U.S. patent application number 12/355108 was filed with the patent office on 2009-05-21 for method for determining plasma characteristics.
Invention is credited to Daniel J. Hoffman, Tarreg Mawari, Jeremiah T.P. Pender, Steven C. Shannon.
Application Number | 20090132189 12/355108 |
Document ID | / |
Family ID | 38607118 |
Filed Date | 2009-05-21 |
United States Patent
Application |
20090132189 |
Kind Code |
A1 |
Shannon; Steven C. ; et
al. |
May 21, 2009 |
METHOD FOR DETERMINING PLASMA CHARACTERISTICS
Abstract
Methods for determining characteristics of a plasma are
provided. In one embodiment, a method for determining
characteristics of a plasma includes obtaining metrics of current
and voltage information for first and second waveforms coupled to a
plasma at different frequencies, determining at least one
characteristic of the plasma using the metrics obtained from each
different frequency waveform. In another embodiment, the method
includes providing a plasma impedance model of a plasma as a
function of frequency, and determining at least one characteristic
of a plasma using model. In yet another embodiment, the method
includes providing a plasma impedance model of a plasma as a
function of frequency, measuring current and voltage for waveforms
coupled to the plasma and having at least two different
frequencies, and determining ion mass of a plasma from model and
the measured current and voltage of the waveforms.
Inventors: |
Shannon; Steven C.; (San
Mateo, CA) ; Hoffman; Daniel J.; (Saratoga, CA)
; Pender; Jeremiah T.P.; (San Jose, CA) ; Mawari;
Tarreg; (Manassas, VA) |
Correspondence
Address: |
PATTERSON & SHERIDAN, LLP - - APPM/TX
3040 POST OAK BOULEVARD, SUITE 1500
HOUSTON
TX
77056
US
|
Family ID: |
38607118 |
Appl. No.: |
12/355108 |
Filed: |
January 16, 2009 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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11758299 |
Jun 5, 2007 |
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12355108 |
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11424705 |
Jun 16, 2006 |
7286948 |
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11758299 |
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Current U.S.
Class: |
702/76 |
Current CPC
Class: |
H01J 37/32935 20130101;
H01L 21/67005 20130101; H01J 37/32174 20130101; H05H 1/0081
20130101 |
Class at
Publication: |
702/76 |
International
Class: |
G01R 23/16 20060101
G01R023/16 |
Claims
1. A method for determining characteristics of a plasma,
comprising: obtaining metrics of current and voltage information of
a first waveform coupled to a plasma; obtaining metrics of current
and voltage information of a second waveform coupled to the plasma,
the first and second waveforms having different frequencies;
determining at least one characteristic of the plasma using the
metrics obtained from each different frequency waveform; and
performing a plasma process on a substrate using a process selected
in response to the determined at least one characteristic of the
plasma.
2. The method of claim 1, wherein the step of determining further
comprises: determining an ion mass of the plasma.
3. The method of claim 2, wherein the step of determining the ion
mass further comprises: determining distribution of ion mass
species within the plasma.
4. The method of claim 1, wherein the step of determining further
comprises: determining asymmetry of the plasma.
5. The method of claim 1, wherein the step of determining further
comprises: determining electron temperature of the plasma.
6. The method of claim 1, wherein the step of determining further
comprises: determining electron-molecule collision frequency within
the plasma.
7. The method of claim 1, wherein the step of determining further
comprises: analyzing the plasma using a frequency dependent
model.
8. The method of claim 7, wherein the frequency dependent model
further comprises: an impedance model of the plasma.
9. The method of claim 1 further comprising: generating the first
waveform from a first power source utilized to sustain the plasma;
and generating the second waveform from a power source utilized to
control a characteristic of the plasma.
10. The method of claim 1, wherein the second waveform does not
significantly change an operational characteristics of the
plasma.
11. The method of claim 10, wherein generating the second waveform
from the low power diagnostic source further comprises: coupling
between about 1 milliWatt to about 10 Watts to the plasma.
12. The method of claim 1, wherein obtaining metrics of the second
waveform further comprises: obtaining metrics of a plasma harmonic
waveform.
13. The method of claim 12, wherein obtaining metrics of the first
waveform further comprises: obtaining metrics of a second plasma
harmonic waveform.
14. The method of claim 12, wherein obtaining metrics of the first
waveform further comprises: generating the first waveform from a
first power source utilized to sustain the plasma.
15. A method for determining characteristics of a plasma,
comprising: measuring current and voltage of a first waveform
coupled to a plasma; measuring current and voltage information of a
second waveform coupled to the plasma, the first and second
waveforms having different frequencies; and determining at least
one characteristic of the plasma using the metrics obtained from
each different frequency waveform.
16. The method of claim 15 further comprising: performing a plasma
process on a substrate using a process selected in response to the
determined at least one characteristic of the plasma.
17. The method of claim 15, wherein the step of determining further
comprises: determining an ion mass of the plasma or a distribution
of ion mass species within the plasma.
18. The method of claim 15, wherein the step of determining further
comprises: determining at least one plasma characteristic selected
from the group consisting of asymmetry of the plasma, electron
temperature of the plasma and electron-molecule collision frequency
within the plasma.
19. The method of claim 15, wherein the step of determining further
comprises: analyzing the plasma using a frequency dependent plasma
impedance model.
20. The method of claim 15, wherein the second waveform further
comprises: a waveform selected from the group consisting of a
waveform that does not significantly change an operational
characteristics of the plasma, a waveform driven by about 1
milliWatt to about 10 Watts coupled to the plasma, and a plasma
harmonic waveform.
Description
CROSS REFERENCE TO RELATED APPLICATIONS
[0001] This application is a divisional of U.S. patent Ser. No.
11/758,299, filed Jun. 5, 2007 (Attorney Docket No. APPM/10780C2),
which is a continuation of U.S. patent Ser. No. 11/424,705, filed
Jun. 16, 2006 (Attorney Docket No. APPM/10780), both of which are
hereby incorporated by reference in their entireties.
BACKGROUND OF THE INVENTION
[0002] 1. Field of the Invention
[0003] The present invention generally relates to plasma processing
technologies and, more specifically, to a method for determining
characteristics of a plasma in a plasma processing system.
[0004] 2. Description of the Related Art
[0005] Plasma enhanced semiconductor processing chambers are widely
used in the manufacture of integrated devices. The process
performance generally depends on the physical, chemical, and
electrical properties of the plasma. For example, the uniformity
and selectivity of a plasma etching process will be strongly
related to the kinetic properties of energetic ions of the plasma
at or near the surface of a processing substrate. In an anisotropic
etch process, incident ions are made to strike a substrate surface
with a narrow angular velocity distribution that is nearly
perpendicular to the surface, thereby providing an ability to etch
high aspect ratio features into the substrate. An ion velocity
distribution that is substantially isotropic, however, may result
in undesirable etching effects such as bowing or toeing of profile
cavity sidewalls.
[0006] Furthermore, the kinetic energy distribution of plasma ions
may also influence substrate processing result. Generally, a plasma
contains chemically reactive species such as atomic radicals
(Cl.sup.-), atomic ions (Cl.sup.+), molecular ions
(Cl.sub.2.sup.+), and excited molecular (Cl.sub.2*), that are
produced by electron-molecule collusions. Plasma generated during
processing may have different concentration and/or ratios of atomic
ions (Cl.sup.+) with respect to molecular ions (Cl.sub.2.sup.+).
The dynamics of etching processes having different distribution
density and/or mixture of atomic and molecular ions (Cl.sup.+,
Cl.sub.2.sup.+) in the plasma may product different etch
results.
[0007] Additionally, in plasma etching processes using fluorocarbon
gases, released CF.sub.x and/or CF.sub.xH.sub.y from the plasma may
redeposit on the sidewall of the etched surface in a process known
as sidewall passivation. Sidewall passivation is utilized to
control the sidewall profile during etching to enable a
predetermined depth to be reached while maintaining a desired
sidewall profile. However, as the component and/or ratios of the
ions impacting the substrate surface are not controlled and/or
known in conventional plasma processes, activated chemical
reactions and material sputtered etched from the substrate surface
may vary chamber to chamber and even process to process, thereby
adversely impacting process control, repeatability and
predictability of the etch processes.
[0008] We have determined that quantitative information about the
properties, distribution and energy of ions in a plasma and other
plasma characteristics will enable meaningful indications of the
effectiveness of the process and quality of the process results,
thereby enhancing process control, repeatability and predictability
of the etch processes. We have also determined that the ability to
provide plasma characteristics enables corresponding improvements
in other plasma processes, such as plasma enhanced chemical vapor
deposition, physical vapor deposition, plasma surface treatments,
among other plasma processes.
[0009] Therefore, there is a need for methods for determining the
effective ion energy and other plasma characteristics that can be
used for improving plasma processes.
SUMMARY OF THE INVENTION
[0010] Methods for determining characteristics of a plasma are
provided. In one embodiment, a method for determining
characteristics of a plasma includes obtaining metrics of current
and voltage information of first and second waveforms coupled to a
plasma at different frequencies, determining at least one
characteristic of the plasma using the metrics obtained from each
different frequency waveform.
[0011] In another embodiment, a method for determining
characteristics of a plasma includes providing a plasma impedance
model of a plasma as a function of frequency, and determining at
least one characteristic of a plasma using model.
[0012] In yet another embodiment, a method for determining
characteristics of a plasma includes providing a plasma impedance
model of a plasma as a function of frequency, measuring current and
voltage for waveforms coupled to the plasma and having at least two
different frequencies, and determining ion mass of a plasma from
model and the measured current and voltage of the waveforms.
BRIEF DESCRIPTION OF THE DRAWINGS
[0013] So that the manner in which the above recited features of
the present invention are attained and can be understood in detail,
a more particular description of the invention, briefly summarized
above, may be had by reference to the embodiments thereof which are
illustrated in the appended drawings.
[0014] FIGS. 1A-C are schematic diagram of exemplary plasma
enhanced processing chambers in which embodiments of the invention
may be practiced;
[0015] FIG. 2 is a process flow diagram of one embodiment of a
method for determining plasma characteristics; and
[0016] FIG. 3 is a simplified circuit diagram of a plasma
model.
[0017] To facilitate understanding, identical reference numerals
have been used, where possible, to designate identical elements
that are common to the figures. It is contemplated that elements
and features of one embodiment may be beneficially incorporated in
other embodiments without further recitation.
[0018] It is to be noted, however, that the appended drawings
illustrate only exemplary embodiments of this invention and are
therefore not to be considered limiting of its scope, for the
invention may admit to other equally effective embodiments.
DETAILED DESCRIPTION
[0019] Embodiments of the present invention include methods for
determining plasma characteristics using a frequency dependant
plasma model. By analyzing the plasma at different frequencies, the
model facilitates determination of a plurality of plasma
characteristics. Some plasma characteristics that may be determined
include ion mass, distribution of species of the ion mass, ions
density, plasma asymmetry, electron temperature, sheath potential
and collision frequency. It is contemplated that the method may be
utilized to determine other plasma characteristics.
[0020] The plasma characteristics are determined by model analysis
using information obtained from RF waveforms coupled to the plasma.
In one embodiment, a first RF waveform used in the model analysis
may be used to sustain the plasma discharge. The second RF waveform
used in the model analysis may also be used to drive the plasma, be
a low power diagnostic waveform coupled to the plasma, or a
waveform harmonic of the plasma. The analysis may also be performed
with more than two RF waveforms coupled to the plasma obtained from
other sources, some of which are further described below.
[0021] The model takes advantage of the frequency dependence of a
plasma discharge's electrical impedance. The model includes a
frequency dependent expression that has plasma characteristics as
different variables. In practice, a first variable of the model may
be solved in terms of a second variable in a first model expression
representing the plasma state at a first frequency, which can then
be substituted into second model expression representing the plasma
state at a second frequency to solve for the second variable. Once
a value for the second variable has been determined, the value for
the second variable may then be utilized to determine a value for
the first variable.
[0022] In the embodiments described herein, the model of the RF
waveform analysis is based on expressions for plasma impedance.
Current and/or voltage are utilized as inputs for solving the
expressions in terms of the plasma characteristics. It is
contemplated that other models may be derived to utilize the
methods described herein. It is also contemplated that the models
may utilize inputs other than, or in addition to, voltage and/or
current, such as the phase of the waveform. Although the methods
described herein are illustratively presented in terms of an etch
application, the methods are equally suitable for use in any plasma
processes (i.e., physical vapor deposition, plasma enhanced
chemical vapor deposition, plasma ion implantation and plasma film
treatment, among others) for characterizing plasma parameters which
can be utilized to improve process results, prediction and
repeatability.
[0023] FIGS. 1A-C presents schematic diagrams of plasma processing
chambers 100A-C in which the present invention may be performed.
Examples of plasma etch chambers that may be adapted to benefit
from the present include, but are not limited to, the Decoupled
Plasma Source (DPS.RTM., DPS.RTM. II), EMAX.RTM., MXP.RTM., and
ENABLER.RTM. processing chambers, all available from Applied
Material, Inc., of Santa Clara, Calif. It is contemplated that
other plasma chambers, including those from other manufacturers,
may be adapted to practice the invention. Although the plasma
processing chambers 100A-C illustratively described below is
configured as an etch chamber, the invention may be utilized for
other plasma processes as indicated above.
[0024] Common to all embodiments is at least one RF metrology
system 198 interfaced with the plasma processing chambers 100A-C
which is suitable for measuring at least one of voltage, current
and phase of an RF waveform coupled to a plasma 110 formed in the
chamber from gases provided by a gas panel 108. The metrology
system 198 may include one or more sensors. Generally, the
metrology system 198 is positioned to interface with the RF
waveform between its source (such as an RF power source, or the
plasma itself).
[0025] Referring now to FIG. 1A, the plasma processing chamber 100A
includes a grounded chamber body 102 coupled to the gas panel 108,
one or more RF power sources and a controller 190. The gas panel
108 provides process and other gases to the process region defined
in the chamber body 102. At least one of the RF power sources is
utilized to sustain the plasma 110 formed from the process gases
within the process region, typically to promote substrate
processing, chamber or component seasoning and/or coating, and/or
chamber cleaning.
[0026] A substrate support pedestal 116 disposed within the chamber
body 102 below a gas distributor 132. The pedestal 116 may include
an electrostatic chuck (not shown) for retaining a substrate 114
below the gas distributor 132. The electrostatic chuck is driven by
a DC power supply to develop an electrostatic force that holds the
substrate 114 to the chuck surface, as is conventionally known.
Alternatively, the substrate 114 may be retained to the pedestal by
clamping, vacuum or gravity.
[0027] In one embodiment, the substrate support pedestal 116 is
configured as a cathode and is coupled to a plurality of RF power
sources. RF power, provided by at least a first RF power source
104, is coupled between the cathode and another electrode, such as
the gas distributor 132 or ceiling of the chamber body 102. The RF
power excites and sustains a plasma discharge (e.g., plasma 110)
formed from the gases disposed in the processing region of the
chamber body 102.
[0028] In the embodiment depicted in FIG. 1A, a plurality of RF
power sources 104, 106 are coupled to the cathode through a
matching circuit 112. Although not as depicted in FIG. 1A, the
matching circuit 112 may incorporate or interface with the RF
metrology system 198. The signal generated by the RF power sources
104, 106 is delivered through matching circuit 112 to the substrate
support pedestal 116 through a single feed forming to ionize the
background gas mixture provided in the plasma processing chamber
100A, thereby providing ion energy necessary for performing an
etching or other plasma enhanced process. The RF power sources 104,
106 are generally capable of producing an RF signal having a
frequency of from about 50 kHz to about 200 MHz and a power between
about 0 Watts and about 5000 Watts. Another optional RF source 120
is shown in FIG. 1A and is representative of one or more additional
power sources that may be used to control the characteristics of
the plasma 110.
[0029] The gas distributor 132 may comprise one or more nozzles or
a showerhead. The gas distributor 132 is coupled to the gas panel
108 such that gases provided to the gas distributor 132 from the
gas panel 108 may introduced into the chamber and, when ignited,
formed into the plasma 110 utilized for processing the substrate
114.
[0030] In one mode of operation, the substrate 114 is disposed on
the substrate support pedestal 116 in the plasma processing chamber
100. A process gas and/or gas mixture is introduced into the
chamber body 102 through the gas distributor 132 from the gas panel
108. A vacuum pumping system 122 maintains the pressure inside the
chamber body 102 while removing etch by-products. The vacuum
pumping system 122 typically maintains an operating pressure
between about 10 mTorr to about 20 Torr.
[0031] The RF source 104, 106 provides RF power at separate
frequencies to the cathode through the matching circuit 112,
thereby providing energy to form the plasma 110 and excite the gas
mixture in the chamber body 102 into ions to perform a plasma
process, in this example, an etching process. The RF metrology
system 198 measures metrics of the waveform coupled to the plasma
110 to provide a metric indicative of the power provided by each
power source 104, 106. The metric is transmitted to the controller
190 and utilized to determine characteristics of the plasma as
further detailed below. The characteristics of the plasma may be
analyzed to adjust the process in-situ processing, to correct
process drift, to match processes between different chambers,
and/or to achieve certain process results.
[0032] The controller 190 is coupled to the various components of
the plasma processing chamber 100 and is used to facilitate control
of an etch process. The controller 190 generally includes a central
processing unit (CPU) 192, a memory 194, and support circuits 196
for the CPU 192. The CPU 192 may be one of any form of computer
processor that can be used in an industrial setting for controlling
various chambers and subprocessors. The memory 194 is coupled to
the CPU 192. The memory 194, or computer-readable medium, may be
one or more of readily available memory such as random access
memory (RAM), read only memory (ROM), floppy disk, hard disk, or
any other form of digital storage, local or remote. The support
circuits 196 are coupled to the CPU 192 for supporting the
processor in a conventional manner. These circuits include cache,
power supplies, clock circuits, input/output circuitry and
subsystems, and the like.
[0033] A process, for example a method 200 for determining plasma
characteristics described below, is generally stored in the memory
194, typically as a software routine. The software routine may also
be stored and/or executed by a second CPU (not shown) that is
remotely located from the hardware being controlled by the CPU 192.
Although the process of the present invention is discussed as being
implemented as a software routine, some of the method steps that
are disclosed therein may be performed in hardware as well as by
the software controller. As such, the invention may be implemented
in software as executed upon a computer system, in hardware as an
application specific integrated circuit or other type of hardware
implementation, or a combination of software and hardware.
[0034] FIG. 1B depicts another embodiment of a plasma processing
chamber 100B in which the present invention may be performed. The
plasma processing chamber 100B is substantially similar to the
plasma processing chamber 100A described above, and a low power
diagnostic power source 130 is coupled to the plasma 110. The
processing chamber 100B may utilize a single RF source 104 to
sustain the plasma 110, or alternatively other optional RF power
sources 120 may be additionally utilized. The metrology system 198
is configured to obtain a metric of at least one of current,
voltage and phase from both the low power RF diagnostic power
source 130 and the RF power source 104.
[0035] The low power RF diagnostic power source 130 is coupled to
the plasma at frequency different that of the power provided by the
primary or plasma RF source 104. The diagnostic power only serves
as a source of additional frequency information for plasma
impedance measurement, and does not significantly change the
operational characteristics of the plasma discharge. In one
embodiment, the diagnostic power form the source 130 is provides
between about 10 milliWatts to about 10 Watts to the plasma.
[0036] FIG. 1C depicts another embodiment of a plasma processing
chamber 100C in which the present invention may be performed. The
plasma processing chamber 100C is substantially similar to the
plasma processing chambers 100A-B described above, except wherein
the metrology system 198 is configured for measuring one or more RF
waveforms that are harmonics of the plasma, i.e., the plasma serves
as a source of the waveform, as well as waveforms from the RF
source 104. The metrology system 198 is generally disposed between
a circuit element 140 and the plasma 110. The circuit element 140,
such as a low pass filter, is selected to create an open circuit
for waveforms having a frequency greater than the fundamental
frequency (i.e., the frequency provided by the RF source 104),
thereby protecting the RF sources from reflected plasma
harmonics.
[0037] The plasma 110 formed in the chamber 100C may be sustained
by a single RF source 104, or alternatively other optional RF power
sources 120 may be additionally utilized. It is contemplated that a
low power diagnostic power source 130 (as shown in FIG. 1B, may
also be coupled to the chamber 100C.
[0038] FIG. 2 depicts a process flow diagram of one embodiment of a
method 200 for determining characteristics of the plasma 110 that
may be performed in the plasma processing chambers 100A-C using
information obtained by the RF metrology system 198. For sake of
clarity, plasma processing chambers 100A-C will be collectively
referred henceforth as "the plasma processing chambers" without
further the reference to the numerals 100A-C.
[0039] The method 200 begins at step 202 by placing the substrate
114 on the support pedestal 116 disposed in the plasma processing
chamber. It is noted that the method 200 may be performed without a
substrate within the chamber.
[0040] At step 204, one or more process gases are supplied from the
gas panel 108 into the plasma processing chamber and are formed
into the plasma 110 to provide reactive species (e.g., ions or
radicals) used for processing. At step 206, power is provide from
one or more RF power sources to sustain the plasma 110.
[0041] At step 208, the metrology system 198 obtains metrics
indicative of the RF waveforms coupled to the plasma 110. In one
embodiment, the RF waveforms are from the RF sources 104, 106 which
provide power at different frequencies to sustain the plasma, as
shown in FIG. 1A. Some common frequencies pairs include 2 and 13
kHz, 2 and 60 kHz, and 13 and 60 kHz. In embodiments where three RF
power sources are used to sustain the plasma, common frequencies
groupings include 2, 13 and 60 kHz and 2, 13 and 162 kHz.
[0042] In another embodiment, one of the RF waveforms is from a
first RF source utilized to provide power sustain the plasma, while
another RF waveform is from a second RF source that generates a low
power diagnostic power that is coupled to the plasma at different
frequency different that the power provided by the first RF source,
as shown in FIG. 1B. It is also contemplated that multiple low
power diagnostic power sources may be utilized to generate the
different waveforms. The diagnostic waveforms may be used alone, or
in conjunction with the waveforms obtained from other sources.
[0043] In yet another embodiment, one of the RF waveforms is from a
first RF source utilized to provide power sustain the plasma, while
another RF waveform is a harmonic of the plasma, i.e., the plasma
serves as a source of the second frequency waveform which is at a
frequency different that the power provided by the first RF source,
as shown in FIG. 1C. It is also contemplated that waveforms from
more than one harmonic frequency may be utilized. The harmonic
waveforms may be used alone, or in conjunction with the waveforms
obtained from other sources.
[0044] It is contemplated that waveforms forms difference
frequencies may be obtained by any combination of the examples
given above. For example, one or more RF sustaining waveforms (at
one or more frequencies) may be analyzed with waveforms obtained
from harmonic and/or diagnostic sources. In another example, one or
more harmonic waveforms may be analyzed with waveforms obtained
from one or more diagnostic RF sources.
[0045] In one embodiment, the metrology system 198 is utilized to
obtain current and voltage metrics of RF waveforms measured between
the source and plasma. The metrics are provided to the controller
190.
[0046] At step 210, the controller 190 determines two or more
characteristics of the plasma utilizing the metrics provided form
the metrology system 198. In one embodiment, the metrics are
utilized by the controller 190 to determine sheath voltage and ion
density. The sheath voltage is approximately equal to the amplitude
of the RF voltage modulation, while the ion density if
approximately equal to the magnitude of the RF current. The sheath
voltage and ion density are utilized as input variables for a model
that expresses the plasma impedance as a function of frequency.
[0047] The model is generally a lump element circuit expression of
the plasma using known electrical plasma characteristics. For
example, the portion of the expression for sheath impedance may be
based on Childs Law, while the portion of the expression for bulk
impedance may be based on homogeneous plasma models. It is
contemplated that the model may be based on other theories or
derived empirically, and resolved to obtain plasma characteristics
utilizing the method described herein.
[0048] The model generally includes variables for ion mass,
collision frequency, electron temperature, plasma asymmetry, sheath
voltage and ion density. As values for ion density and sheath
voltage are provided as discussed above, the expression of the
model may be resolved for any of the remaining variables, e.g., ion
mass, collision frequency, electron temperature and plasma
asymmetry. If waveform information is available at only two
frequencies, two of the four remaining variables may be assigned
approximated values so that the other variables of greater interest
may be resolved. If waveform information is available at three or
more frequencies, all of the four remaining variables may be
determined.
[0049] The model is utilized by solving for a first variable using
a model expression at a first frequency, than substituting the
first variable, expressed in terms of the first frequency model
expression, into the model expression for the second frequency,
wherein a second variable of interest may be resolved. Using the
resolve value of the second variable, the valve for the first
variable may be resolve. Utilizing this method, any pair of ion
mass, collision frequency, electron temperature and plasma
asymmetry may be determined using two frequency model analysis, or
all may be determined using model analysis at three or more
frequencies. It is contemplated that the model may be resolved
using other analytical approaches, for example, neural networks,
best fit, regression analysis, solving for a unique solution for
all equations, among others
[0050] FIG. 3 is one embodiment of a simplified circuit diagram of
a plasma model. The plasma model may assume an asymmetric
capacitive discharge (homogeneous, constant ion MFP) using high
frequency bulk plasma approximation (see, for example, Godyak V
1986 Soviet RF Discharge Research and Child Law High Voltage Sheath
Approximation (C. D. Child, Phys. Rev., 32)). In an illustrative
embodiment, an Argon plasma may have center point parameters of
n.sub.e=1010 cm.sup.-3, V.sub.DC=500 Volts, .nu..sub.me=0.01/ns,
.alpha.=0.5, and T.sub.e=5 eV.
[0051] The sheath reactance may be expressed as:
J d = .omega. 0 V s ##EQU00001## I d = .omega. 0 V Area s 0 =
.omega. C sheath V ##EQU00001.2## C sheath = 0 Area s
##EQU00001.3## Sheath thickness can be approximated by
##EQU00001.4## s = 32 0 2 V DC 3 81 .372 n e 2 e T e 4
##EQU00001.5## 1 s = 81 0.61 n e 2 e T e 32 0 2 V DC 3 4
##EQU00001.6## C sheath = 0 Area s ##EQU00001.7## X sheath = - s
.omega. 0 Area ##EQU00001.8## x sheath = - 1 .omega. 0 Area 32 0 2
V DC 3 81 .372 n e 2 e T e 4 ##EQU00001.9##
[0052] The sheath resistance may be expressed as:
J i = 2 .omega. i 3 .pi. .omega. J d = 2 .omega. i 0 V 3 .pi. s
##EQU00002## J i = J e ##EQU00002.2## J c = J i + J e = 2 J i = 4
.omega. i 0 V 3 .pi. s ##EQU00002.3## R sheath = V J c Area = 3
.pi. s 4 .omega. i 0 Area ##EQU00002.4## .omega. i = .pi. .omega.
pi 2 T e e V DC 4 ##EQU00002.5## R sheath = 3 s 4 .omega. pi 0 Area
e V DC 2 T e 4 ##EQU00002.6## .omega. pi = e n e 0 M ##EQU00002.7##
R sheath = 3 s 4 e 0 Area e V DC 0 2 M 2 2 T e n e 2 4
##EQU00002.8## R sheath = 3 V DC 2 e n e Area M 2 T e 2 81 0.372 4
##EQU00002.9##
[0053] Treating as parallel elements, starting with the powered
sheath, and scaling the grounded sheath due to asymmetry
conditions:
R shRF = 2 9 .omega. 2 0 e Area n e T e 2 V DC 3 M 0.61 e 4 9
.omega. 2 0 2 V DC e T e + V DC M 4 e 2 n e T e ##EQU00003## x shRF
= - V DC M 2 e 2 n e T e .omega. 0 Area 2 0 2 V DC 3 81 .372 n e 2
e T e 4 4 9 .omega. 2 0 2 V DC e T e + V DC M 4 e 2 n e T e
##EQU00003.2## V GND V RF = ( Area Area GND ) q .alpha. = Area Area
GND V GND = V D C .alpha. q ##EQU00003.3## R shGND = 2 9 .omega. 2
0 e Area n e T e 2 V DC 3 .alpha. 3 q M 0.61 e 4 9 .omega. 2 0 2 V
DC .alpha. q e T e + v DC .alpha. q M 4 e 2 n e T e x shGND = - V
DC .alpha. q M 2 e 2 n e T e .omega. 0 Area 2 0 2 V DC 3 .alpha. 3
q 81 .372 n e 2 e T e 4 4 9 .omega. 2 0 2 V DC .alpha. q e T e + V
DC .alpha. q M 4 e 2 n e T e ##EQU00003.4##
[0054] The bulk impedance may be expressed as Z.sub.bulk, and thus
the total discharge impedance verses n.sub.e, V.sub.DC,
.nu..sub.me, .alpha., M.sub.ion and T.sub.e may be expressed
as:
z bulk = ( .omega. C 0 + 1 .omega. L p + R p ) - 1 ##EQU00004## L p
= 1 .omega. pe 2 C 0 R p = v me .omega. pe 2 C 0 ##EQU00004.2## z
bulk = ( .omega. C 0 + .omega. pe 2 C 0 .omega. + v me ) - 1
##EQU00004.3## C 0 = 0 Area ( 1 + .alpha. ) L - s 0 ( 1 + 1 .alpha.
q 2 ) ##EQU00004.4## s = 32 0 2 V DC 3 81 .372 n e 2 e T e 4
##EQU00004.5## C 0 = 0 Area ( 1 + .alpha. ) L - 32 0 2 V DC 3 81
.372 n e 2 e T e 4 ( 1 + 1 .alpha. q 2 ) ##EQU00004.6## [0055]
where n.sub.e, V.sub.DC, .nu..sub.me, .alpha., M.sub.ion and
T.sub.e respectively are electron density, sheath voltage,
collision frequency, discharge asymmetry, ion mass and electron
temperature.
[0056] Therefore, by measuring the impedance of the equivalent
circuit at frequencies 1, 2, . . . n and relating the circuit
elements C.sub.shGND, R.sub.shGND, C.sub.0, R.sub.p, L.sub.p,
C.sub.shRF, and R.sub.shRF to plasma parameters n.sub.e, V.sub.DC,
.nu..sub.me, .alpha., m.sub.ion, and T.sub.e using the equations
above, the plasma parameters can be directly determined from
impedance measurement.
[0057] The plasma characteristics determined at step 210 may be
utilized to determine the energy of the effective ions mass
generated by the plasma as calculated in accordance with the
simulated voltage and current magnitudes obtained by the simulated
models. Plasma characteristics, for example ion mass determined at
step 210, may also be utilized to resolve the distribution of ions
and species within a plasma. As the dissociation of the gas mixture
in the processing chamber may be ionized with different forms, such
as atomic radicals (Cl.), atomic ions (Cl.sup.+), molecular ions
(Cl.sub.2.sup.+) and excited molecular (Cl.sub.2*), an accurate
determination of the distribution of the ions species within the
plasma may be utilized to more effectively control plasma
processing. The distribution of species may be resolved for either
atomic and/or molecular distributions. For example, atomic radicals
(Cl.) and/or atomic ions (Cl.sup.+) may be recombined and formed as
molecular ions (Cl.sub.2.sup.+) instead of reacting with the
material (e.g., SiO.sub.2 or metal) on the substrate, thereby
adversely influencing the process performance as desired and
alternating the ions distributed in the process region. By knowing
the ion mass and resolving the ion distribution for a particular
set of process parameters, process performance may more accurately
be estimated without lengthy process characterization. As such, the
estimation of the effective ion energy and/or distribution may be
calculated by the voltage and current magnitudes of RF waveforms
coupled to the plasma, thereby identifying the actual reactive
species remained and generated in the process chamber. As such, the
invention is particularly useful for determining the molecular and
atom distributions of diatomic gases (for example, Cl.sub.2,
O.sub.2 and N.sub.2, among others) within the plasma. The invention
is also useful for determining the distributions of compound
fragments within the plasma, such as the distribution of CF.sub.4
process gas fragments (CF.sup.+3, CF.sub.2.sup.+2, etc). Thus, the
process will allow immediate identification of process drift or
variations between items, such as process kit variation, chamber to
chamber variation and even variation in the composition of gas
sources (of a process gas).
[0058] Thus, the present application provides methods determining
plasma characteristics using a frequency dependant, plasma model.
By analyzing the plasma at different frequencies, the model
facilitates determination of plasma characteristics such as ion
mass, the distribution of ion mass species, ions density, plasma
asymmetry, electron temperature, sheath potential and collision
frequency. As a result, the methods advantageously facilitate
enhanced process control, management and repeatability of plasma
processes.
[0059] While the foregoing is directed to embodiments of the
present invention, other and further embodiments of the invention
may be devised without departing from the basic scope thereof, and
the scope thereof is determined by the claims that follow.
* * * * *