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`UNITED STATES PATENT AND TRADEMARK OFFICE
`
`BEFORE THE PATENT TRIAL AND APPEAL BOARD
`
`
`
`
`
`MICRON TECHNOLOGY, INC., INTEL CORPORATION,
`AND GLOBALFOUNDRIES U.S., INC.
`Petitioners
`
`
`v.
`
`DANIEL L. FLAMM,
`
`Patent Owner
`
`
`
`U.S. Patent No. 5,711,849
`
`Issued: January 27, 1998
`
`Named Inventor: Daniel L. Flamm
`
`Title: PROCESS OPTIMIZATION IN
`GAS PHASE DRY ETCHING
`
`
`
`DECLARATION OF DAVID B. GRAVES IN SUPPORT OF PETITION
`FOR INTER PARTES REVIEW OF U.S. PATENT NO. 5,711,849
`
`Mail Stop: PATENT BOARD
`Patent Trial and Appeal Board
`U.S. Patent & Trademark Office
`P.O. Box 1450
`Alexandria, VA 22313-1450
`
`Page 1 of 97
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`Samsung Exhibit 1003
`
`
`
`
`
`I, David B. Graves, declare as follows:
`
`I.
`
`INTRODUCTION
`1.
`
`I am over 18 years of age and otherwise competent to make this
`
`Declaration.
`
`2.
`
`I have been asked to provide my views regarding technical issues in
`
`connection with the above-captioned inter partes review of U.S. Patent
`
`No. 5,711,849 (“the 849 Patent”). I have also have been asked to provide my
`
`opinion on whether claims 1-29 of the 849 Patent are valid in light of the prior art
`
`in Grounds 1 and 2 and the knowledge of one of ordinary skill in the art at the time
`
`of the alleged invention. It is my opinion that claims 1-29 are invalid for the
`
`reasons set forth in this declaration.
`
`II. QUALIFICATIONS AND PROFESSIONAL EXPERIENCE
`3.
`I am currently a Professor of Chemical and Biomolecular Engineering
`
`at the University of California, Berkeley. I was the Lam Research Distinguished
`
`Professor in Semiconductor Processing 2011-16. I have been a full professor since
`
`1997. I was an Associate Professor from 1997-1997, and an Assistant Professor
`
`from 1986-1991. My prior employment also includes being a computer process
`
`control engineer for Standard Oil of California from 1978-1981. I have also
`
`provided research support for a number of major semiconductor manufacturing and
`
`processing companies.
`
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`4.
`
`I obtained my Ph.D. in Chemical Engineering from the University of
`
`Minnesota in 1986. I also received my Master’s degree in Chemical Engineering
`
`from the University of Arizona in 1981, and my Bachelor’s degree in Chemical
`
`Engineering from the University of Arizona in 1978.
`
`5.
`
`I have significant research experience in many issues relating to
`
`semiconductor devices and their processing, including thin film etching and
`
`deposition in semiconductor manufacturing, plasma chemistry and plasma
`
`processing for semiconductors, modeling and simulation of low temperature
`
`nonequilibrium plasmas, plasma-surface
`
`interactions and plasma-surface
`
`chemistry, nanofeature profile evolution simulation, molecular dynamics of
`
`plasma-surface interactions, particles and photons in plasmas, optical and mass
`
`spectroscopy in low temperature plasmas, and microplasmas. I have published
`
`over two hundred peer-reviewed papers and given many presentations on these
`
`topics.
`
`6.
`
`I have taught courses in solid state device processing, process control,
`
`transport processes, and mathematical methods at the undergraduate and graduate
`
`level. I have supervised the research of approximately 50 students and scholars in
`
`the area of semiconductor plasma processing and manufacturing as part of their
`
`work for their PhDs as well as post-doctoral work.
`
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`7. My curriculum vitae (CV) (Ex.1004) includes additional details about
`
`my experience and professional background.
`
`8.
`
`I am being compensated for my time at my standard hourly rate of
`
`$400 in connection with this proceeding. My compensation is in no way contingent
`
`upon my performance or the outcome of this case.
`
`9.
`
`I have been asked my technical opinions regarding the understanding
`
`of a person of ordinary skill in the art (discussed below) as it relates to the 849
`
`Patent and other reference documents. I have also been asked to provide my
`
`technical opinions on concepts discussed in the 849 Patent and other reference
`
`documents, as well as my technical opinions on how these concepts relate to
`
`several claim limitations of the 849 Patent in the context of the specification.
`
`Finally, I have been asked to provide my opinion regarding whether claims 1-29 of
`
`the 849 Patent are invalid in light of the prior art in Ground 1, viewing that art
`
`from the perspective of one of ordinary skill in the art.
`
`10.
`
`In reaching the opinions stated herein, I have considered the 849
`
`Patent, its prosecution history, and the Exhibits to the Petition. I have also drawn,
`
`as appropriate upon my own education, training, research, knowledge, and
`
`personal and professional experience.
`
`
`
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`III. RELEVANT LEGAL STANDARDS
`11. My opinions are informed by my understanding of the relevant law. I
`
`understand that the patentability analysis is conducted on a claim-by-claim basis.
`
`12.
`
`I understand that the 849 Patent has expired. Accordingly, in my
`
`analysis, all claim terms have been accorded their plain and ordinary meaning, as
`
`understood by a person having ordinary skill in the art and consistent with the
`
`specification and file history of the 849 Patent.
`
`13.
`
`I understand that a single piece of prior art “anticipates” a claim if
`
`each and every element of the claim is disclosed in that prior art. I further
`
`understand that, where a claim element is not explicitly disclosed in a prior art
`
`reference, the reference may nonetheless anticipate a claim if the missing claim
`
`element is necessarily present in the apparatus or a natural result of the method
`
`disclosed—i.e., if the missing element is “inherent.”
`
`14.
`
`I understand that the prior art may render a patent claim “obvious.” I
`
`understand that two or more pieces of prior art that each disclose fewer than all
`
`elements of a patent claim may nevertheless be combined to render a patent claim
`
`obvious if the combination of the prior art collectively discloses all elements of the
`
`claim and a person having ordinary skill in the art at the time would have had
`
`reason to combine the prior art. I understand that this reason to combine need not
`
`be explicit in any of the prior art, but may be inferred from the knowledge of a
`
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`person having ordinary skill in the art at the time the patent application was filed. I
`
`also understand that a person having ordinary skill in the art is not an automaton,
`
`but is a person having ordinary creativity. I further understand that one or more
`
`pieces of prior art that disclose fewer than all of the elements of a patent claim may
`
`render a patent claim obvious if including the missing element would have been
`
`obvious to a person having ordinary skill in the art (e.g., the missing element
`
`represents only an insubstantial difference over the prior art or a reconfiguration of
`
`a known system).
`
`15.
`
`I understand that a patent claim is obvious if the differences between
`
`the subject matter claimed and the prior art are such that the subject matter as a
`
`whole would have been obvious at the time the alleged invention was made. I
`
`understand that the obviousness analysis must focus on the knowledge available to
`
`one of skill in the art at the time of the alleged invention in order to avoid
`
`impermissible hindsight. I further understand that the obviousness inquiry assumes
`
`that the person having ordinary skill in the art would have knowledge of all
`
`relevant references available at the time of the alleged invention.
`
`16.
`
`I also understand that the USPTO has identified exemplary rationales
`
`that may support a conclusion of obviousness, and I have considered those
`
`rationales in my analysis. The rationales include:
`
`
`
`Combining prior art elements according to known methods to yield
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`predictable results;
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`U.S. Patent No. 5,711,849
`Declaration of Dr. Graves
`
`
`
`
`
`
`
`
`
`Simple substitution of one known element for another to obtain
`
`predictable results;
`
`Use of a known technique to improve similar devices (methods or
`
`products) in the same way;
`
`Applying a known technique to a known device (methods or products)
`
`ready for improvement to yield predictable results;
`
`Choosing from a finite number of identified, predictable solutions,
`
`with a reasonable expectation of success, such that the effort was
`
`“obvious to try”;
`
`
`
`Known work in one field of endeavor that may prompt variations on
`
`the work for use in either the same field or a different one based on
`
`design incentives or other market forces if the variations are
`
`predictable to a person having ordinary skill in the art;
`
`
`
`Some teaching, suggestion, or motivation in the prior art that would
`
`have led a person having ordinary skill in the art to modify the prior
`
`art reference or to combine prior art reference teachings to arrive at
`
`the claimed invention.
`
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`17.
`
`I appreciate that secondary considerations may be considered, if
`
`present, as part of the overall obviousness analysis. Such considerations do not
`
`appear to be present here. For example:
`
`
`
`
`
`
`
`I have never heard anyone offer praise for the 849 Patent, nor am I
`
`aware of any commercial success attributable to the 849 Patent.
`
`I am unaware of any copying of the alleged invention of the 849
`
`Patent.
`
`I am unaware of any use to which the owner of the 849 Patent has put
`
`the patent except to assert it in litigation.
`
`IV. TECHNOLOGY TUTORIAL
`18.
`I provide in this section a brief description of certain concepts of the
`
`849 Patent that are relevant to my opinions.
`
`A. Chemical Reaction Engineering Overview
`19. The discipline of Chemical Engineering began in the late 19th century
`
`when physicists, industrial chemists and mechanical engineers began to tackle the
`
`challenges of designing large-scale chemical plants. Chemical engineering has its
`
`origins in designing factories and equipment that safely and profitably transformed
`
`raw materials like crude oil and natural gas into valuable products like gasoline and
`
`fertilizers. Over many decades, chemical engineers developed general analytical
`
`methods that are applied to design essentially any industrial chemical process.
`
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`20.
`
`It was recognized near the beginning of the semiconductor industry
`
`that chemical engineers could apply their standard analytical principles to
`
`problems in manufacturing integrated circuits (i.e. “microelectronics materials
`
`processing”). As Jensen writes, “[c]hemical engineers have a long history of
`
`solving multidisciplinary problems in other specialized fields, such as food
`
`processing and polymer processing, and there is a growing recognition of the
`
`useful contributions that chemical engineers can make to electronic materials
`
`processing.” Ex.1008 (K. F. Jensen, “Chemical Engineering in the Processing of
`
`Electronic and Optical Materials: A Discussion,” Adv. Chem. Eng., 16(9): 395-412
`
`(1991)).
`
`21. Like all engineers, chemical engineers use mathematical models in
`
`order to predict how a piece of equipment will operate even before it is built. A
`
`chemical reactor is one such piece of equipment. Specifically, a chemical reactor
`
`is a temperature- and pressure-controlled vessel within which fluid reactants
`
`transform chemically into desired products.
`
`22. The “chemical reaction engineer” combines equations that describe
`
`the motion, temperature and chemical composition of the fluid (most often a gas or
`
`plasma) that moves through the reactor. The underlying mathematical equations
`
`originate from the principles of thermodynamics, continuum mechanics and
`
`chemical kinetics.
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`23. For example, the first law of thermodynamics states that all energy is
`
`conserved but can change form. Equations describing chemical kinetics predict
`
`how fast various chemical reactions will occur as a function of chemical
`
`concentrations, temperature, pressure and perhaps the presence of accelerating
`
`agents (i.e. catalysts).
`
`B.
`
`Temperature Dependent Reactions
`Relationship
`24. At the most basic level, a chemical reaction results from a collision of
`
`and
`
`the Arrhenius
`
`molecules with sufficient energy to create a new product. For example, the 849
`
`Patent discloses the simple bimolecular etching reaction:
`
`O+S→SO
`
`where S is a substrate atom and O is the gas-phase etchant. Ex.1001 at 3:41-48.
`
`25. The mere collision of these two atoms is insufficient to break the
`
`bonds between atoms. Rather the collisions between the atoms must be
`
`sufficiently energetic to bring about bond disruption. The critical energy required
`
`to stretch, bend, or otherwise distort one or more bonds and bring about a chemical
`
`reaction is known as the activation energy of the reaction. Additionally, the
`
`molecules in the collision must have the correct orientation for the particular
`
`chemical reaction.
`
`26. As early as 1890, it was well known that higher temperatures speed up
`
`chemical reactions. This is unsurprising as thermal energy directly relates to
`
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`motion at the molecular level. As the temperature rises, molecules move faster and
`
`collide with more energy, greatly increasing the likelihood of bond cleavages and
`
`rearrangements.
`
`27.
`
`In 1899 Svante Arrhenius, a Swedish chemist, proposed an equation
`
`empirically describing a rate constant of a chemical reaction as a function of
`
`temperature:
`
`k = Ae-Ea/(RT)
`
`where k is the rate constant, T is the absolute temperature (in Kelvin), A is a pre-
`
`exponential factor, Ea is the activation energy for the reaction, and R is the
`
`universal gas constant. The pre-exponential factor is a parameter for each
`
`chemical reaction that is related to the frequency of collisions in the correct
`
`orientation. Note that the Arrhenius relationship can also be expressed as a
`
`function of the Boltzmann constant (kB) in place of the universal gas constant (R).
`
`The only difference is the units of Ea, which is in energy per mole for the former,
`
`and energy per molecule in the later.
`
`28. The basic Arrhenius equation described above is one of the most
`
`important relationships in physical chemistry and chemical engineering. The
`
`reaction rate constant, k, is predominantly dependent on temperature. This
`
`relationship allows for the calculation of the activation energy of a reaction from
`
`values of k observed at different temperatures. It also allows for the calculation of
`
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`the reaction rate constant from the known activation energy for a given
`
`temperature.
`
`29. The Arrhenius equation can also be expressed in a manner that makes
`
`explicit a weak temperature dependence of the preexponential term:
`
`k = ATne-Ea/(RT)
`
`In this form, the preexponential is a constant A multiplied by the temperature
`
`raised to a fractional power n, where n=0 for a temperature-independent
`
`preexponential factor. A typical value of n is 0.5. See, e.g., Ex.1018, Steinfeld et
`
`al., Chemical Kinetics and Dynamics, 14-16 (1989); Ex.1017, Manos and Flamm,
`
`Plasma Etching: An Introduction, 118-19 (1989).
`
`C.
`
`and Chemical Vapor Deposition
`Plasma Etching
`Semiconductor Manufacturing
`30. By
`
`the 1980s
`
`the application of chemical engineering
`
`In
`
`to
`
`semiconductor manufacturing was well known and many persons in the art were
`
`developing models for both the process of depositing layers through chemical
`
`vapor deposition and the process of removing layers through plasma etching.
`
`31. The impetus for chemical engineers to take a greater involvement in
`
`the semiconductor manufacturing field was to reduce the time and cost of
`
`developing equipment to create semiconductor devices. Jensen and Graves (1983)
`
`wrote: “The development of CVD (chemical vapor deposition) reactors and the
`
`selection of operating regimes have hitherto mainly been based on empirical design
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`rules. This limits the operation of existing reactors to certain fixed conditions and
`
`severely hampers the development of novel deposition processes . . . Thus,
`
`reaction engineering analysis and design should be a key element in the
`
`development and operation of CVD reactors.” Ex.1009 at p.1 (K. F. Jensen and D.
`
`B. Graves, “Modeling and Analysis of Low Pressure CVD Reactors,” J.
`
`Electrochem. Soc., 130(9): 1950-1957 (1983)).
`
`32. The generality of the principles of chemical reaction engineering can
`
`be seen in the remarkable fact that the mathematical model of the low pressure
`
`chemical vapor deposition (LPCVD) reactor described by Jensen and Graves
`
`(1983) originated as a model of a packed bed chemical reactor used in the chemical
`
`and petroleum refining industries, among others. Jensen and Graves (1983) write:
`
`“The combined reactor equations [(i.e. of the LPCVD reactor)] have the same form
`
`as the ones for a catalytic-fixed bed reactor, and consequently the concepts
`
`developed for fixed bed reactors also apply to LPCVD reactors.” Id. at p.7.
`
`33. LPCVD reactors are typically on the order of one meter in length and
`
`fractions of a meter in diameter. The pressure is usually about 1/1000 atmospheric
`
`pressure and the gas flow rate is about one standard liter per minute. By contrast,
`
`an industrial fixed-bed catalytic reactor is filled with small, porous catalyst pellets
`
`about 1 cm in diameter, and operates at atmospheric pressure. It is usually tens of
`
`meters in height and several meters in diameter with flow rates many thousands of
`
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`times higher than in the LPCVD reactor. It would be far from obvious to an
`
`untrained observer that these two, seemingly very different classes of “chemical
`
`reactor” could be fruitfully modeled with identical equations.
`
`34. By the late 1980s, it was well known that there are substantial
`
`similarities between plasma etching and chemical vapor deposition (and other
`
`applications). Models for one process (e.g. chemical vapor deposition) can often
`
`be easily adapted to, and in some cases are identical to, the models for another
`
`process (e.g. plasma etching).
`
`35. For example, Hess and Graves write: “etching or deposition processes
`
`are merely chemical reactions that yield a volatile or involatile product,
`
`respectively . . . .” Ex.1010 at p.12 (D. W. Hess and K. F. Jensen, eds.,
`
`Microelectronics Processing, 221(7-8): 362, 377-440 (May 5, 1989)). Plasmas can
`
`be used to either deposit or etch films.
`
`36.
`
`Indeed, it is well known that both deposition and etching usually take
`
`place simultaneously in plasma reactors. Etching can happen on the surface of the
`
`substrate being processed inside a plasma etch reactor while deposition of a film
`
`simultaneously occurs on the inside chamber wall surfaces. The chamber walls of
`
`industrial plasma etch reactors must be periodically cleaned to remove this
`
`accumulated film.
`
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`37. For example, Jensen in 1987 noted that the chemical aspects of
`
`plasma etching (including diffusion controlled plasma etching that neglects plasma
`
`effects) can be modeled in the same manner as chemical vapor deposition: “Since
`
`the plasmas used in microelectronics processing are weakly ionized gases, plasma
`
`reactor modelling may be separated into two subproblems: the discharge structure
`
`as a function of electric parameters, and the transport and reaction of neutral
`
`species governing the deposition/etch performance. The latter problem is
`
`equivalent to those of conventional reaction engineering and CVD as discussed.”
`
`Ex.1011 at p.24 (K. F. Jensen, “Micro-Reaction Engineering: Applications of
`
`Reaction Engineering to Processing of Electronic and Photonic Materials,” Chem.
`
`Eng. Sci., 42(5): 923-958 (1987)).
`
`38.
`
`Jensen provides the following figure to illustrate the components of
`
`plasma processes:
`
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`Ex.1008, Jensen 1991 at Fig. 2.
`
`
`
`Note that the two parts of the plasma process are: “plasma chemistry” and “neutral
`
`species chemistry.” Ex.1008 at Figure 2. The second of these is identical to the
`
`processes occurring in chemical vapor deposition reactors. Equations modeling
`
`these processes are correspondingly identical.
`
`39. Moreover, the inventor of the 849 Patent acknowledged that the same
`
`reactors and technology for plasma etching and chemical vapor deposition were
`
`complementary. Dr. Flamm applied for U.S. Patent No. 4,918,031 in 1988. In the
`
`031 Patent, he describes the use of a single plasma processing device for “plasma
`
`etching” as well as “plasma induced deposition.” See Ex.1012 at Abstract.
`
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`Dr. Flamm described two plasma procedures to either perform “chemical vapor
`
`deposition” or plasma for “etch[ing] a substrate.” Id. at 1:16-19. Similarly,
`
`Dr. Flamm applied for U.S. Patent No. 5,304,282 in 1991. In the 282 Patent, Dr.
`
`Flamm stated that “[p]lasma etching and deposition is accomplished utilizing a
`
`helical resonator . . . .” Ex.1013 at Abstract.
`
`40. Simply put, it was obvious to people working in this field since at
`
`least the 1980’s that models used in CVD are often equally valid for plasma etch
`
`and vice versa, depending on the reactor conditions.
`
`V. THE 849 PATENT
`41.
`I understand Petitioners are challenging claims 1-29 (“challenged
`
`claims”) of the 849 Patent (Ex.1001).
`
`42.
`
`I understand that the 849 Patent was filed on May 3, 1995 and issued
`
`on January 27, 1998. I understand that the 849 Patent does not claim priority to
`
`any other patent application or provisional application. I have been asked to
`
`assume that the filing date of the 849 Patent is the priority date. I further
`
`understand that the references relied upon in the Petition all predate the filing of
`
`the 849 Patent.
`
`A.
`Independent Claim 1
`43. Claim 1 is representative of the claimed subject matter. For example,
`
`claim 1 recites a method for fabricating a device comprising: (a)” providing a
`
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`plasma etching apparatus comprising a substrate therein, said substrate comprising
`
`a top surface and a film overlying said top surface, said film comprising a top film
`
`surface;” (b) “etching said top film surface to define a relatively non-uniform
`
`etching profile on said film, and defining etch rate data comprising an etch rate and
`
`a spatial coordinate which defines a position within said relatively non-uniform
`
`etching profile on said substrate, said etching comprising a reaction between a gas
`
`phase etchant and said film;” and (c) “extracting a surface reaction rate constant
`
`from said etch rate data, and using said surface reaction rate constant in the
`
`fabrication of a device.” Ex.1001 at 17:36-50.
`
`44. The dependent claims are merely minor modifications to the claimed
`
`methods that are largely independent of the modeling method disclosed. For
`
`example, dependent claims cover: using a diffusion limited reaction (claims 2, 11),
`
`using cylindrical or Cartesian coordinates (claims 3, 4, 12, 13), using an ashing
`
`method of etching (claims 7, 8, 16, 17), using a reaction that is dominated by
`
`chemical reactions over ion bombardment effects (claims 21, 28), and using a
`
`method that calculates the surface reaction rate constant with a “diffusivity value
`
`that is determined by an equation” (claim 27). These dependent claims do not
`
`materially affect the underlying chemical reaction engineering.
`
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`B.
`The 849 Patent Disclosure
`45. The 849 Patent, at a high level, relates to modeling of gas diffusion
`
`and a surface chemical reaction between a gas phase and a substrate, in order to
`
`predict the etch rate in a plasma reactor. This model can be used to design a
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`reactor for the manufacture of integrated circuits. Ex.1001 at Abstract, 1:6-7. The
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`focus of the alleged invention is a method for applied chemical reaction
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`engineering, which models the “reaction between a neutral gas phase species and a
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`surface material layer, typically for removal,” id. at 1:20-21, and is “illustrated in
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`an example with regard to plasma etching.” Id. at 1:6-7.
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`46.
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`In the 849 Patent, Dr. Flamm argues that the “conventional technique
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`for obtaining and maintaining uniform etching relies upon a ‘trial and error’
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`process.” Id. at 1:28-30. He also contends that “reaction rates between the etching
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`species and the etched material are often not available,” and so “it is often
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`impossible to anticipate actual etch rates from reaction rate constants.” Id. at 1:36-
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`39.
`
`47. The 849 Patent describes a method of “determining a reaction rate
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`coefficient based upon etch profile data” to “provide[] for an easy and cost
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`effective way to select appropriate etching parameters such as reactor dimensions,
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`temperature pressure, radio frequency (rf) power, flow rate and the like” which
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`helps to avoid the need to build “[f]ull scale prototype equipment.” Id. at 1:42-55.
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`In other words, the 849 Patent is directed to using chemical reaction engineering to
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`model the etching reaction, determine the reaction rate coefficient by applying the
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`model to experimental data, and then to use the model to design or modify the
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`plasma reactor.
`
`48. The 849 Patent discloses two types of plasma etching apparatuses.
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`See id. at Figs. 1, 2. The first type of plasma reactor is illustrated in Figure 1.
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`Figure 1 is a very high-level diagram of a co-axial barrel plasma etcher. The
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`etcher is illustrated as divided into three processing zones: a plasma generating
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`zone 13, a transport zone 15, and a plate stack zone 17. Id. at 2:56-62.
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`Ex.1001, 849 Patent at Fig. 1.
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`49. The “gas phase species” enter through the chemical feed (marked “F”
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`above) into the plasma generating zone, diffuse through the transport zone, and
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`react with the substrate material as they diffuse “over surfaces of the substrates
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`[21].” Id. at 2:63-3:25. The exhaust (marked “E” above), allows for the removal
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`of the gas phase species. Id. This type of barrel plasma etcher “relies substantially
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`upon diffusion to obtain the desired etching uniformity” and “a chemical etch rate
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`which is diffusion limited.” Id. at 3:6-9.
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`50. The second type of plasma reactor is illustrated at a high-level in
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`Figure 2. Figure 2 is identified as “an alternative example” of a reactor that can be
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`used to perform the claimed methods. Id. at 4:14-15.
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`
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`Ex.1001, 849 Patent at Fig. 2.
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`51. This type of reactor is a “single wafer etching apparatus” with two
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`electrodes (marked 55 and 57 above) which contain the plasma in the region
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`marked 54 above. Id. at Fig. 2, 4:16-22. Like the barrel plasma etcher of Figure 1,
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`the gas phase species enter the reactor through the chemical feed (marked “F”
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`above), and are removed through an exhaust (marked “E” above). Id. at 4:27-28.
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`The gas phase species diffuse to the substrate (marked 61 above) where they react
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`with the substrate. Id. at 4:18-31.
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`52. While the specification of the 849 Patent illustrates two types of
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`plasma reactors, “the invention may be applied to other reactors such as large
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`batch, high pressure, chemical, single wafer, and others.” Id. at 4:61-63. The 849
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`Patent specifically states that, “[o]ne of ordinary skill in the art would easily
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`recognize other applications” of the modeling methods claimed. Id. at 5:5-7. I
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`agree with this statement.
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`53. The 849 Patent models the surface etching reaction with “a first order
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`form:
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`O+S→SO
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`where S is a substrate atom . . . and O is the gas-phase etchant.” Id. at 3:34-47.
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`The rate of this reaction is a function of the concentration of the gas-phase etchant
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`(O), and can result in a non-uniform etching profile as a result of “different etch
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`rates along the r-direction of the substrate corresponding to different etchant
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`species concentrations.” Id. at 4:2-6.
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`54. The 849 Patent charts the concentration of the gas-phase etchant as a
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`function of the substrate radius in the top graph of Figure 1A. It also illustrates the
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`convex etching profile of the substrate film in Figure 1A (marked 27 below). Id. at
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`3:66-4:9. The 849 Patent discloses that the etching profile “can be measured by
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`conventional techniques” and can be used to derive “an etching rate constant.” Id.
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`at 4:45-49.
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`
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`Ex.1001, 849 Patent at Fig. 1A.
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`55. The etching rate constant is also described in the 849 Patent as the
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`surface reaction rate constant, ks. The etch rate (ROS) is equal to this surface
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`reaction rate constant multiplied by the concentration of the etchant species (no):
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`ROS = (no) ks See id. at 7:15-21, 10:33-38. “From the concentration and the
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`surface reaction rate, the particular etching step can be improved by way of
`
`adjusting selected etching parameters.” Id. at 7:22-24.
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`56. The 849 Patent assumes that the gap above a substrate is sufficiently
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`small relative to the radius of the substrate that concentration differences in this
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`direction can be ignored. Id. at 3:34-38. This assumption allows for the
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`transformation of the partial differential equations from the mathematical model
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`and in their place use ordinary differential equations in which the only spatial
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`coordinate is the radial position across the substrate. This transformation results in
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`an equivalent volumetric reaction rate constant kvo.
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`57. The 849 Patent provides examples of the solution of the mathematical
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`model for the relationship between the relative etch rate, u(r) (in this example in
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`cylindrical coordinates), and kvo/D where D is the diffusivity of the etchant:
`
`
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`where IO is a “modified Bessel function of the first kind,” and “a is an outer radius
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`(or edge) of the substrate.” Id. at 6:17-29. Different geometries result in different
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`equations for u(r), but in all cases the mathematical solution relates a relative etch
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`rate as a function of position across the substrate to kvo/D and the size of the
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`substrate, here defined as the parameter a.
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`58. The 849 Patent discloses one method to calculate the surface reaction
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`rate constant, ks: (1) derive an “etch constant (or reaction rate constant) over
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`diffusivity (kvo/D)”, (2) multiply that value by a calculated diffusivity (DAB) to
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`derive a volumetric reaction rate constant (kvo), and (3) multiply the volumetric
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`reaction rate constant by the gap between two substrates, (dgap) to determine a
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`surface reaction rate constant (ks). Id. at 5:62-6:62, Fig. 3.
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`59. The first step of this method calculates kvo/D. Id. “kvo is the volume
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`equivalent surface reaction rate constant.” Id. at 12:8-9. In other words, this value
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`is equivalent to the surface reaction rate for the volume abo
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