_________________________________________________________________________________________________________
Electrical Engineering Department
Los Angeles, California 90095-1594
UNIVERSITY OF CALIFORNIA • LOS ANGELES
Low Temperature Plasma
Technology Laboratory
Performance of a Permanent-Magnet Helicon
Source at 27 and 13 MHz
Francis F. Chen
LTP-1207 July, 2012
Performance of a permanent-magnet helicon source at 27 and 13 MHz
Francis F. Chen
Electrical Engineering Department, University of California, Los Angeles, California 90095
Abstract
A small helicon source is used to create dense plasma and inject it into a
large chamber. A permanent magnet (PM) is used for the dc magnetic field (B-
field), making the system very simple and compact. Though theory predicts that
better antenna coupling will occur at 27.12 MHz, it was found that 13.56 MHz
surprisingly gives even higher density due to practical effects not included in
theory. Complete density n and electron temperature T
e
profiles are measured at
three distances below the source. The plasma inside the source is also measured
with a special probe, even under the antenna. The density there is lower than
expected because the plasma created is immediately ejected, filling the
experimental chamber. The advantage of helicons over ICPs (Inductively
Coupled Plasmas, with no B-field) increases with RF power. At high B-fields,
edge ionization by the Trivelpiece-Gould mode can be seen. These results are
useful for design of multiple-tube, large-area helicon sources for plasma etching
and deposition because problems are encountered which cannot be foreseen by
theory alone.
I. Background
Helicon discharges are known to be good sources of dense plasma for industrial
applications, but they normally require a large, heavy electromagnet and its power supply. This
disadvantage has been overcome by the invention
1
of permanent-magnet helicon discharges
using the remote, reverse field of small annular magnets in combination with the Low-Field
Peak
2
in density caused by constructive interference of the reflected backward wave. This effect
causes a useful increase in density occurring at a density that depends on the magnetic field and
the length of the discharge tube. An array of eight small tubes, built several years ago
3
,
successfully produced plasmas of density in the 10
11
cm
-3
range, uniform over 56 cm width. This
experiment demonstrated that a simple, inexpensive helicon arrays can cover large substrates
with uniform plasma for roll-to-roll processing. In the present work, one of the helicon sources
in the array is studied in detail in a cylindrically symmetric system to see if PM helicons can
used for other applications such as spacecraft thrusters or optical coatings. It has been shown
4
that helicon sources can produce an interesting amount of thrust for that purpose, but
experiments so far have used large electromagnets for the DC field, and these may be
incompatible with the weight limits of spacecraft. The use of PM helicons for thrusters has
already been investigated extensively by Takahashi et al.
5,6,7
Their configuration of PMs is quite
different from ours and does not use annular magnets. For thruster applications, that work is
much more advanced than ours, since the ion energy distributions were measured in detail. The
present paper deals instead with the physics of PM helicon discharges and how their design for
ejecting plasma has unexpected considerations. Comparisons between 13.56 and 27.12 MHz
frequencies and between B = 0 and B > 0 operation are made.
II. Apparatus
2
A. Helicon discharge. The basic source is shown in Fig. 1a. The B-field is provided by
an annular permanent magnet above the discharge tube and can be adjusted by varying its height.
The NdFeB magnet has 3-inch (7.6 cm) inner and 5-inch (12.7 cm) outer diameters and is 1 incn
(2.54 cm) thick. It is shown at its optimum height. The vertical-probe extension is shown in Fig.
1B, together with a second magnet which can be added for higher fields. The loop antenna is
placed at the bottom to eject the most plasma down into a large chamber. RF frequencies of
27.12 and 13.56 MHz have been used. The top of the discharge is normally a solid, grounded
aluminum plate forming the boundary condition for the low-field peak effect. This condition
determined the height of the tube. In the vertical-probe extension, the top plate is replaced with
one that has a 1/8-inch (3.2mm) diam hole through which two alumina probe shafts are inserted,
one for the probe, and the other for the RF-compensation electrode (not shown). Details of the
probe design are given in a separate paper
8
.
(a) (b)
Fig. 1. Diagram of helicon source: (a) simple configuration; (b) with vertical probe extension and second magnet.
B. Experimental chamber. Figure 2 shows the aluminum experimental chamber to
scale with the helicon source. From its previous use as a plasma processing chamber, the
interior sidewall is aluminized, and the exterior sidewall is covered with rows of small, round
SmCo magnets for better plasma confinement. There are three horizontal Langmuir probes at
Ports 1, 2, and 3 equally spaced below the source. Port 1 accesses the plasma close to the exit
hole of the source. The probe there is close to the furthest reach of the vertical probe and the two
probe yield the same density at the overlap point. Port 2 is at a convenient level for placement of
a substrate. A substrate at Port 3 would see more uniform plasma at densities below 10
11
cm
-3
.
C. Design of the discharge tube. Figure 3 shows the dimensions of the tube. The tube
radius was chosen by standard pipe sizes and the goal of a small, compact source. The height of
the tube was then determined by the condition for a Low Field Peak in density. For this, the
HELIC code by D. Arnush
9
was used. The use of this code was illustrated in a previous paper
10
.
The code computes the plasma resistance R (or R
p
), which is proportional to the deposition of RF
energy for a given antenna current. Since R
p
is of the order of 1Ω, it is important to maximize it
to overcome circuit losses. Figure 4 shows calculated curves of R vs. n for various B-fields. It
shows that a large gain in loading accrues from raising the frequency to 27.12 MHz; hence, this
frequency was used for the first time. Stable operation occurs on the right side of each peak. To
3
obtain high 10
11
cm
-3
downstream, we expected n to be in the high 10
12
cm
-3
range, which
requires high B. This turned out to be incorrect.
The water-cooled antenna is a coil of 1/8-in (3.2mm) o.d. copper tube, three turns for 13
MHz and 1 turn for 27 MHz. When cable length is taken into account, manual matching by a
standard matching circuit fixes a maximum value for antenna inductance; hence the antenna
change for 27 MHz. Details on the inductance limit are given in Ref. 3. Note that the quartz
tube is flared out into a “skirt” at the bottom. This is to move the antenna away from the flange
on which the tube sits, to prevent induction of large eddy currents in the flange.
Fig. 2. Diagram of the experimental chamber. Dimensions are in cm.
Fig. 3. Nominal dimensions of the discharge tube.
4
0.0
0.5
1.0
1.5
2.0
1E+11 1E+12 1E+13n (cm
-3
)
R (ohms)
200
150
100
50
B
(
G
)
13 MHz
H= 2 cm
0.0
0.5
1.0
1.5
2.0
1E+11 1E+12 1E+13n (cm
-3
)
R (ohms)
200
150
100
50
B (G)
27 MHz
H = 1.5 cm
(a) (b)
Fig. 4. Plasma resistance calculated for 13 and 27 MHz. The peaks occur at higher n for higher B (color online).
Here H is the antenna distance below the top plate.
D. Diagnostics. Langmuir probes were used exclusively for diagnostics. The horizontal
probes are encased in ¼-inch (6.35 mm) diam alumina tubes housing the RF chokes and
connectors. The probe tip is a 5-mil (0.127 mm) diam tungsten rod, 0.7-1.2 cm long, centered in
a 94-mil (2.39 mm) o.d. alumina tube 2.9 cm in length. An RF-compensation electrode made of
1-mil (25μm) thick Ni foil is wrapped around the thin tube and connected to the choke chain
through a small capacitor. The choke chain consists of one self-resonant choke for 13.56 MHz
and three broadly self-resonant chokes in series for 27.12 MHz. The chokes are individually
selected. Their impedance varies from 300 to 1000 kΩ at 13.56 MHz and roughly 150-300 kΩ
at 27.12 MHz.
The current-voltage (I – V) curves were taken by the ESP Mk2
®
system of Hiden
Analytical, Ltd. Each scan consisted of about 200 points from -100 to ≈ +20V, taking about 5
sec. The I – V curves were analyzed with an Excel program based on Langmuir’s OML (Orbital
Motion Limited) formula. Each data point shown below was found by fitting its I
2
– V plot to a
straight line for n, and its ln(I
e
)-V plot to another straight line for KT
e
, where I
e
is the electron
current found by subtracting the ion fit from I. The electron distribution is almost always
consistent with a Maxwellian.
III. Measurements.
Unless otherwise specified, measurements were made under the standard conditions of 15
mTorr of argon and 400W of RF. The discharge can be run continuously, but to protect the
probes it is normally turned off as soon as the probe sweep s finished.
A. Downstream profiles at 27.12 MHz. Initially, it was thought that the high densities
covered by the right-most curve in Fig. 4b could be achieved, and two magnets were used to
produce a high field of 200G at the antenna. In Fig. 5 the axial field strength B
z
(B
r
is negligible)
is shown vs. distance below the magnet. The tube is shown positioned with the antenna at 200G.
Radial profiles in Port 1, 6.8 cm below the tube, are shown in Fig. 6. The density is double-
peaked, showing edge ionization by the Trivelpiece-Gould (TG) mode. KT
e
, however, is peaked
at the center, possibly because of neutral depletion, though this could not be confirmed. The TG
mode is more strongly peaked at high B, and its visibility indicated that perhaps the B-field was
too high for the relatively low density. One magnet was removed to lower the field to about 65G.
For a given n, as seen in Fig. 4, too high a B-field would put the operating point to the left of the
peak in R, which is an unstable regime of operation. Figure 7 shows the great improvement in
Port 1 density. Figure 8 shows that KT
e
is now peaked at the edge due to the TG mode. As
