Data processing: measuring – calibrating – or testing – Measurement system in a specific environment – Electrical signal parameter measurement system
Reexamination Certificate
2002-05-22
2004-05-25
Hoff, Marc S. (Department: 2857)
Data processing: measuring, calibrating, or testing
Measurement system in a specific environment
Electrical signal parameter measurement system
C702S022000, C702S031000, C702S047000, C702S108000, C702S127000, C702S189000
Reexamination Certificate
active
06741944
ABSTRACT:
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™ 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 &ohgr; that satisfy the condition:
&ohgr;
2
>>&ohgr;
p
2
≡3.18×10
9
N
e
where &ohgr;
p
is the plasma (radian) frequency, and N
e
is the electron density in electrons/cm
3
. Consequently, for the diagnosis of plasmas with electron densities of the order of 10
12
cm
−3
, the magnitudes of interest here, a microwave signal frequency (&ohgr;/2Π) 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−&lgr;
g
/8, where &lgr;
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
Johnson Wayne L.
Sirkis Murray D.
Verdeyen Joseph T.
Tokyo Electron Limited
Tsai Carol S. W.
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