U.S. patent application number 11/239471 was filed with the patent office on 2007-04-05 for method and apparatus for measuring plasma density in processing reactors using a long dielectric tube.
Invention is credited to Samuel S. Antley, Paul Moroz, Bill H. Quon, Janusz Sosnowski.
Application Number | 20070074811 11/239471 |
Document ID | / |
Family ID | 37900783 |
Filed Date | 2007-04-05 |
United States Patent
Application |
20070074811 |
Kind Code |
A1 |
Moroz; Paul ; et
al. |
April 5, 2007 |
Method and apparatus for measuring plasma density in processing
reactors using a long dielectric tube
Abstract
An apparatus for measuring plasma density of a plasma processing
reactor, comprises a probe having a dielectric tube with a coaxial
cable inserted therein. The coaxial cable has an open antenna tip,
distance constancy is kept between the antenna tip and the
dielectric tube despite varying thermal conditions. The probe can
be utilized to determine resonant plasma frequency near its tip
location and the corresponding plasma density.
Inventors: |
Moroz; Paul; (Marblehead,
MA) ; Quon; Bill H.; (Aliso Viejo, CA) ;
Antley; Samuel S.; (Cottonwood, AZ) ; Sosnowski;
Janusz; (Clarkdale, AZ) |
Correspondence
Address: |
Dale S. Lazar;DLA Piper Rudnick Gray Cary US LLP
Post Office Box 9271
Reston
VA
20195
US
|
Family ID: |
37900783 |
Appl. No.: |
11/239471 |
Filed: |
September 30, 2005 |
Current U.S.
Class: |
156/345.28 |
Current CPC
Class: |
H01J 37/32935 20130101;
H05H 1/0081 20130101 |
Class at
Publication: |
156/345.28 |
International
Class: |
C23F 1/00 20060101
C23F001/00 |
Claims
1. An apparatus for measuring plasma density in a plasma-processing
reactor, comprising: a probe comprising a coaxial cable inserted
into a closed dielectric tube and having an open metal antenna tip;
a coaxial cable connected to the probe; a network analyzer
connected to the probe through the coaxial cable, supplying a
high-frequency signal to the probe and measuring the intensity of
the reflected signal; and a high-pass filter located between the
coaxial cable or the probe and the network analyzer to cut off
strong low frequency signals; wherein distance constancy is kept
between the antenna tip and the dielectric tube; and plasma density
can be measured in a chemically active environment.
2. The apparatus of claim 1, wherein the high frequency signal is
in the range of 0.5-5 GHz.
3. The apparatus of claim 1, wherein the antenna tip is a straight
naked metal wire at least a few millimeters long representing the
center electrode of the coaxial cable stripped of isolation and
metal screening.
4. The apparatus of claim 3, wherein an end of the antenna tip does
not touch an inner end of the dielectric tube, and there is a space
of at least a few millimeters between them.
5. The apparatus of claim 4, wherein a space between the antenna
tip end and the inner end of the dielectric tube is maintained
constant.
6. The apparatus of claim 5, wherein space is maintained constant,
in spite of possible thermal expansion of the coaxial cable.
7. The apparatus of claim 6, further comprising a dielectric spacer
disposed inside the main dielectric tube and placed around the
antenna tip so that the space is maintained constant.
8. The apparatus of claim 7, wherein the dielectric spacer includes
a dielectric tube with an inner radius approximately equal to the
radius of the antenna tip to increase constancy of the antenna tip
shape under varying thermal conditions.
9. The apparatus of claim 1, wherein various resonances in the
reflected signal are interpreted based on surface wave modes.
10. The apparatus of claim 9, wherein resonances are mapped with
corresponding plasma density values.
11. The apparatus of claim 10, wherein resonance modes are selected
from the measured absorption resonances, wherein the selected
resonance modes are those modes that are the strongest and also
provide information about local values of the plasma density around
the antenna tip.
12. The apparatus of claim 1, wherein the dielectric tube is made
of material selected to have a dielectric property used in
correspondence with an expected plasma density range to produce a
resonance in a frequency range of the network analyzer.
13. The apparatus of claim 12, wherein a material with higher
dielectric permittivity is chosen for the dielectric tube for
measurements in a higher plasma density range to maintain the
resonant frequency below about 5 GHz.
14. The apparatus of claim 1, wherein the coaxial cable has a
smaller radius than the inner radius of the dielectric tube, and a
spacer ring is provided at the end of the coaxial cable between the
radius of the coaxial cable and the inner radius of the dielectric
tube, the ring providing more sharply emphasized boundary
conditions for the surface wave reflection, making absorption
resonances more pronounced.
15. The apparatus of claim 1, wherein the coaxial cable has a
smaller radius than the inner radius of the dielectric tube, and
there is at least one dielectric ring or short dielectric tube
along the coaxial cable, surrounding the coaxial cable, and located
inside the dielectric tube, diminishing the amplitude of parasitic
surface waves running along the dielectric tube, which otherwise
might interfere with the main absorption resonances used for
measurements.
16. The apparatus of claim 7, wherein the dielectric spacer is
metal.
17. An apparatus for determining plasma density of plasma in a
plasma processing reactor, comprising: a probe comprising a long
dielectric tube and a coaxial cable inserted in the dielectric
tube, the coaxial cable having an open antenna tip; wherein
distance constancy is kept between the antenna tip and the
dielectric tube despite varying thermal conditions.
18. The apparatus of claim 17, wherein distance constancy is also
kept between the coaxial cable and the dielectric tube despite
varying thermal conditions.
19. The apparatus of claim 17, wherein plasma density is measured
in a chemically active environment.
20. The apparatus of claim 17, further comprising a spacer
proximate the antenna tip to keep the distance constancy.
21. The apparatus of claim 18, further comprising: a spacer
proximate the antenna tip to keep the distance constancy between
the antenna tip and the dielectric tube; and a spacer proximate the
coaxial cable to keep the distance constancy between the coaxial
cable and the dielectric tube.
22. The apparatus of claim 17, further comprising a dielectric tube
spacer, an inner radius of the dielectric tube spacer being equal
to or about the radius of the antenna tip, the tube spacer
extending from a portion of the coaxial cable from which the
antenna tip extends to the dielectric tube in the direction of the
antenna tip to keep the distance constancy.
23. The apparatus of claim 18, further comprising: a dielectric
spacer; a metal spacer; or any combination thereof, disposed
between the coaxial cable and the dielectric tube, to keep the
distance constancy between the coaxial cable and the dielectric
tube.
24. The apparatus of claim 18, further comprising a ring spacer
disposed between the coaxial cable and the dielectric tube to keep
the distance constancy between the coaxial cable and the dielectric
tube.
25. The apparatus of claim 17, wherein the antenna tip is a naked
metal wire representing a center electrode of the coaxial cable
without isolation and/or metal screening.
26. The apparatus of claim 17, wherein the antenna tip is
straight.
27. The apparatus of claim 17, wherein the antenna tip is not
straight.
28. The apparatus of claim 27, wherein the antenna tip bent in one
direction.
29. The apparatus of claim 17, wherein the antenna tip is bent in
the shape of a partial loop.
30. The apparatus of claim 17, wherein the shape of the antenna tip
stays constant under varying thermal conditions.
31. The apparatus of claim 17, wherein a material for the
dielectric tube corresponds to an expected plasma resonant
frequency.
32. The apparatus of claim 17, wherein the dielectric tube is made
of a material with a high dielectric permittivity when a high
plasma density is expected to keep the resonant frequency under 3
GHz.
33. The apparatus of claim 32, wherein the dielectric permittivity
is selected so a plasma resonant frequency falls in a
pre-determined range of values.
34. The apparatus of claim 17, wherein the distance constancy kept
between the antenna tip and the dielectric tube provides more
sharply emphasized boundary conditions for surface wave reflection,
making absorption resonances more pronounced.
35. The apparatus of claim 17, farther comprising a base coupled to
the dielectric tube.
36. The apparatus of claim 35, wherein the base is made of
dielectric material.
37. The apparatus of claim 17, further comprising a network
analyzer coupled to the probe through the coaxial cable.
38. The apparatus of claim 37, wherein the network analyzer
supplies a high-frequency signal to the probe and measures
intensity of a reflected signal.
39. The apparatus of claim 38, further comprising a high-pass
filter located between and the probe and the network analyzer, the
high-pass filter reducing low frequency signals.
40. The apparatus of claim 17, wherein the distance constancy is
selected so as to diminish the amplitudes of parasitic surface
waves running along the dielectric tube, which otherwise might
interfere with main absorption resonances used for
measurements.
41. The apparatus of claim 17, wherein the plasma density is
determined around at least one probe, and the plasma density at
other locations in the plasma processing reactor is determined
based on the determined plasma density around the at least one
probe and a model of relative plasma densities in the plasma
processing reactor.
42. A method for determining plasma density of plasma in a plasma
processing reactor, comprising: utilizing a probe configured and
arranged so that resonancy of a chosen mode is maximized, the probe
comprising a dielectric tube and a coaxial cable inserted therein,
the coaxial cable having an open antenna tip, wherein distance
constancy is kept between the antenna tip and the dielectric tube
despite varying thermal conditions; determining a resonant
frequency or wavelength of the plasma in the plasma processing unit
in the chosen mode; and determining the dielectric permittivity of
the plasma using the resonant frequency or wavelength; and
determining the density of the plasma using the resonant frequency
or wavelength.
43. The method of claim 42, wherein determining the resonant
frequency or wavelength of the plasma in the plasma processing unit
comprises: providing radio frequency signals to the probe antenna
tip; receiving back reflected radio frequency signals which carry a
plasma wave resonance signature; reducing strong low frequency
signals; determining the resonant frequency or wavelength of the
plasma waves.
44. The method of claim 42, wherein various resonances in the
reflected signal are interpreted based on surface wave modes.
45. The method of claim 44, wherein resonances are mapped with
corresponding plasma density values.
46. The method of claim 45, wherein resonance modes are selected
from the measured absorption resonances, wherein the selected
resonance modes are those modes that are the strongest and also
provide information about local values of the plasma density around
the antenna tip.
47. The method of claim 45, wherein the dielectric permittivity of
the plasma is determined as described in the body of this patent
using the dispersion relation: D .times. ( .omega. , k z , m ) = p
- d K m .times. ( k z .times. a ) K m ' .times. ( k z .times. a )
.alpha. .times. .times. I m ' .times. ( k z .times. a ) + .beta.
.times. .times. K m ' .times. ( k z .times. a ) .alpha. .times.
.times. I m .times. ( k z .times. a ) + .beta. .times. .times. K m
.times. ( k z .times. a ) = 0 ##EQU5## where: .omega.=2.pi.f (where
f is a wave frequency) k.sub.z=2.pi./.lamda. (where k.sub.z is a
longitudinal wave vector; .lamda. is a longitudinal wavelength)
m=azimuthal mode number .epsilon..sub.d=dielectric permittivity of
the dielectric tube 115 a=external radius of dielectric tube 115
b=internal radius of dielectric tube 115 I.sub.m=modified Bessel
function of first kind of order m K.sub.m=modified Bessel function
of second kind of order m I'.sub.m and K'.sub.m are derivatives,
respectively, for I.sub.m and K.sub.m. and .alpha. = 1 d sK m
.function. ( k z .times. b ) - p .times. .times. d .times. K m '
.function. ( k z .times. b ) K m .function. ( k z .times. b )
.times. I m ' .function. ( k z .times. b ) - I m .function. ( k z
.times. b ) .times. K m ' .function. ( k z .times. b ) ##EQU6##
.beta. = 1 d p .times. .times. .times. d .times. I m ' .function. (
k z .times. b ) - sI m .function. ( k z .times. b ) K m .function.
( k z .times. b ) .times. I m ' .function. ( k z .times. b ) - I m
.function. ( k z .times. b ) .times. K m ' .function. ( k z .times.
b ) ##EQU6.2## where r.sub.a=radius of antenna tip
48. The method of claim 42, wherein various resonances in the
reflected signal are interpreted based on surface wave modes.
49. The method of claim 42, wherein resonances are mapped with
corresponding plasma density values.
50. The method of claim 42, wherein resonance modes are selected
from measured absorption resonances, wherein the selected resonance
modes are those modes that are the strongest and also provide
information about local values of the plasma density around the
antenna tip.
51. The method of claim 42, wherein the dielectric tube is made of
material selected to have a dielectric property used in
correspondence with an expected plasma density range to produce a
resonance in a desired frequency range.
52. The method of claim 42, wherein a material with higher
dielectric permittivity is chosen for measurements in a higher
plasma density range.
53. The method of claim 42, wherein the coaxial cable has a smaller
radius than the inner radius of the dielectric tube, and a spacer
ring is provided at the end of the coaxial cable between the radius
of the coaxial cable and the inner radius of the dielectric tube,
the ring providing more sharply emphasized boundary conditions for
the surface wave reflection, making absorption resonances more
pronounced.
54. The method of claim 42, wherein the coaxial cable has a smaller
radius than the inner radius of the dielectric tube, and there is
at least one dielectric ring or short dielectric tube along the
coaxial cable, surrounding the coaxial cable, and located inside
the dielectric tube, diminishing the amplitude of parasitic surface
waves running along the dielectric tube, which otherwise might
interfere with the main absorption resonances used for
measurements.
55. The method of claim 54, wherein the dielectric spacer is
metal.
56. The method of claim 44, wherein resonances are mapped with
corresponding plasma density values.
57. The method of claim 44, wherein resonance modes are selected
from the measured absorption resonances, wherein the selected
resonance modes are those modes that are the strongest and also
provide information about local values of the plasma density around
the antenna tip.
58. The apparatus of claim 17, wherein the probe is slidable
through a wall of the plasma processing reactor.
59. The apparatus of claim 17, further comprising a spring coupled
to the coaxial cable to bias the coaxial cable into the dielectric
tube to maintain the relative positions of the antenna tip and the
dielectric tip.
60. The method of claim 42, further comprising sliding the probe
through a wall in the plasma processing reactor so that the antenna
tip is positioned at a desired position within the plasma
processing reactor.
61. The method of claim 42, further comprising biasing the coaxial
cable into the dielectric tube to maintain the relative positions
of the antenna tip and the dielectric tip.
62. The apparatus of claim 1, wherein the probe is slidable through
a wall of the plasma processing reactor.
63. The apparatus of claim 1, further comprising a spring coupled
to the coaxial cable to bias the coaxial cable into the dielectric
tube to maintain the relative positions of the antenna tip and the
dielectric tip.
64. The apparatus of claim 1, wherein the dielectric tube is of a
shape which limits cable expansion and helps provide a relatively
constant distance between the antenna tip and the dielectric
tube.
65. The apparatus of claim 17, wherein the dielectric tube is of a
shape which limits cable expansion and helps provide a relatively
constant distance between the antenna tip and the dielectric
tube.
66. The method of claim 42, wherein the dielectric tube is of a
shape which limits cable expansion and helps provide a relatively
constant distance between the antenna tip and the dielectric
tube.
67. The apparatus of claim 64, wherein the corner of the coaxial
cable abuts against the dielectric tube, and the antenna tip
extends into a portion of the dielectric tube with reduced
diameter.
68. The apparatus of claim 65, wherein the corner of the coaxial
cable abuts against the dielectric tube, and the antenna tip
extends into a portion of the dielectric tube with reduced
diameter.
69. The method of claim 66, wherein the corner of the coaxial cable
abuts against the dielectric tube, and the antenna tip extends into
a portion of the dielectric tube with reduced diameter.
Description
[0001] This application is related to patent application attorney's
docket number 313530-P00015 entitled "Method and Apparatus for
Measuring Plasma Density in Processing Reactors using a Short
Dielectric Cap", filed concurrently herewith, the contents of which
are incorporated herein in their entirety.
FIELD OF THE INVENTION
[0002] The present invention relates generally to measuring plasma
density, and relates specifically to measuring plasma density in
plasma processing reactors.
BRIEF DESCRIPTION OF THE DRAWINGS
[0003] FIG. 1 is a schematic representation of an apparatus for
measuring plasma density of a plasma processing reactor where a
probe is moveable, according to one embodiment of the
invention.
[0004] FIG. 2 is a schematic representation of an apparatus for
measuring plasma density of a plasma processing reactor where a
probe is not moveable, according to one embodiment of the
invention.
[0005] FIG. 3 illustrates geometrical parameters of a probe 101,
according to one embodiment of the invention.
[0006] FIGS. 4-5 illustrate a probe 101 utilizing an element that
keeps distance constancy, according to one embodiment of the
invention.
[0007] FIG. 6 illustrates a probe 101 with a dielectric tube in an
alternative shape, according to one embodiment of the
invention.
[0008] FIGS. 7-8 illustrate a probe 101 with alternative antenna
tip shapes, according to embodiments of the invention.
[0009] FIG. 9 illustrates a probe 101 that is moveable, according
to one embodiment of the present invention.
[0010] FIG. 10 is a graph illustrating resonance frequencies
.omega./.omega..sub.p versus tip distance in the m=1 mode,
according to one embodiment of the invention.
DESCRIPTION OF EMBODIMENTS OF THE INVENTION
Apparatus for Measuring Plasma Density
[0011] FIGS. 1 and 2 are schematic representations of an apparatus
for measuring plasma density in a plasma processing reactor,
according to one embodiment of the invention. Plasma is used in
material processing reactors because it has significant advantages
in processing rate, accuracy, and processing capabilities over
non-plasma methods. Plasma density defines the radical content in
the processing gas and the processing speed, and is important for a
process engineer to know. Plasma density in a processing chamber
depends on many factors, including gas composition, gas pressure,
flow rate, RF power, pumping speed, geometry of the chamber, and
the materials of the chamber walls and the electrodes. Plasma
density in a processing chamber also depends on the power of
ionizing sources, which is typically radio frequency (RF) power
applied from various types of coils (i.e., inductively coupled
plasma sources, or ICP), RF power applied to electrodes (i.e.,
capacitive coupled plasma sources, or CCP), microwave power, etc.
Furthermore, plasma density in the processing chamber depends on
the rate of loss of the plasma due to, for example, direct loss to
the walls, the electrodes, and various recombination and
neutralization processes.
[0012] In FIGS. 1 and 2, the apparatus comprises a probe 101, which
comprises a coaxial cable 105 with an open antenna tip 110,
surrounded by a dielectric tube 115. The coaxial cable 105 is a
round, flexible, two-conductor cable consisting of, from the center
outwards, a center wire, a dielectric layer, a braided metal mesh
sleeve, and an outer shield. The shield prevents signals
transmitted on the center wire from affecting nearby components and
prevents external interference from affecting the signal carried on
the antenna.
[0013] In the embodiment of FIGS. 1 and 2, the center wire extends
out beyond the other layers to form open antenna tip 110. The
antenna tip 110 can be straight or not straight. In one embodiment,
the antenna tip can be a straight naked metal wire of at least a
few millimeters long. As examples of antenna tips 110 that are not
straight, see FIGS. 7 and 8, illustrating an antenna tip 110 bent
in one direction, and an antenna tip 110 bent in the shape of a
partial loop, respectively.
[0014] The dielectric tube 115 isolates the coaxial cable 105 and
the antenna tip 110 from the plasma and prevents direct currents on
the coaxial cable 105 and the antenna tip 110. The material of the
dielectric tube 115 can be selected to adjust a resonant frequency
for the system. The dielectric permittivity of the material of the
dielectric tube 115 can thus be chosen to correspond to an expected
plasma density range (e.g., quartz has a lower dielectric
permittivity than ceramic). In one embodiment, a high dielectric
permittivity can be used with an expected high plasma density to
keep the resonant frequency within the range of the network
analyzer 120 (see below) under about 5 GHz. Note that the higher
the plasma density, the higher the dielectric permittivity that can
be used. Possible dielectric depositions on the dielectric tube 115
in a chemically active environment do not affect the probe data, at
least until the thickness of the deposition layer becomes thick
enough to be comparable with the thickness of the dielectric tube
115. The tip 110 of the dielectric tube 115 is located within the
area where the plasma density has to be measured. Note that spacers
305, which will be described in more detail with respect to FIG. 4
and 5, are optional.
[0015] In one embodiment, the probe 101 comprises a long dielectric
tube 115 and coaxial cable 105, which can be used for scanning
plasma parameters. The long dielectric tube 115 has a long coaxial
cable so that the antenna tip 110 is located in a position remote
from the base 135 so that the long dielectric tube 115 can detect
plasma parameters in a position remote from the base 135. The base
135 can be movable, as demonstrated in FIG. 1, or stationary, as
demonstrated in FIG. 2.
[0016] A base 135 closes the probe 101. In FIG. 1 where the base
135 is moveable, a flange 133 can be used to guide dielectric tube
115. Seals 134 enable the probe 101 to move relative to flange 133
and component 130. The base 135 can be made of, for example, metal
(e.g., aluminum). If the probe 101 is embedded in some other
structure (e.g., the substrate holder or a vacuum chamber wall,
which can be metal), then the base 135 might be absent because the
body of the substrate holder or vacuum chamber wall (e.g.,
component 130) will be the base 135. A vacuum seal can be included
in base 135 to seal the probe 101.
[0017] The network analyzer 120 generates RF signals that are
transmitted through the high pass filter (HPF) 125 to the probe
101. After interacting with the plasma, RF energy is reflected back
through the high pass filter 125 to the network analyzer 120,
providing a plasma wave resonance signature.
[0018] FIG. 3 illustrates geometrical parameters of a probe 101,
according to one embodiment of the invention. The external radius
of the dielectric tube 115 is a. The internal radius of the
dielectric tube 115 is b. The horizontal distance between the
coaxial cable end and the dielectric tube end is d. The external
radius of the coaxial cable 105 is c. The radius of the antenna tip
110 is r.sub.a. The horizontal distance between the coaxial cable
end and the antenna tip end is d.sub.a. The horizontal distance
(i.e., the space) between the external radius of the dielectric
tube 115 and the antenna tip 110 is d.sub.d. In one embodiment, the
space is at least a few millimeters.
[0019] It is often beneficial to add elements (e.g., spacers,
in-and-out feature), change elements (e.g., antenna shape), or add
additional probes 101 to improve the sharpness of the absorption
resonances (as shown in FIG. 10), compensate for the possible
geometry modification due to heat fluxes on the probe 101 from the
plasma or other sources, or gain additional information about the
plasma density.
[0020] Spacers. FIG. 4 illustrates a probe 101 utilizing an element
that keeps distance constancy, according to one embodiment of the
invention. The distance constancy is selected so as to diminish the
amplitudes of parasitic surface waves running along the dielectric
tube, which otherwise might interfere with main absorption
resonances used for measurements. Also, the distance constancy can
help the resonant frequency to change in time with the heating of
the probe due to particle and heat fluxes from the plasma. In one
embodiment, a spacer can be used to keep distance constancy. The
spacers are placed inside the dielectric tube 115 around the
antenna tip 110 and/or the coaxial cable 105. The spacers can be in
the form of tubes or rings. The spacers can be made of a dielectric
material or of a metal material. In one embodiment, the spacer is a
dielectric tube with an inner radius approximately equal to the
radius of the antenna tip to increase constancy of the antenna tip
shape under varying thermal conditions.
[0021] Spacers around the antenna tip 110 can be tubes 310, and can
be made of a dielectric material to ensure relative constancy of
the antenna tip distance, d.sub.d, in spite of possible thermal
expansions of the coaxial cable 105. In addition, spacers around
the antenna tip 110 ensure relative constancy of the antenna tip
shape (e.g., staying straight and not being bent under varying
thermal conditions).
[0022] To fix the coaxial cable 105 inside the dielectric tube 115,
spacers are provided between the coaxial cable 105 and the
dielectric tube 115. These spacers can be in the form of tubes or
rings 305. Spacers between the coaxial cable 105 and the dielectric
tube 115 can be of a dielectric material, metal material, or a
combination of a dielectric material 412 with a metal material 414,
as illustrated in FIG. 5. In one embodiment, the metal material 414
is used to reflect waves, so it is put against the coaxial cable.
The dielectric spacer fixes the cable end at a specified position.
The metal spacer provides a sharp reflecting boundary for the
plasma surface waves, so the plasma absorption resonances are more
clearly pronounced and measured. In one embodiment, a high
dielectric permittivity can be used with an expected high plasma
density to keep the resonant frequency within the frequency range
of network analyzer 120, such as under about 5 GHz. Note that the
higher the plasma density, the higher the dielectric permittivity
that can be used.
[0023] FIG. 6 illustrates a probe 101 with a dielectric tube 115 in
an alternate shape, according to one embodiment of the invention.
Spacers around the antenna tip 110 can be replaced by a dielectric
tube 115 of a special shape which limits cable expansion and
ensures a relative constancy of the antenna tip distance, d.sub.d.
In one embodiment, the corner of coaxial cable 105 abuts against
dielectric tube 115 and antenna tip 110 extends into a portion of
dielectric tube 115 with reduced diameter. With this particular
shape, the probe 101 is highly sensitive to the plasma because the
radial distance between the antenna tip 110 and the external
surface of the dielectric tube 115 is short. The heat transfer to
the antenna tip 110 increases, and thus, this type of a probe can
be used with low power discharges with relatively low heat
fluxes.
[0024] Note that, in one embodiment, various resonances in
reflected signals are interpreted based on surface wave modes. The
resonances are mapped with corresponding plasma density values
around the antenna tip. Resonance modes are selected from measured
absorption resonances, and the selected modes are those modes that
are the strongest and also provide information about local values
of the plasma density around the antenna tip. The dielectric spacer
can be made of material selected to have a dielectric property used
in correspondence with an expected plasma density range to produce
a resonance in a desired frequency range. The material of the
dielectric spacer can be chosen to have a higher dielectric
permittivity for measurements in a higher plasma density range.
[0025] In one embodiment, if the coaxial cable has a smaller radius
than the inner radius of the dielectric tube, and a dielectric
spacer ring is provided at the end of the coaxial cable between the
radius of the coaxial cable and the inner radius of the dielectric
tube, the spacer ring provides more sharply emphasized boundary
conditions for the surface wave reflection, making absorption
resonances more pronounced. In another embodiment, the coaxial
cable has a smaller radius than the inner radius of the dielectric
tube, with at least one dielectric ring or short dielectric tube
along the coaxial cable, surrounding the cable and located inside
the dielectric tube. This provides a larger distance between the
cable surface and the plasma edge and diminishes the amplitude of
parasitic surface waves running along the dielectric tube, which
otherwise might interfere with the main absorption resonances used
for measurements.
[0026] Alternate Antenna Shapes. FIGS. 7-8 illustrate a probe 101
with alternative antenna tip shapes, according to embodiments of
the invention. The alternative antenna tip shapes can be used with
certain modes of resonance, corresponding to various standing wave
patterns of the electromagnetic field caused by the interaction of
the probe with the plasma. For example, in mode 0, the intensity is
constant within a plane perpendicular to the center conductor at a
constant distance from the center conductor. In mode 1, the
intensity has one maximum and one minimum in the plane at a
constant distance from the center conductor. In mode 2, the
intensity has two maximums and two minimums in the plane at a
constant distance from the center conductor.
[0027] A probe 101 with a straight antenna tip 110, as shown in
FIG. 1, is beneficial for picking up the main m=0 mode of the
plasma surface waves. However, other modes might be of importance
as well. FIG. 7 illustrates a probe 101 with the antenna tip bent
on one side, which picks up the m=1 mode of the plasma surface
waves. FIG. 8 illustrates a probe 101 with the antenna tip the
shape of a partial loop, which picks up the m =2 mode of the plasma
surface waves.
[0028] FIG. 9 illustrates another moveable probe 750, according to
one embodiment of the present invention. The components of the
probe, the spacers 305 and 710, the antenna tip 110, the dielectric
tube 115, and the plasma 150 are indicated on FIG. 7. Cable 706 is
connected to the coaxial cable 105 by an SMA connector 745.
[0029] Feed-through bracket 727 is attached to chamber wall 760.
Dielectric tube 115 extends through chamber wall in a slidable
fashion as a result of vacuum seals 728. Tube 717 is attached to
the end of dielectric tube 115 and spring housing 742 is attached
to the end of tube 717. Spring 740 is compressed between housing
742 and SMA connector 745 to bias coaxial cable 706 and 105 into
dielectric tube 115 to maintain the relative positions of antenna
tip 110 and dielectric tube 115.
[0030] Dielectric tube 115, tube 717 and housing 742 can slide
relative to chamber wall 760 so that the position from chamber wall
760 that probe 101 extends into the chamber can be varied. Once the
desired position is obtained, screw 724 can clamp tube 717 in
place. The network analyzer 720 generates RF signals that are
transmitted through the high pass filter 725 to the probe 750.
After interacting with the plasma, RF energy is reflected back
through the high pass filter 725 to the network analyzer 720,
providing a plasma wave resonance signature.
[0031] Distance constancy is kept between the antenna tip 110 and
the dielectric tube tip via the spacers 710 and via the spring 740.
The spring 740 allows the cable to expand when it is heated and at
the same time to help the cable provide pressure against the
spacers 710. This configuration is capable of providing distance
constancy even where the length of the cable 105 is long, and even
when the cable has significant thermal expansion due to its
heating.
Method for Measuring Plasma Density
[0032] To use the probe, the frequency or wavelength at which
resonance occurs is measured, which provides information needed to
determine the plasma density. For example, FIG. 10 is a graph
illustrating resonance frequencies .omega./.omega..sub.p versus tip
distance, according to one embodiment of the invention. The
discontinuities 1401 on the graph identify the frequency at which
resonance occurs. RF signals from the network analyzer 120 are
reflected back to the network analyzer 120, providing the plasma
wave resonance signature. The HPF 125 is located between the probe
101 and the network analyzer 120, and reduces low frequency signals
which otherwise would eminate from the plasma region. As an
example, a cut off frequency for the HPF can be chosen to be a
factor of 10 lower than the main RF power frequency. Once the low
frequency signals are cut off, the network analyzer 120 can measure
the frequency or wavelength at which resonance occurs, which is
related to the plasma density.
[0033] In one embodiment, a method is provided to relate observed
resonances with the plasma density. Once the resonant frequency for
the known wave mode is measured and the dielectric permittivity of
the dielectric tube .epsilon..sub.d is known, the dielectric
permittivity .epsilon..sub.p of the plasma is determined using the
following dispersion relation: D .function. ( .omega. , k z , m ) =
p - d K m .function. ( k z .times. a ) K m ' .function. ( k z
.times. a ) .alpha. .times. .times. I m ' .function. ( k z .times.
a ) + .beta. .times. .times. K m ' .function. ( k z .times. a )
.alpha. .times. .times. I m .function. ( k z .times. a ) + .beta.
.times. .times. K m .function. ( k z .times. a ) = 0 ( 1 )
##EQU1##
[0034] where:
[0035] .omega.=2.pi.f (where f is a wave frequency)
[0036] k.sub.z=2.pi./.lamda. (where k.sub.z is a longitudinal wave
vector; .lamda. is a longitudinal wavelength)
[0037] m=azimuthal mode number
[0038] .epsilon..sub.d=dielectric permittivity of the dielectric
tube 115
[0039] a=external radius of dielectric tube 115
[0040] b=internal radius of dielectric tube 115
[0041] I.sub.m=modified Bessel function of first kind of order
m
[0042] K.sub.m=modified Bessel function of second kind of order
m
[0043] I'.sub.m and K'.sub.m are derivatives, respectively, for
I.sub.m and K.sub.m.
[0044] and .alpha. = 1 d sK m .function. ( k z .times. b ) - p
.times. .times. d .times. K m ' .function. ( k z .times. b ) K m
.function. ( k z .times. b ) .times. I m ' .function. ( k z .times.
b ) - I m .function. ( k z .times. b ) .times. K m ' .function. ( k
z .times. b ) .times. .times. .beta. = 1 d p .times. .times.
.times. d .times. I m ' .function. ( k z .times. b ) - sI m
.function. ( k z .times. b ) K m .function. ( k z .times. b )
.times. I m ' .function. ( k z .times. b ) - I m .function. ( k z
.times. b ) .times. K m ' .function. ( k z .times. b ) ( 2 )
##EQU2##
[0045] Parameters s and p depend on the region of the probe,
particularly the antenna tip region. They are given by the
expressions: p = I m .function. ( k z .times. b ) - I m .function.
( k z .times. r a ) K m .function. ( k z .times. r a ) * K m
.function. ( k z .times. b ) ( 3 ) s = I m ' .function. ( k z
.times. b ) - I m .function. ( k z .times. r a ) K m .function. ( k
z .times. r a ) * K m ' .function. ( k z .times. b ) ( 4 )
##EQU3##
[0046] where r.sub.a=radius of antenna tip
[0047] Once .epsilon..sub.p is known, the plasma frequency
.omega..sub.p is determined using the following formula: p = 1 -
.omega. p 2 .omega. 2 ( 5 ) ##EQU4##
[0048] Once the plasma frequency .omega..sub.p is determined, the
plasma density n.sub.e can be determined using the following
formula: .omega..sub.p {square root over
(4.pi.n.sub.ee.sup.2/m.sub.e)}.apprxeq.5.64.times.10.sup.4 {square
root over (n.sub.e)} (6)
[0049] Once the plasma density is know at one or more points within
the plasma reactor, the plasma density at any other point in the
reactor can be determined using the measured value(s) and a model
of relative plasma densities throughout the reactor. The model can
be the result of measurements taken in the reactor or a
mathematical model.
Conclusion
[0050] While various embodiments of the present invention have been
described above, it should be understood that they have been
presented by way of example, and not limitation. It will be
apparent to persons skilled in the relevant art(s) that various
changes in form and detail can be made therein without departing
from the spirit and scope of the present invention. In fact, after
reading the above description, it will be apparent to one skilled
in the relevant art(s) how to implement the invention in
alternative embodiments. Thus, the present invention should not be
limited by any of the above-described exemplary embodiments.
[0051] It should also be noted that when a claim refers to "a"
component, this language also covers "at least one" of that
component. If a claim refers to "a" probe, an invention that
includes more than one probe would necessarily include "a" probe or
"one" probe.
[0052] In addition, it should be understood that the figures, which
highlight the functionality and advantages of the present
invention, are presented for example purposes only. The
architecture of the present invention is sufficiently flexible and
configurable, such that it may be utilized in ways other than that
shown in the accompanying figures.
[0053] Further, the purpose of the Abstract of the Disclosure is to
enable the U.S. Patent and Trademark Office and the public
generally, and especially the scientists, engineers and
practitioners in the art who are not familiar with patent or legal
terms or phraseology, to determine quickly from a cursory
inspection the nature and essence of the technical disclosure of
the application. The Abstract of the Disclosure is not intended to
be limiting as to the scope of the present invention in any
way.
* * * * *