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Patent No. 6741944 Electron density measurement and plasma process control system using a microwave oscillator locked to an open resonator containing the plasma (Verdeyen, et al., May 25, 2004)
Abstract
A system for measuring plasma electon densities (e.g., in the range of 10.sup.10 to 10.sup.12 cm.sup.-3) and for controlling a plasma generator (240). Measurement of the plasma density is essential if plasma-assisted processes, such depositions or etches, are to be adequately controlled using a feedback control. Both the plasma measurement method and system generate a control voltage that in turn controls the plasma generator (240) to maintain the plasma electron density at a pre-selected value. The system utilizes a frequency stabilization system to lock the frequency of a local oscillator (100) to the resonant frequency of an open microwave resonator (245) when the resonant frequency changes due to the introduction of a plasma within the open resonator. The amplified output voltage of a second microwave discriminator may be used to control a plasma generator (240).
Notes:
BACKGROUND
OF THE INVENTION
1. Field of the Invention
The present invention provides a method and system for measuring electron densities
in a plasma processing system, such as is used in semiconductor processing systems.
2. Description of the Background
Following the Second World War, several university research groups used microwave
technology that had been developed during the war to study partially ionized
gases. In particular, Professor Sanborn C. Brown's group at Massachusetts Institute
of Technology developed and exploited the so-called "cavity technique" for the
measurement of electron density in partially ionized, electrically quasi-neutral
gases, which have come to be called plasmas.
In this procedure, changes in the resonant behavior of a microwave cavity were
studied as a consequence of the presence of a plasma within it. Typically, a
right, circularly cylindrical cavity operating in its lowest or nearly lowest
order resonant mode was used, and the gas was contained within a coaxial Pyrex.TM.
or quartz tube. An aperture was provided in each planar end surface to permit
passage of the tube through the cavity.
The presence of a plasma within a microwave cavity will, in general, affect
both the resonant frequency of a particular cavity mode and the sharpness (Q)
of the resonance; i.e., the precision with which the frequency of a microwave
signal must be fixed if the resonant mode is to be appreciably excited. Using
a form of perturbation theory, it is possible to relate the changes in these
parameters to the electron density and the electron collision frequency in the
plasma. The perturbation theory is valid only for (radian) frequencies .omega.
that satisfy the condition:
where .omega..sub.p is the plasma (radian) frequency, and N.sub.e is the electron
density in electrons/cm.sup.3. Consequently, for the diagnosis of plasmas with
electron densities of the order of 10.sup.12 cm.sup.-3, the magnitudes of interest
here, a microwave signal frequency (.omega./2.PI.) in excess of tens of GHz
is required.
The requirement of signal frequencies on the order of tens of GHz causes a significant
problem. The physical dimensions of a cavity designed to resonate in its lowest
or nearly lowest order resonant mode are on the order of the wavelength of the
signal. Thus, a cavity designed to resonate at about 35 GHz has dimensions on
the order of only a centimeter. The use of such a small cavity for electron
density measurements is difficult.
In principle it is possible to use a cavity designed to resonate in a "higher
order" mode to overcome the problem associated with the small physical size
of a lowest or low order mode. However, if this approach is taken, it becomes
extremely difficult to know with certainty the identity of a particular excited
cavity mode. Consequently, it becomes practically very difficult, if not impossible,
to apply perturbation theory to determine the electron density and the electron
collision frequency.
One way to circumvent this problem is to use an "open" resonator, i.e., a resonator
in which the electromagnetic field is not confined by a (nearly) completely
enclosing conducting surface. A practical example of an open resonator is a
pair of large aperture, circularly symmetrical end mirrors, with planar or curved
surfaces and with no confining circularly symmetrical conducting surface between
them. Open resonators of this type were considered in great detail by A. G.
Fox and T. Li in "Resonant modes in a MASER interferometer," Bell System Technical
Journal, vol. 40, pp. 453-488, March 1961. They showed that any mode that could
be regarded as including a plane wave component propagating at a significant
angle with respect to the axis of symmetry would not be appreciably excited,
i.e., would have a very low Q. In effect, for an open resonator, the number
of practically useful modes with resonant frequencies in a particular frequency
range is far less than the equivalent number for a closed resonator of similar
size. This property of open resonators provided an enormous opportunity for
researchers to extend resonant plasma diagnostic techniques to frequencies above
35 GHz.
Microwave energy may be coupled from a waveguide feed to an open resonator using
the same principles that govern coupling from a waveguide feed to a closed resonator.
The location, spatial rotation, and size of a coupling aperture in a resonator
mirror has to be appropriately related to the configuration of the electromagnetic
field for the desired resonator mode. The input and output coupling apertures
may both be on the same mirror or the input aperture may be on one mirror and
the output aperture on the other.
Known electronically tunable microwave oscillators are frequency stabilized
with the aid of a resonant cavity and a microwave discriminator. The basic concepts
are documented in detail in various M.I.T. Radiation Laboratory Reports and
in the Radiation Laboratory Series published by McGraw-Hill in 1947. One use
of those oscillators is to cause an electronically tunable oscillator to track
the resonant frequency of a microwave resonator as that frequency is changed.
An extensive discussion of the techniques is presented in Vol. 11, Technique
of Microwave Measurements, M.I.T. Radiation Laboratory Series, Carol H. Montgomery,
Editor, McGraw-Hill Book Company, New York, 1947, pp. 58-78 (hereinafter "Montgomery").
The entire contents of Montgomery are hereby incorporated by reference. A block
diagram for a stabilization circuit 102 is shown in FIG. 1. FIG. 1 is similar
to FIG. 2.29 on page 60 of Montgomery. The use of a microwave interferometer
is also described in two known publications: (1) "A Microwave Interferometer
for Density Measurement Stabilization in Process Plasmas," by Pearson et al.,
Materials Research Society Symposium Proceedings, Vol. 117 (Eds. Hays et al.),
1988, pgs. 311-317, and (2) "1-millimeter wave interferometer for the measurement
of line integral electron density on TFTR," by Efthimion et al., Rev. Sci. Instrum.
56 (5), May 1985, pgs. 908-910.
When the frequency of the oscillator 100 differs from the resonant frequency
of the microwave cavity 105, a signal is produced by the discriminator 110.
The output of the discriminator 110 is amplified by an amplifier 115. The amplified
discriminator signal 120 is then fed to the oscillator 100 with the polarity
required to move the frequency of the oscillator 100 toward the resonant frequency
of the microwave cavity 105.
If the frequency of the oscillator 100 is locked to the resonant frequency of
the microwave cavity 105 using the stabilization circuit 102, tuning the microwave
cavity 105 will cause the oscillator 100 to track the resonant frequency within
a range that will be limited by the electronic tuning capability of the amplifier
115 and the frequency sensitivity of the ancillary microwave circuitry. Page
69 of Montgomery discloses a tunable oscillator.
As shown in FIG. 1, the major components of the stabilization system 102 are
the microwave discriminator 110 and the amplifier 115. Two configurations for
the discriminator 110 exist. FIG. 2 shows a first embodiment of the discriminator
110 that includes a directional coupler 150 and a bridge 160 (also known as
a magic Tee). The bridge 160 compares the signal reflected by a short-circuited
waveguide 165 of length x with the signal reflected from the microwave cavity
105 fed by a line 175 of length x-.lambda..sub.g /8, where .lambda..sub.g is
the guide wavelength. The microwave signal enters the bridge 160 at arm 180
(the H-plane arm) through the directional coupler 150. The arm of the directional
coupler 150 is the input to the discriminator from the microwave oscillator
100. At the Tee junction 185 of the bridge 160, waves of equal amplitude and
phase traveling away from the junction are excited in the short-circuited waveguide
165 and the line 175 (collectively called the S arms).
In the second embodiment, the microwave discriminator 110 may also be realized
by replacing the directional coupler 150 with a second magic Tee. This is not
surprising since a magic Tee is equivalent to a 3 dB directional coupler. Thus,
the analyses are similar and will not be considered further herein.
SUMMARY OF THE INVENTION
It is an object of the present invention to provide an improved plasma electron
density measurement and control system using a microwave oscillator locked to
an open resonator containing a plasma.
It is another object of the present invention to provide a robust control of
the plasma electron density by tracking to another resonant mode when the oscillator
loses its lock on one resonant mode.
These and other objects of the present invention are achieved by using a frequency
stabilization system to lock the frequency of a local oscillator to a pre-selected
resonant frequency of an open microwave resonator when the resonant frequency
changes due to the introduction of a plasma within the open resonator.