theoretical difficult. Using the technique
mentioned above it is possible to get the
desired results.
Fig 3 – Schematic of IV Sensor (reproduced
from [1])
On Fig. 13 and 14 calculated electron density values are
presented.
Slits’ plane
Various RF discharges are widely used in
different kinds of production technologies.
Still, questions of quality improvement often
arise. That leads companies to look for a way
of improving and optimising production
processes. This cannot be done without
appropriate diagnostic techniques.
RESULTS
Two measurement series have been carried out: the 1st - Power
variation, with keeping the pressure constant (0.10 ± 0.005 Torr),
and the 2nd - Pressure variation with constant amplitude of
fundamental voltage harmonic (100 Volts).
Fig.10. Gives a schematic drawing of the experiment.
Voltage, Volts
Several spectrum peaks were examined during preliminary
experiments. Fig. 7 shows results for 4 of total 7 observed modes.
Those that are not presented showed no change in frequency
within the error of the measurements.
INTRODUCTION
Electron dencity, E14 m-3
I.
I [0], Ampers
I [3], Ampers
I [1], Ampers
I [4], Ampers
I [2], Ampers
Fig. 16. Current RMS. Fixed Voltage[0] (100 Volts).
10
[2] E. Stoffels, W.W. Stoffels, D. Vender, M. Kando,
G.M.W. Kroesen, and F.J. de Hoog. Phys. Rev. 51, 24252435 (1995)
[3] J.D. Jackson, “Classical Electrodynamics” Second
Edition, Wiley, p.335