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BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a plasma deposition or etching method and
various apparatus for depositing a thin film onto a substrate or for
removal (etching) of a film from a substrate. The present invention
includes the use of a new and significantly better high density plasma
deposition and etching apparatus, a significantly improved magnetic means
for the plasma source region and operation with a specified range of
processes and gases. Applications of the present invention include the
removal by etching of a layer from a surface, the removal by sputtering of
a layer from a surface, or the deposition of a layer onto a surface.
2. Related Art
Etching
Plasma etching involves using chemically active atoms or energetic ions to
remove material from a substrate. It is a key technology in the
fabrication of semiconductor integrated circuits. However, before the
advent of microwave plasmas utilizing electron cyclotron resonance (ECR),
it was becoming difficult for conventional plasma etching techniques to
satisfy the requirements dictated by the increase in device packing
density. Specifically, the requirement for fine pattern etching without
undercutting (anisotropic etching) and the requirements for low damage and
high selectivity could hardly be satisfied at the same time.
Deposition
Plasma Enhanced Chemical Vapor Deposition (PECVD) is a widely used
technique to deposit materials on substrates in a host of applications. In
normal Chemical Vapor Deposition (CVD) the chemical reaction is driven by
the temperature of the substrate and for most reactions this temperature
is high (>800.degree. C.). The high substrate temperature needed precludes
use of this method in a number of applications particularly in
microelectronics, displays and optical coatings. The role of the plasma is
to dissociate and activate the chemical gas so that the substrate
temperature can be reduced. The rate of dissociation, activation and
ionization is proportional to the density of the plasma. It is therefore
of importance to make the plasma as dense as possible.
Sputtering
Sputtering is also a widely used method for depositing materials onto
substrates for a wide variety of applications such as the production of
hard or decorative coatings and the coating of glass. In general, a plasma
is produced at the sputter target material and the sputter target is
biased to a negative voltage of around 700 V. Plasma ions (generally
argon) impact the surface and sputter the material which then transports
as neutral atoms to a substrate. Reactive gases can be introduced to
chemically react with the sputtered atoms at the host substrate in a
process called reactive sputter deposition. Rate is often important and it
is therefore important to make the plasma as dense as possible. Ionization
of reactive gases is also important and is helped by having plasma in the
vicinity of the substrate material. Sputtering is also done by ions
accelerated in an ion or plasma gun and then made to bombard the sputter
target. In this case, a bias voltage on the target is not necessary. For
sputtering insulating materials, RF voltage bias can be applied to the
sputter target.
Existing Methods
There are presently two widely used methods for plasma deposition and
etching, the parallel plate reactor and the ECR plasma deposition system.
There are also methods based on the use of RF to produce plasma including
ordinary induction techniques and techniques based on whistler waves.
Parallel Plate Reactor (Diode)
The RF diode has been widely used for both deposition and etching. It is
described in detail in the book by Chapman ("Glow Discharge Processes"
John Wiley & Sons 1980). It uses RF at 13.56 MHz capacitively coupled to
one electrode while the other electrode is grounded. The pressure in the
system is typically 1 mtorr to 1 torr and the plasma density is typically
10.sup.10 electrons per cm.sup.3. The rate at which both deposition or
etching occurs is dependent on the density of the plasma and the density
(pressure) of the reactive gas used to etch, or, in CVD processes, to
deposit.
In etching, the high pressure needed to sustain the discharge causes
collisions between the ions and the background gas. This causes the paths
of the etching ions or atoms to be randomized or non-directional, leading
to undercutting of the mask. This is referred to as an isotropic etch. It
is desirable to have the etch atoms or ions be directional so that
straight anisotropic etches can be achieved. At the high pressure used in
RF diode discharges, it is necessary for the ions to have high energy (up
to 1 KeV) to achieve an anisotropic etch. However, the high energy of the
ions can cause damage to the substrate, film materials or photoresist.
The plasma is sustained by secondary electrons that are emitted by ions
impacting the cathode. These electrons are accelerated by the voltage drop
across the sheath which is typically 400-1000 V. These fast electrons can
bombard the substrate causing it to have a high voltage sheath drop. This
high voltage can accelerate the ions leading to damage of the substrate or
film material. The presence of high energy electrons leading to high
voltage sheath drops is undesirable.
Electron Cyclotron Resonance Plasmas
The advent of using microwaves at 2.45 GHz and a magnetic field of 875
Gauss to utilize electron cyclotron resonance allowed the generation of
high density plasmas at low pressure. The advantages of this technique for
plasma etching are described by Suzuki in U.S. Pat. No. 4,101,411 and in
an article entitled "Microwave Plasma Etching" published in Vacuum, Vol.
34, No. 10/11, 1984. Due to a low gas pressure (0.04-0.4 Pa) and high
plasma density (1.7-7.times.10.sup.11 electrons/cm.sup.3) anisotropic etch
with high etch rates is achievable.
Suzuki, in U.S. Pat. No. 4,101,411, describes a plasma etching apparatus
using ECR. Matsuo, in U.S. Pat. No. 4,401,054 describes a plasma
deposition apparatus utilizing ECR. In U.S. Pat. No. 4,876,983 there is
described a plasma etching apparatus to improve uniformity and have the
specimen close to the source chamber.
While this technique is desirable over the parallel plate reactor in many
respects, it has several limitations. The magnetic field needed is very
high (1-2 kGauss) which means that heavy, power consuming electromagnets
must be used. The maximum density is limited by either cut-off in certain
configurations or by refraction in other configurations to the value of
1.times.10.sup.12 electrons/cm.sup.3 in the source. The expense of the
power supply and necessary hardware to generate and transmit the
microwaves is high. The uniformity (or width of the plasma profile) is not
very good.
RF Helicon Whistler Wave Plasmas
The first use of helicon type whistler waves to generate dense plasmas was
described in 1970 by Boswell in the journal, Physics Letters, Vol. 33A, pp
457-458 (1970) which showed an antenna configuration used by Ovchinnikov.
This type of antenna excites an m=1 mode. The frequency of excitation was
8 MHz. The density profile of the 10 cm plasma was found to be quite
peaked, particularly at the higher magnetic field strengths needed for
high densities. In Boswell, U.S. Pat. No. 4,810,935, two mathematical
relationships are required to be satisfied. These equations are in fact
overly restrictive and not applicable to the approach outlined by
Campbell, Conn and Shoji in U.S. Pat. Nos. 4,990,229 and 5,122,251.
In these publications the mechanism for efficient coupling of the RF energy
to the plasma could not be explained. Chen, in an Australian National
University report, explained the mechanism as Landau damping.
Chen, in a paper presented in August 1988 and published in the journal,
Plasma Physics and Controlled Fusion, Vol. 33, 1991, describes a system
using whistler waves to generate dense plasmas for use in advanced
accelerators. The type of antenna used in this arrangement was similar to
that used by Boswell in that it excited the m=1 mode and was a type known
as the Nagoya Type III antenna. This type of antenna is explained in a
paper by Watari (1978). The frequency of excitation was 30 MHz.
Campbell, Conn and Shoji, in U.S. Pat. No. 4,990,229 and Pat. No. 5,122,251
describe new and highly efficient antenna means designed to excite the m=0
and the m=1 modes, and to control the wave number of the excited wave.
This is important in obtaining the maximum plasma density, in generating
the broadest spatial plasma density profile in the source and process
chamber regions, and in providing control over the electron temperature in
the plasma.
Efficiency of plasma production by low frequency whistler waves depends on
the coupling of RF energy into the plasma. As discussed by Campbell et al.
in U.S. Pat. No. 4,990,229, an important mechanism for damping of the RF
energy is Landau damping. The phase velocity of the whistler wave is given
by .omega./k.sub.z, where k.sub.z is given by the dispersion relation and
depends on the plasma density and vacuum magnetic field strength. Ideally,
the phase velocity of the wave should be near the maximum of the
ionization potential of the gas we wish to ionize. From the dispersion
relation for the m=0 mode, the higher the value of k.sub.z, the higher the
density. However, the phase velocity of the wave is .omega./k.sub.z and so
increasing k.sub.z decreases the energy of the electrons that are
accelerated by the wave. If the k.sub.z is too high then the energy of the
electrons may fall below the ionization potential.
Also, Campbell, Conn and Shoji in the above-mentioned patents use a
magnetic bucket means in conjunction with the plasma generator to provide
a uniform plasma density over large circular or rectangular areas. They
use one or multiple plasma generators in conjunction with cylindrical or
rectangular magnetic buckets to provide a uniform density over a large
area for the coating or etching of substrates such as are needed for IC or
flat panel display processing. They use expansion of the magnetic field to
allow deposition or etching over a large area.
Other RF Induction Sources
Other existing methods use RF circuit resonances to generate plasma. These
methods are less efficient than those using low frequency whistler waves,
and do not generate high density plasmas. Ogle, in U.S. Pat. No. 4,948,458
describes an RF means to produce planar plasma in a low pressure process
gas using an external planar spiral coil (or series of concentric rings)
and connected to a second loop which is positioned to allow for effective
coupling of the circuit and for loading of the circuit at the frequency of
operation. Steinberg et al., in U.S. Pat. No. 4,368,092, describes a
plasma generating system employing a helical inductive resonator for
producing the plasma external to an etching chamber. The plasma is
non-uniform and passes through a tube before utilization. U.S. Pat. No.
4,421,898, describes an inductively-coupled plasma generating apparatus,
where a transformer having a magnetic core induces electron circulation in
an insulating tube carrying a process gas. Gas ionization is non-uniform,
and exposure to the wafer occurs downstream. U.S. Pat. No. 4,626,312,
describes a conventional parallel plate plasma etcher where the wafer is
situated on a lower electrode and a plasma is generated by applying
radiofrequency energy across the lower electrode and a parallel upper
electrode. U.S. Pat. Nos. 4,668,338 and 4,668,365, describe
magnetically-enhanced plasma processes for reactive ion etching and
chemical vapor deposition, respectively. Flamm et al. in U.S. Pat. No.
4,918,031 describes an L-C circuit referred to as a helical resonator
which consists of an inner helically shaped copper coil surrounding a
quartz tube and attached at one end to a cylindrical copper shield. The
opposite end of the inner coil is unterminated. No external magnetic field
is employed in these approaches and all generate plasmas at low pressure
in the 1-10 mtorr range but at moderate density in the quartz source tube
or just below a planar spiral coil and without a high degree of spatial
uniformity. No externally generated magnetic field is employed in these RF
plasma generators.
SUMMARY OF THE INVENTION
The present invention utilizes low frequency RF whistler waves to generate
plasmas of high density for use in plasma etching, deposition, and
sputtering equipment. Plasma is generated in a source tube which is
typically made of quartz or a fluorine-resistant material such as alumina
or sapphire. In conjunction with the source tube into which a gas is
injected and along the central axis of which a magnetic field is
established, a single loop antenna is disposed in a plane transverse to
the central axis. The angle of the antenna plane is 90.degree. if it is
desired to excite only M=0 mode, or at less than 90.degree. if it is
desired to excite components in both M=0 and M=1 mode. The gas is a noble
or reactive gas at a pressure of 0.1 mtorr to 200 mtorr. The magnetic
field strength is in the range of 10 to 1000 gauss and the antenna is
driven with RF energy of 100 W to 5 KW at a frequency range of 2 MHz to 50
MHz. With the antenna placed along the tube source at a sufficient
distance along the axis from the gas injection end, the other end defining
an open egress zone leading to a process chamber, the single loop antenna
surprisingly provides highly efficient wave coupling to establish a high
density and high current plasma.
In accordance with other features of the invention, the plasma generated by
this plasma source is supplied to a process chamber including a magnetic
bucket system for holding the plasma away from the process chamber walls.
The arrangement provides, in combination, a uniform plasma density over a
large circular area, so that a large substrate may be etched or otherwise
processed. Another feature is that a magnetic cusp zone may be
established, at the material surface being processed, to homogenize and
make more uniform the plasma at that location. An aspect of this is that
the magnetic cusp position relative to the substrate may be time modulated
to enhance uniformity and reduce sensitivity to substrate location.
Further, the magnetic field may be expanded to allow deposition or etching
over a large area and current flows may be equalized by serial driving of
antennas in systems having more than one antenna. Other features reside in
configurations which employ one or more multiple geometrical areas for
coating or etching of square or rectangular substrates, or a linear
juxtaposition for coating or etching large substrates.
The invention provides a module with a highly efficient magnetic means of
transporting plasma from a plasma generator means to a substrate located
on a cooled substrate holder located in a substrate process chamber and in
which the processing of the substrate is highly uniform and the substrate
process module is compact. The invention shields the magnet means from RF
signals generated by the antenna and thereby prevents false signals from
being received by a control system which drives the magnet means. The
shielding may be a thin sheet of conducting material wrapped around the
magnet means.
The invention provides a gas distribution means in the top of the process
chamber as an integral part of the process chamber structure in order to
attain highly efficient plasma operation and highly uniform processing of
the substrate while permitting the process module to be reduced in height.
The invention attains highly efficient plasma operation in a compact
substrate process module which can attain excellent characteristics for
the etching of IC wafers as represented by high etch rate, high
uniformity, high selectivity, high anisotropy, and low damage.
The invention achieves high density and highly uniform plasma operation at
low pressure from 0.3 mtorr to 5 mtorr for etching an IC substrate and
from 1 mtorr to 30 mtorr for deposition of films on to substrates.
The invention provides a substrate processing system capable of operating
with a wide variety of gases and combinations of gases, including highly
reactive and corrosive gases.
The invention provides such a substrate processing system capable of
etching or depositing films listed in Table 1 and Table 2 using gases fed
into the plasma generator region, into the process chamber region, or into
both regions.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a schematic diagram depicting the principle of operation and RF
current flow in an antenna constructed according to the invention as shown
in U.S. Pat. No. 4,990,229.
FIGS. 2A, 2B and 2C are schematic views of antennas constructed according
to the principles of the invention.
FIG. 3 is a schematic diagram depicting the principle of operation and RF
current flow in a plasma source constructed according to the invention as
shown in U.S. Pat. No. 5,122,251.
FIGS. 4A and 4B illustrate in schematic form two basic configurations of a
plasma deposition or etching apparatus accordance with this invention.
FIG. 5A is a schematic diagram of a second example of a system in
accordance with the present invention in which the plasma source region is
connected to a magnetic bucket region where uniformity requirements are
important.
FIG. 5B is a plan view of the arrangement of FIG. 5A, taken along the line
3A--3A in FIG. 5A.
FIG. 6A is a perspective view of a third example of a system in the present
invention for deposition or etching over a large rectangular area where
uniformity is important.
FIG. 6B is a plan view of the arrangement of FIG. 6A, taken along the line
4A--4A in FIG. 6A.
FIG. 7A is a schematic diagram of yet another example of a system in
accordance with the present invention in which a bottom magnet is added
behind the plane of the substrate holder to provide a magnetic cusp field,
the plane of the cusp being approximately the same as the plane of the
substrate holder.
FIG. 7B is a plan view of the arrangement of FIG. 7A, taken along the line
5A--5A in FIG. 7A.
FIG. 8 is a schematic diagram of an example of a system in accordance with
the invention for sputter deposition.
FIG. 9 is a graph depicting the plasma current density at the substrate
location according to the example of FIG. 5A using the plasma source
depicted in FIG. 3 as a function of magnetic field in the source region.
FIG. 10 is a graph of the same data as in FIG. 9 but graphed on a linear
scale for magnetic field to show the plasma current density at the
substrate location where the magnetic field is low, varying from zero to
160 gauss.
FIG. 11 is a graph depicting the total plasma current (or total flux) at
the substrate location according to the invention as depicted in FIG. 5A
using the plasma source as depicted in FIG. 3 as a function of RF power to
the source at a gas pressure of 2 mtorr.
FIG. 12 is a graph depicting the plasma current density at the substrate
location according to the invention as depicted in FIG. 5A using the
antenna as depicted in FIG. 3 as a function of the gas pressure.
FIG. 13 is a graph depicting the plasma current density at the substrate
location according to the invention as depicted in FIG. 5A and the plasma
source of FIG. 3 as a function of position to show the excellent
uniformity over a substantial width.
FIGS. 14A to 14C are diagrams showing the arrangement of the
electromagnetic system in the plasma generator region according to the
present invention to make efficient the transport of plasma from the
plasma generator tube to the substrate process chamber which includes a
magnetic bucket and where uniformity and high plasma flux to the substrate
are required.
FIG. 15A is a plot of the magnetic field lines obtained using one
electromagnet surrounding the plasma source tube.
FIG. 15B is a plot of the magnetic field lines obtained using two
electromagnets surrounding the source tube and where the outer magnet coil
carries a current in the opposite direction from the inner magnet coil and
has a coil current that is 40% as large in magnitude as that of the inner
coil.
FIG. 16A is a schematic diagram of the configuration of a plasma etching or
deposition apparatus.
FIG. 16B is a plan view of the substrate process chamber section of the
arrangement of FIG. 16A taken along the line 7A--7A in FIG. 16A.
FIG. 17A is a plan view of the substrate process chamber showing the gas
feed lines, the nozzle holes for gas injection into the chamber, the water
cooling lines and the grooves for the ceramic permanent magnets.
FIG. 17B is a detail showing the entrance to the gas feed line at the top
of the substrate process chamber shown in FIG. 17A.
FIG. 17C shows in larger size the gas feed structure of FIG. 17A.
FIG. 18 is a cross sectional SEM image obtained for the etching of poly-Si
in pure Cl.sub.2 using the MORI plasma source etching system. In this
case, the SEM shows structure with 100% overetch. One sees highly
anisotropic profiles, no notching, and less than 50 .ANG. oxide loss.
FIG. 19 shows the aluminum etch rate, the oxide etch rate, and the PR etch
rate (left ordinate) and selectivity to photoresist etching and to oxide
etching (right ordinate) as a function of RF wafer bias power applied at
13.56 MHz. The gas mixture is 85% Cl.sub.2 -15% BCl.sub.3, the MORI source
power is 1 KW, and the substrate is located in the process chamber 20 cm
below the end of the source tube.
FIG. 20 is a cross sectional SEM image obtained for sub micron etching of W
on a TiW adhesion layer on thermal oxide in pure SF.sub.6 using the MORI
plasma source etching system. The anisotropy is excellent, there is no CD
loss, and there are no residues.
DETAILED DESCRIPTION OF THE INVENTION
FIGS. 1A, 2B, and 2C illustrate schematically the RF current flow in two
antennas constructed according to the invention disclosed in U.S. Pat. No.
4,990,229 issued Feb. 5, 1991. For a more detailed description of the
operation of these antennas, U.S. Pat. No. 4,990,229 is incorporated
herein by reference in its entirety.
A simplified view of principal elements and relationships in a device in
accordance with the invention is provided by the representation of FIG. 3,
wherein high density plasma 9 is to be generated within a source tube 10
of generally cylindrical form about a central (here vertical) axis. At one
(here upper) end an injector 11 feeds gas to be ionized into the interior
volume of the source tube, where the gas is excited by an external loop
antenna 12 that encompasses an intermediate region of the source tube 10.
The antenna loop 12 comprises in this example a not fully circular element
lying in a plane that is at 90.degree. or less in either sense relative to
the central axis. The direction of propagation of the plasma is here
downward toward an exit aperture 13. The antenna loop 12 has its opposite
ends coupled to the outer conductor 14 and center conductor 15 of a
coaxial driver line 16 which is energized through a matching box 18 by an
RF energy source 19. A pair of variable vacuum capacitors 20, 21 in the
matching box 18 are adjustable to tune the circuit so that the antenna
loading plus the reactive load of the matching box 18 is approximately 50
ohms to minimize the reflected power.
The antenna tuning and wave spectrum are adjusted to match the conditions
in the plasma field, and also in relation to an interior axial magnetic
field 8 generated by at least one magnetic field coil (not shown) about
the source tube 10. The matching condition is predicted by theory to be
dictated by the dispersion relation:
[.omega./.omega..sub.c -.omega..sub.p.sup.2 /C.sup.2 K.sub.z.sup.2 ].sup.2
=1+(3.83/k.sub.z a).sup.2
To effect wave coupling and establish a high plasma current density,
measured in mA/cm.sup.2, the antenna loop 12 is driven at 13.56 MHz and
with RF energy of the order of 2.0 KW (in the range of 100 W to 5 KW) by
the RF energy source 19. The magnetic field established by the magnetic
field coil is in the range of 10 to 1000 gauss, for different useful
applications. The gas is argon and maintained at a pressure of about 1
mtorr in this example. However, in addition to a noble gas such as argon,
reactive gases such as SF.sub.6, chlorine, oxygen, and mixtures with
oxygen have been used with comparably useful results. A pressure range of
0.1 mtorr to 200 mtorr can be used if other variables are properly taken
into account. With a 5 KW power supply less than the maximum available
power can be used, to a substantially lower level of several hundred
watts, depending on the application. Although the 13.56 MHz frequency is
available from many industrial sources, the range of 2 MHz to 50 MHz can
be usefully employed.
In FIG. 3, the antenna loop 12 is shown at 90.degree. to the longitudinal
axis of the source tube 10. This orientation generates the M=0 mode, while
reducing the angle from 90.degree. in either sense introduces components
of the M=1 mode as well as components of the M=0 mode. Angles of less than
90.degree. to the longitudinal axis require correspondingly longer antenna
loops 12, so there is a practical limit of about 45.degree. to the angle
which can be used. Most orientations are preferred to be in the range of
60.degree. to 90.degree.. It should be noted that the loop 12 is disposed
within a flat plane that is directly perpendicular or tilted to the
longitudinal axis. In the prior art constructions with double loops and
other configurations it has usually been postulated that the looped
portions must describe a helical path in order to establish a helical wave
property, but this is disproven by the results given below as to the
efficacy of the present invention. It is important, however, that the
antenna loop 12 be sufficiently spaced apart from the closed (gas entry)
end of the source tube 10 for the necessary interactions to occur between
the plasma and the RF energy, and for the dispersion relation to be
satisfied so that proper excitation can be realized and high density can
be achieved. Too long a length, however, can also preclude establishment
of the proper wave numbers. In practice source tubes 10 of 1" to 4" in
diameter and 8" to 9" in length have been used, with the antenna loop
being about one-third or more of the distance from the closed end.
This arrangement establishes low frequency whistler waves, but the
mechanism of the wave energy-plasma interaction is not fully understood.
Simple analysis in accordance with the dispersion relation is not
feasible. The presence of the plasma load in the RF field appears to give
rise under proper conditions to selective interactions in which the gas
density and dielectric characteristics determine the wave numbers that
exist. In a sense, therefore, the plasma itself appears to predetermine
the wavelengths for interaction, and thus the value of k.sub.z, out of the
spectrum of radiation from the antenna that excites the plasma.
The physics of whistler wave propagation in plasmas has been studied in
other contexts. In a cylindrical geometry, these waves are generally
referred to as helicon waves. The classical helicon wave was first
investigated by Lehame and Thonemann and is governed by the following
equations:
.gradient..times.E=.delta.B/.delta.t, .gradient..times.B=.mu..sub.o i,
.gradient.. B=0E=i.times.B.sub.o /en.sub.o, E.sub.z =.eta.J.sub.z
where E is the electric field, B is the magnetic field, i is the current
density, B.sub.o is the vacuum magnetic field, e is the charge on an
electron, n.sub.o is the density of the plasma and .eta. is the
resistivity of the plasma.
Following the derivation of Chen one can easily find perturbations of the
form B exp(i(m.theta.+k.sub.z Z-.omega.t)), and in the limit as .eta.
tends to 0, the above equations lead to:
.gradient..sup.2 B+.alpha..sup.2 B=0 where .alpha.=(.omega./k) (.mu..sub.o
en.sub.o /B)
where i=(.alpha./.mu..sub.o) B
and .omega. is the angular frequency of the wave, .mu..sub.o is the
permittivity, k is the wave number, 2.pi./.lambda., where .lambda. is the
wavelength. These equations can be solved in cylindrical coordinates to
yield the dispersion relation:
m.alpha.J.sub.m (T a)+TkaJ.sub.m ' (T a)=0
where, J.sub.m is a Bessel function of the first kind, J.sub.m ' is a
derivative of J.sub.m with respect to its argument, a is the plasma radius
and T is a transverse wave number defined by
T.sup.2 =.alpha..sup.2 -k.sup.2
It is important to remember that m is the mode number that describes the
.theta. dependence of perturbations of the form B exp(i(m.theta.+k.sub.z
-.omega.)).
The two lowest modes satisfy
J.sub.1 (T a)=0 (m=0)
J.sub.1 (T a)=T k a/2 .alpha.(J.sub.2 -J.sub.0) (m=1)
This leads to the simple relation
[(.omega./.omega..sub.c)-(.omega..sub.p.sup.2 /C.sup.2
k.sub.z.sup.2)].sup.2 =1+(3.83/k.sub.z a).sup.2
where
.omega..sub.c =cyclotron angular frequency
.omega..sub.p =plasma frequency
for the m=0 mode. The above derivation is important to understand the
excitation of the desired mode by the antenna.
Another important mechanism to understand is the damping of the wave by the
plasma. In the papers by Boswell, wave damping by electron collisions
could not explain the experimentally observed results. Chen, however,
determined that Landau damping was responsible for the large damping
observed experimentally. Landau damping is a collisionless damping of
waves in a plasma due to particles in the plasma that have a velocity
nearly equal to the phase velocity of the wave. These particles travel
with the wave, do not see a rapidly fluctuating electric field and so can
effectively exchange energy with the wave. In a plasma there are electrons
both faster and slower than the wave. In a Maxwellian distribution,
however, there are more slow electrons than fast ones and so there are
more particles taking energy from the wave than vice versa.
The damping rate due to Landau damping has been calculated by Chen for
helicon waves and can be expressed as:
Damping Rate=Jm(k.sub.z)/Re(k.sub.z) 2.pi.c.sup.2 (3.8/a).sup.2 .xi..sup.3
e-.xi..sup.2
where .xi.=.omega./k.sub.z V.sub.th
and V.sub.th is the thermal velocity of the plasma electrons. It is of
interest to demonstrate how sensitive the damping rate is to the value of
k because it is such a steep function of .xi.. Take for example a plasma
with a density of 10.sup.12 electrons/cm.sup.3, an electron temperature of
3 eV and a driving frequency of 8 MHz. The collisional damping rate would
be 0.065 and the Landau damping rate would be 0.6 for k.sub.z =0.25
cm.sup.-1 and 0.0005 for k.sub.z =0.125 cm.sup.-1. It is clear that Landau
damping is the important damping mechanism and that it is very dependent
on the wave number k.sub.z.
There are a number of factors important in devising an antenna structure
which excites whistler waves for generation of plasmas, including a)
frequency of excitation, b) wave mode and c) efficiency of coupling RF
power to plasma. The frequency of the waves should be such that it
satisfies .OMEGA..sub.c <.omega.<.omega..sub.c where .OMEGA..sub.c is the
ion cyclotron frequency, eB.sub.o /M.sub.i and .omega..sub.c is the
electron cyclotron frequency eB.sub.o /M. These waves are low frequency
waves that operate far below the electron cyclotron frequency.
The mode structure of the wave electric and magnetic fields should be
understood so that the antenna arrangement can efficiently couple the RF
power into wave excitation. As discussed above, the two lowest modes are
the m=0 and m=1 modes. The mode structure of the wave electric field for
an m=0 mode has radial and circumferential electric field vectors,
spatially disposed at different transverse planes along the direction of
wave travel, z. Within a wavelength of wave travel, the electric field
varies between purely radial and purely azimuthal. The azimuthal electric
field varies between being anticlockwise at one plane and being clockwise
one-half wavelength away. With this understanding, it is found that the
wave can be efficiently excited in this mode with an antenna that has a
single loop located in a plane perpendicular to the magnetic field
generating a spectrum of wave numbers such that a portion of the spectrum
generated includes 2.pi./k.sub.z, where k.sub.z is given by the stated
dispersion relation. The mode structure of the wave electric field for an
m=1 mode imparts a natural helical pitch to the electric and magnetic
field vectors as the wave propagates along the z direction. The electric
field vector rotates in a righthanded sense, i.e., it rotates clockwise as
it travels along B.sub.o which is in the z direction. This mode can be
excited with the present invention if the single loop is canted at an
angle to the magnetic field such that the wave spectrum generated contains
a significant portion around 2.pi./k.sub.z, where k.sub.z is given from
the dispersion relations.
The efficiency of plasma production depends on the coupling of RF energy
into the plasma. As discussed above, the important mechanism for damping
of the RF energy is believed to be Landau damping. The phase velocity of
the whistler wave is given by .omega./k.sub.z, where k.sub.z is given by
the dispersion relation and depends on the plasma density and magnetic
field strength without plasma. Ideally, the phase velocity of the wave
should be near the maximum of the ionization potential of the gas we wish
to ionize. From the above dispersion relation for the m=0 mode:
n=.alpha.B.sub.o k.sub.z (T.sub.2 +k.sub.z.sup.2).sup.1/2
where .alpha.=B.sub.o k.sub.z.sup.2 for T<k.sub.z.
In other words, the higher the value of k.sub.z, the higher the density.
However, the phase velocity of the wave is .omega./k.sub.z and so
increasing k.sub.z decreases the energy of the electrons that are
accelerated by the wave. If the k.sub.z is too high, then the energy of
the electrons may fall below the ionization potential. It is therefore
important to control k.sub.z in order to be able to increase the density
and control the electron temperature.
The present invention uses low frequency whistler waves to generate plasmas
with high density exceeding 10.sup.13 per cm.sup.3. The first use of
whistler waves to generate dense plasmas was de | | |
