United States Patent
`
`[191
`
`[11] Patent Number:
`
`5,711,849
`
`Flamm et al.
`
`[45] Date of Patent:
`
`Jan. 27, 1998
`
`US00571 1849A
`
`[54] PROCESS OPTIMIZATION IN GAS PHASE
`DRY ETCHING
`
`Thompson et al. “Introduction to Microlithography” © 1983
`ACS pp. 228—235.
`
`[75]
`
`Inventors: Daniel L. Flamm, 476 Green View Dr.,
`Walnut Creek, Calif. 94596; John P.
`Verboncoeur, Hayward, Calif.
`
`[73] Assignee: Daniel L. Flamm, Walnut Creek, Calif.
`
`[21] Appl. No.: 433,623
`
`[22] Filed:
`
`May 3, 1995
`
`Int. CLG ................................................. H01L 21/3065
`[51]
`[52] U.S. Cl. ..................................... 156/643.1; 156/625.1;
`156l346 P; 156/626.1; 156/659.11; 156/646.1;
`204/298.31; 204/298.32; 216/58; 216/59
`[58] Field of Search ......................... 204/29831, 298.32;
`216/39, 58, 74, 79, 246 P, 625.1, 643.1,
`626.1, 646.1, 659.1, 662.1, 659.11
`
`Giapis et al. Appl. Phys Lett 57(10) 983—985 (Sep. 1990).
`
`Gregus et a1. Plasma Chem. Plasma Process. 13(3) 521—537
`(1993).
`
`Babanov et a1. Plasma Chem. Plasma Process. 13(1) 37—59
`(1993).
`
`Ha et al. Plasma Chem. Plasma Process. 11(2) 311—321
`(1991).
`
`Rayn et a1. Plasma Chem. Plasma Process. 10(2) 207—229
`(1990).
`
`Elliott “Integrated Circuit Fabrication Technology” © 1982
`pp. 242—243 and 258—271.
`
`Manos et al. “Plasma Etching, An Introduction”, © 1989,
`Academic Press, pp. 91—183.
`
`[56]
`
`References Cited
`U.S. PATENT DOCUMENTS
`
`Primary Examiner—Martin Angebranndt
`Attorney, Agent, or Firm—Townsend and Townsend and
`Crew LLP
`
`3/1980 Horiike ................................ 156/643.1
`4,192,706
`10/1980 Mogab
`156/643.1
`4,226,665
`
`1/1981 Ikeda et al.
`156/345 P
`4,243,506
`..
`4,297,162 10/1981 Mundt et al.
`.. 156/345 P
`
`4,340,461
`7/1982 Hendricks et al.
`156/345 P
`.. 204/298.32
`9/1992 Bobbio .........
`5,147,520
`
`5,330,606
`7/1994 Kubota et al.
`156/345 P
`
`5,399,229
`3/1995 Stefani et a1.
`156I626.1
`....................... 156l622.1
`5,445,709
`8/1995 Kojima et a1.
`
`OTHER PUBLICATIONS
`
`Bird et al., Transport Phenomena, 1960, John Wiley & Sons,
`p. 510.
`Manos, D. M. and Flamm, D. L., Plasma Etc/rings, An
`Introduction, 1989, Academic Press, (title page and table of
`contents only).
`
`[57]
`
`ABSTRACT
`
`A method of designing a reactor 10. The present reactor
`design method includes steps of providing a first plasma
`etching apparatus 10 having a substrate 21 therein. The
`substrate includes a top surface and a film overlying the top
`surface, and the film having a top film surface. The present
`reactor design method also includes chemical etching the top
`film surface to define a profile 27 on the film, and defining
`etch rate data from the profile region. A step of extracting a
`reaction rate constant from the etch rate data, and a step of
`using the reaction rate constant in designing a second plasma
`etching apparatus is also included.
`
`29 Claims, 8 Drawing Sheets
`
`
`
`Page 1 of 19
`
`Samsung Exhibit 1009
`
`Page 1 of 19
`
`Samsung Exhibit 1009
`
`

`

`US. Patent
`
`Jan. 27, 1998
`
`Sheet 1 of 8
`
`5,711,849
`
`10
`
`17 \ Plate
`Stack /
`
`
`
`
`13
`\
`Plasma
`, Generating
`
`
`AMIQV {hihinia'ifiu'fififififiifiaiixi-aimfiifinfiififiu
`.4..-
`
`
`
`
`
`
`Page 2 of 19
`
`Page 2 of 19
`
`

`

`U S. Patent
`
`Jan. 27, 1998
`
`Sheet 2 of 8
`
`5,711,849
`
`M.mm NM.MWMvMN“-N»3
`
` “ta-gumw a... W NA. w. on“: ox») not:
`
`
`
`
`
`
`
`Page 3 of 19
`
`Page 3 of 19
`
`

`

`US. Patent
`
`Jan. 27, 1998
`
`Sheet 3 of 8
`
`5,711,849
`
`Measure etch profile
`
` Etch film at constant pressure and preferably
`constant plasma source characteristics and:
`
`
`I. do not etch to endpoint or 2. Etch exactly to
`first sign of endpoint. Best to do isothermally,
`
`
`but can probably handle complex case if
`measure temperature-time history.
`
`[— 100
`
`101
`
`Get etch rate profile data as (Etch rate,x,y) or
`(Etch rate, r, B) triads, an n x 3 array where
`n is the number of points sampled.”
`
`temperature varies it will be average etch rate.
`
`107
`
`105
`
`
`
`Fit to model with kvo/D and
`etch rate as parameters
`
`New temperatures
`in order to get
`
`ksiTz), ksiTs)
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`Run a least squares fit using differences between the
`data array and analytical model for etch rate to
`compute: kvo/D and the etch rate at edge of the plate
`or wafer.
`»
`
`
`Calculate D and with
`it kvo 81 k5
`
`
`
`Calculate D from Chapman-Enskog kinetic theory
`formulas (see Fl. B. Bird, W. E. Steward. E. N.
`
`
`nghtfoot, pp. 510-513, Transport Phenomena. Wiley
`(1960). Multiply kvo/D by D(T,P) to obtain
`kVO(T,dgap) = k5(T)(AreaNolume)=kS/dgap
`
`S
`t
`epara e
`pre-exp & Ea
` From kS(T1), kS(T2)... do least square fit to
`
`extract Ea and preexponential where
`
`
`ks(T)=A(T1I2)Ae-EafkT Or, if Ea is known,
`just extract preexponential.
`
`1 08
`
`1 11
`
`109
`
`
`
`Use ER(edge)=kvo no to
`deduce no, the atom
`concentration at the edge
`
`of the wafer.
`
`FIG. 3
`
`Page 4 of 19
`
`Page 4 of 19
`
`

`

`US. Patent
`
`Jan. 27, 1998
`
`Sheet 4 of 8
`
`5,711,849
`
`200
`
`201 J
`
`
`
`Measure etch rate vs. effective area of
`
`
`substrate.Plasma source temperature, pressure
`
`
`(T,P), power held constant. However substrate stack
`
`or single substrate T,P may be varied to alter Aeff.
`
`
`
`
`
`
`
`
`
`Alter gap (d) bemeen
`Change number of
`vary SUbstrate
`
`-
`(3t SimUHanEQUSlY) $Upport
`waters and surface
`
`waters In the reactor
`member dlmensmns
`above
`
`
`
`.
`.
`.
`208
`
`Is uniformity very high
`(>90-95%)?
`
`
`Measure etching profile
`and compute Aeff
`(loading eqn)
`
`
` Has data for n Aeff values
`
`been measured? (n2 3)?
`
`
`
`Fit to eqn. 5, & from slope
`(m Aeff) obtain 1/ST, the supply of
`
` J 203
`
`
`etchant from source to the reactor.
`
`Try new plasma source or
`plasma source parameters.
`
`207
`
`
`
`
`
`
`
`Modify chamber materials etc. to
`reduce slope of the numerator,
`
`(kr Ar + F) or reduce flow if F term is
`major etchant loss.
`
`205
`
`FIG. 4
`
`Page 5 of 19
`
`Page 5 of 19
`
`

`

`US. Patent
`
`Jan. 27, 1998
`
`Sheet 5 of 8
`
`5,711,849
`
`Specify required
`uniformity
`
`
`
`/ 301 f 300
`
`lnput predetermined ks or determine
`ks from uniformity measurements at
`one or more temperatures
`
`
`
`
`
`
`Compute locus of highest T vs. P and
`
`
`d; and highest P vs. T and d where
`uniformity meets specification.
`
`
`
`
`
`
`303
`
`307
`
`309
`
`311
`
`Specify: uniformity limit manifold. Select
`d values and adjust locus of P and T
`values below the calculated manifold
`by a predetermined amount to allow for
`
`
`statistical and experimetnal error and
`
`process drift. (P0,To)
`
`
`
`Determine max edge etch rate & supply
`
`
`of etchant from plasma source (ST) for
`
`
`RF power, flow values and [Pi,Ti](d)
`
`
`within uniformity limits manifold.
`
`Locate intersection space of P<Pi ,T<Ti
`(uniformity manifold) and maximum
`etch rate or etchant supply at selected
`RF power (flow) values.
`
`
`
`
`
`
`If the resulting etch rates are too
`low, change power and/or reduce
`effective etchable area (example:
`
`
`substrates).
`
`
`
`
`
`
`313
`
`increase d, decrease number of
`
`315
`
`FIG. 5
`
`Page 6 of 19
`
`Page 6 of 19
`
`

`

`US. Patent
`
`Jan. 27, 1998
`
`Sheet 6 of 8
`
`5,711,849
`
`Loading Effect Data
`
`1/AshRate
`
`LCD Plates
`
`FIG. 6
`
`
`
`FIG. 7
`
`FIG. 8
`
`Page 7 of 19
`
`Page 7 of 19
`
`

`

`US. Patent
`
`Jan. 27, 1998
`
`Sheet 7 of 8
`
`5,711,849
`
`50
`
`100
`
`150
`
`Radial Distance from the Water Center, millimeters
`
`FIG.9
`
`_L
`
`0.9
`
`U)
`
`8 E
`
`2g
`
`0.8
`D. 0.7
`33
`g 0.6
`
`2’
`E 0.5
`(4‘5
`0.4
`8 0.3
`
`02
`
`g E
`
`2 0.1
`
`0
`
`0
`
`Z
`
`y
`
`_
`_+_d—dgap
`
`V —+_d=0
`V y
`
`b/2
`
`43/2
`
`x
`
`FIG. 10
`
`X
`
`-a/2
`
`a/2
`
`FIG. 11
`
`Page 8 of 19
`
`Page 8 of 19
`
`

`

`US. Patent
`
`Jan. 27, 1998
`
`Sheet 8 of 8
`
`5,711,849
`
`
`
`FIG. 12
`
`Page 9 of 19
`
`Page 9 of 19
`
`

`

`1
`PROCESS OPTIMIZATION IN GAS PHASE
`DRY ETCHING
`
`BACKGROUND OF THE INVENTION
`
`5,711,849
`
`2
`
`fromthe etch rate data, and using the reaction rate constant
`in adjusting a plasma etching apparatus is also included.
`In an alternative specific embodiment, the present inven-
`tion also provides a method of designing a reactor. The
`present method includes providing a first plasma etching
`apparatus having a substrate therein. The substrate has a top
`surface and a film overlying the top surface. The film has a
`top film surface. The present method also includes chemi-
`cally etching the top film surface to define an etching profile
`on the film, and defining etch rate data which has an etch rate
`and a spatial coordinate from the etching profile. A step of
`extracting a reaction rate constant from the etch rate data,
`and using the reaction rate constant in designing a second
`plasma etching apparatus is also included.
`A further alternative embodiment provides another
`method of fabricating an integrated circuit device. The
`present method includes steps of providing a uniformity
`value for an etching reaction. The etching reaction includes
`a substrate and etchant species. The present method also
`includes defining etching parameter ranges providing the
`uniformity value. A step of adjusting at least one of the
`etching parameters to produce a selected etching rate is also
`included. The etching rate provides an etching condition for
`fabrication of an integrated circuit device.
`The present
`invention achieves these benefits in the
`context of known process technology. However. a further
`understanding of the nature and advantages of the present
`invention may be realized by reference to the latter portions
`of the specification and attached drawings.
`
`BRIEF DESCRIPTION OF THE DRAWINGS
`
`FIG. 1 is a simplified diagram of a plasma etching
`apparatus according to the present invention;
`FIG. 1A is a simplified cross-sectional View of a wafer
`profile according to the plasma etching apparatus of FIG. 1;
`FIG. 2 is a simplified diagram of an alternative embodi-
`ment of a plasma etching apparatus according to the prevent
`invention;
`
`FIGS. 3—5 are simplified flow diagrams of plasma etching
`methods according to the present invention;
`FIG. 5A is a plot of uniformity, temperature, pressure, and
`gap for an etching process according to the present inven—
`tion;
`
`FIG. 6 is a simplified plot of flash rate vs. LCD plate
`number according to the present invention;
`FIGS. 7—9 illustrate an example with regard to circular
`substrates according to the present invention; and
`FIGS. 10—12 illustrate an example with regard to rectan—
`gular substrates according to the present invention.
`
`DESCRIPTION OF THE SPECIFIC
`EMBODIMENT
`
`Plasma Etching Apparatus
`FIG. 1 is a simplified diagram of a plasma etching
`apparatus 10 according to the present invention. The plasma
`etching apparatus also known as a co—axial reactor includes
`at least three processing zones. The three processing zones
`are defined as a plasma generating zone (PG) 13, a transport
`zone (TZ) 15, a plate stack zone (PS) 17, and others. Also
`shown are a chemical feed F and exhaust E. The plasma
`generating zone provides for reactant species in plasma form
`and others. Excitation is often derived from a 13.56 MHz rf
`discharge 8 and may use either capacitor plates or a wrapped
`coil, but can also be derived from other sources. The co—axial
`
`5
`
`10
`
`15
`
`20
`
`25
`
`30
`
`35
`
`45
`
`50
`
`55
`
`65
`
`The present invention relates to integrated circuits and
`their manufacture. The present invention is illustrated in an
`example with regard to plasma etching, and more particu-
`larly to plasma etching in resist strippers in semiconductor
`processing. But it will be recognized that the invention has
`a wider range of applicability in other technologies such as
`flat panel displays, large area substrate processing, and the
`like. Merely by way of example, the invention may be
`applied in plasma etching of materials such as silicon,
`silicon dioxide, silicon nitride, polysilicon, photoresist,
`polyirnide, tungsten, among others.
`Industry utilizes or has proposed several techniques for
`plasma etching. One such method is conventional chemical
`gas phase dry etching. Conventional chemical gas phase dry
`etching relies upon a reaction between a neutral gas phase
`species and a surface material layer, typically for removal.
`The reaction generally forms volatile products with the
`surface material layer for its removal. In such method, the
`neutral gas phase species may be formed by way of a plasma
`discharge.
`A limitation with the conventional plasma etching tech—
`nique is obtaining and maintaining etching uniformity
`within selected predetermined
`In fact, the conven-
`tional
`technique for obtaining and maintaining uniform
`etching relies upon a “trial and error” process. The trial and
`error process often cannot anticipate the effects of parameter
`changes for actual wafer production. Accordingly, the con-
`ventional technique for obtaining and maintaining etching
`uniformity is often costly, laborious, and difficult-to achieve.
`Another limitation with the conventional plasma etching
`technique is reaction rates between the etching species and
`the etched material are often not available. Accordingly, it is
`often impossible to anticipate actual etch rates from reaction
`rate constants since no accurate reaction rate constants are
`
`available. In fact, conventional techniques require the actual
`construction and operation of an etching apparatus to obtain
`accurate etch rates. Full scale prototype equipment and the
`use of actual semiconductor wafers are often required,
`thereby being an expensive and time consuming process.
`From the above it is seen that a method and apparatus of
`etching semiconductor wafers that is easy, reliable, faster,
`predictable, and cost etfective is often desired.
`
`SUMMARY OF THE INVENTION
`
`According to the present invention, a plasma etching
`method that includes determining a reaction rate coeflicient
`based upon etch profile data is provided. The present plasma
`etching method provides for an easy and cost effective way
`to select appropriate etching parameters such as reactor
`dimensions,
`temperature, pressure, radio frequency (rf)
`power, flow rate and the like by way of the etch profile data.
`In a specific embodiment, the present invention provides
`an integrated circuit fabrication method. The present method
`includes steps of providing a plasma etching apparatus
`having a substrate therein. The substrate includes a top
`surface and a film overlying the top surface. The film
`includes a top film surface. The present method also includes
`chemically etching the top film surface to define an etching
`profile on the film, and defining etch rate data which
`includes an etch rate and a spatial coordinate from the
`etching profile. A step of extracting a reaction rate constant
`
`Page 10 of 19
`
`Page 10 of 19
`
`

`

`5,711,849
`
`4
`
`3
`reactor 10 also includes a chemical controller 14 and a
`temperature and pressure control 12, among other features.
`Chemical effects are often enhanced over ion induced
`effects and other effects by way of perforated metal shields
`18 to confine the discharge to a region between an outer wall
`16 and shields 18. The co—axial reactor relies substantially
`upon diffusion to obtain the desired etching uniformity. The
`co—axial reactor also relies upon a chemical etch rate which
`is diffusion limited. In particular, the chemical etch rate is
`generally defined as a chemical reaction rate of etchant
`species plus at least a diflusion rate of etchant species. When
`the diffusion rate of etchant species is much greater than the
`chemical reaction rate,
`the chemical etch rate is often
`determined by the diffusion rate. A more detailed analysis of
`such chemical etch rate will be described by way of the
`subsequent embodiments.
`Etchant species from the plasma generating zone diffuse
`through the transport zone 15 of the reaction chamber, and
`enter the plate stack zone space over surfaces of substrates
`21. A concentration of etchant in the transport zone, which
`is often annular, between the plasma generating zone and the
`plate stack zone is defined as n00. As etchant dijfuses
`radially from the transport zone into the plate stack zone and
`over surfaces of the substrates, it is consumed by an etching
`reaction. Areactant concentration above the substrate can be
`defined as na(r,z), where r is the distance from the center of
`the substrate and z is the distance above the substrate. A
`diffusive velocity v0 of etchant species in the plate stack
`zone is characterized by Fick’s law.
`
`va = —D
`
`
`Vno
`"a
`
`In a specific embodiment, a gap dgap above the substrate
`is much less than the lateral extent dgap<<r and gas phase
`mass transfer resistance across the small axial distance is
`negligible so that the axial (z—direction) term of the concen-
`tration gradient can be ignored. The embodiment can be
`applied without this restriction; however, numerical mesh
`computer solutions are then required to evaluate the reaction
`rate constant and uniformity. In the embodiment, the surface
`etching reaction bears a first order form:
`O+S—)SO
`
`where
`S is a substrate atom (e.g., resist unit “mer”); and
`O is the gas-phase etchant (for example oxygen atoms)
`with certain etching kinetics. The first order etching reaction
`can be defined as follows:
`
`R0, = noA \I—T- raw”
`
`Where
`Rm. defines a reaction rate;
`no defines a concentration;
`A defines a reaction rate constant;
`T defines a temperature;
`EACT defines an activation energy; and
`R defines a gas constant. An example of the first reaction
`is described in D. L. Flamm and D. M. Manos “Plasma
`Etching,” (1989), which is hereby incorporated by reference
`for all purposes. Of course, other order reactions, reaction
`relations, and models may be applied depending upon the
`particular application.
`An example of an etched substrate 21 from the plate stack
`zone is illustrated by FIG. 1A. The substrate 21 is defined in
`
`Page 11 ofl9
`
`10
`
`15
`
`20
`
`25
`
`30
`
`35
`
`spatial coordinates such as z and r. The substrate includes a
`bottom surface 23, sides 25, and a top surface film 27. As can
`be seen, the top surface film includes a convex region, or
`etching profile. The etching profile occurs by way of differ-
`ent etch rates along the r—direction of the substrate corre-
`sponding to different etchant species concentrations. A con—
`centration profile na(r,z) is also shown where the greatest
`concentration of reactant species exists at the outer periph-
`ery of the top surface film. In the present invention, an etch
`rate constant may be obtained by correlation to the etching
`profile. Byway of the etch rate constant, other etching
`parameters such as certain reactor dimensions including a
`distance between substrates, pressure, temperature, and the
`like are easily calculated.
`FIG. 2 illustrates an alternative example of an etching
`apparatus 50 according to the present invention. The etching
`apparatus 50 is a single wafer etching apparatus with ele—
`ments such as a chamber 53, a top electrode 55, a bottom
`electrode 57, a power source 59, a platen 64, and others. The
`bottom electrode 57 is at a ground potential, and the top
`electrode is operany coupled to the power source 59 at a
`high voltage potential. A plasma exists in a region 54
`between the top electrode 55 and the bottom electrode 57,
`which is often a grid configuration or the like. Reactant
`species are directed via power source from a plasma source
`to a wafer substrate 61 by diffusion. A temperature and
`pressure controller 67 and a flow controller 69 are also
`shown. The etching apparatus also includes a chemical
`source feed F and a exhaust E. Of course, other elements
`may also be available based upon the particular application.
`By way of a plate 63 interposed between the wafer
`substrate 61 and the bottom electrode 57,
`the reactant
`species do not directly bombard the wafer substrate. The
`plate is preferably made of an inert material appropriate for
`the particular etching such as pyrex or glass for resist ashing,
`alumina for fluorine atom etching of silicon, silicon nitride,
`or silicon dioxide, and the like. In an ashing reaction, the
`plate is placed at a distance ranging from about 5 mm to 50'
`mm and less from the wafer substrate 61. Of course, other
`dimensions may be used depending upon the particular
`application. The reactant species are transported via diffu-
`sion from the plasma source to the wafer substrate around
`the periphery of the plate 63. Accordingly, the reaction rate
`at the wafer substrate is controlled by a balance between
`chemical reaction and diifusion effects, rather than direc-
`tional bombardment.
`
`45
`
`50
`
`55
`
`65
`
`By way of the diffusion effects, an etching rate constant
`may be obtained for the etching apparatus 50 of FIG. 2. In
`particular, the etching rate constant derives from a etching
`profile 65, which can be measured by conventional tech—
`niques. The present invention uses the etching rate constant
`to select other etching rate parameters such as reactor
`dimensions, spacing between the substrate and its adjacent
`surface,
`temperatures, pressures, and the like. But the
`present invention can be used with other reactor types where
`etching may not be controlled by diffusion. For example, the
`present invention provides a reaction rate which can be used
`in the design of reactors where ditfusion does not control
`such as a directional etcher and the like. The reaction rate
`constant may also be used in the directional etcher to predict
`an extent of, for example, undercutting of unprotected
`sidewalls whfle ion bombardment drives reaction in a ver-
`tical direction. Of course, the invention may be applied to
`other reactors such as large batch, high pressure, chemical,
`single wafer, and others. The invention can also be applied
`to diiferent substrate materials, and the like.
`Plasma Etching Method
`FIGS. 3-5 illustrate simplified flow diagrams of plasma
`etching methods according to the present invention. The
`
`Page 11 of 19
`
`

`

`5,711,849
`
`5
`
`present methods provide for improved etching conditions by
`way of a reaction rate constant derived from, for example, an
`etching profile. It should be noted that the present methods
`as illustrated should not be construed as limiting the inven-
`tion as defined in the claims. One of ordinary skill in the art
`would easily recognize other applications of the inventions
`described here.
`In a specific embodiment, a method of extracting a rate
`constant 100 for a plasma etching step according to the
`present invention is illustrated by the flow diagram of FIG.
`3. A substrate with an overlyng film is placed into a plasma
`etching apparatus or the like. The overlying film is defined
`as an etching film. In the present embodiment, the overlying
`film is a photoresist film, but can also be other films such as
`a silicon film, a polysilicon film, silicon nitride, silicon
`oxide, polyimide, and the like.
`A step of plasma etching the film is performed by step
`101. The plasma etching step occurs at constant pressure and
`preferably constant plasma source characteristics. More
`preferably, the plasma etching step occurs isotherrnally at
`temperature T1, but can also be performed with changing
`temperatures where temperature and time histories can be
`monitored. Plasma etching of the film stops before the
`endpoint (or etch stop). Alternatively, plasma etching stops
`at a first sign of the endpoint (or etch stop). The plasma
`etching step preferably stops before etching into an etch stop
`layer underlying the film to define a “clean” etching profile.
`The substrate including etched film is removed from the
`chamber of the plasma etching apparatus. The etched film
`includes an etching profile (step 103) made by way of
`plasma etching (step 101). The etching profile converts into
`a relative etch rate, relative concentration ratio, a relative
`etch depth, and the like at selected spatial coordinates. The
`relative etch rate is defined as an etch rate at a selected
`spatial coordinate over an etch rate at the substrate edge. The
`relative concentration ratio is defined as a concentration of
`etchant species at a selected spatial coordinate over a con—
`centration of etchant at the substrate edge.
`In x-y-z coordinates,
`the relative etch rate in the
`z—direction, and the spatial coordinates are defined in the x-y
`coordinates. The etching profile is thereby characterized as
`a relative etch rate u, a X—location, and a y—location u, (X, y).
`In cylindrical coordinates, the relative etch rate is also in the
`z—direction, and the spatial coordinates are defined in the r
`and 9 coordinates. The etching profile is characterized as a
`relative etch rate u, a r—location, and a e-location (u, r, 9). An
`array of data points in either the x—y coordinates or r—G
`coordinates define the etching profile. The array of data
`points can be defined as an n><i array, where n represents the
`number of points sampled and 3 represents the etch rate and
`two spatial dimensions. Of course, the choice of coordinates
`depends upon the particular application.
`Optionally, in a non-isothermal condition, an average etch
`rate is measured By approximate integration of a time
`dependent etch rate, suitable starting point approximations
`for an etching rate constant pre—exponential and activation
`energy can be selected. The etch rate is integrated over time
`(and temperature) using measured temperature-time data (or
`history). An etched depth profile and the etching rate from
`the integration can then be compared with actual data. Arate
`constant is appropriately readjusted and the aforementioned
`method is repeated as necessary.
`An etch constant (or a reaction rate constant) over diffu—
`sivity (km/D) and an etch rate at an edge is calculated at step
`105. The etch constant over difl’usivity correlates with data
`points representing the etch rate profile. In x-y coordinates,
`the relationship between kw/D and the relative etch rate
`u(x,y) is often defined as follows:
`
`Where
`
`6
`
`a and b define substrate lengths in, respectively, an
`x-direction and a y-direction.
`
`u(xyy) =
`
`cosh” two/D + (m'rr/b)2
`
`x]
`
`
`
`cosh [‘1 kw/D+ (m7r/b)2
`+
`
`cosh[ *1 km/D + (nut/a)2
`
`y]
`
`111112]?
`COS
`a
`
`cosh [ 4 kw/D+ (mt/(1)2
`
`In cylindrical coordinates, the relationship between the etch
`constant over diffusivity kW/D and the relative etch rate u(r)
`is defined as follows:
`
`Where
`
`a is an outer radius (or edge) of the substrate and I0 is
`modified Bessel function of the first kind.
`
`In step 106, a difiusivity is calculated for the particular
`etchauts. The binary diffusivity DAB may be calculated based
`upon the well known Chapman-Enskog kinetic theory equa-
`tion:
`
`
` 1 1
`Tuna)
`DAB = 2.2646 X 10—5W
`
`where
`T is a temperature;
`c is a total molar concentration;
`MA and MB are molecular weights;
`DAB is a binary diffusivity;
`GAB is a collision diameter; and
`QDAB is a collision integral.
`The Chapman-Enskog kinetic theory equation is described
`in detail in part 111 of R. B. Bird, W. E. Stewart. and E. N.
`Lightfoot, ‘Transport Phenomena,” Wiley (1960) which is
`hereby incorporated by reference for all purposes. Of course,
`other techniques for calculating a diifusivity may also be
`used. The equivalent volumetric reaction rate constant kw, is
`derived from the diifusivity as follows.
`
`1.4
`
`km
`D
`
`)0...
`
`10
`
`15
`
`20
`
`25
`
`30
`
`35
`
`40
`
`45
`
`50
`
`55
`
`Once the reaction rate constant kw is extracted, the surface
`reaction rate constant k, may be isolated from the previous
`equation as follows.
`
`K,=(1%o)d,ap
`
`65
`
`Repeat steps 101—106 at ditferent temperatures T2,
`T3. . . Tn to calculate additional reaction rate constants k('I‘2),
`k(T3) . . . k(T,,). The steps are repeated at least two times and
`more, and preferably at least three times and more. Each
`temperature is at least 5° C. greater than the previous
`
`Page 12 of 19
`
`Page 12 of 19
`
`

`

`5,711,849
`
`7
`
`temperature. Of course, the selection of temperatures and
`trial numbers depend upon the particular application.
`Extract an activation energy Em. for a first order reaction
`from the data 1((Tz), k(T3) . . . k(T,,) at T2, T3 . . .Tn collected
`via step 109 by way of the following equation:
`
`’Eac:
`
`19(1):“? e RT
`
`The activation energy is preferably calculated by a least
`square fit of data collected at step 109 or any other suitable
`statistical technique. By way of the same equation,
`the
`present method calculates surface reaction rate constant k, at
`any temperature.
`In step 111, a concentration no at the substrate edge is
`calculated The concentration no deduces from the following
`relationship:
`
`Refills/K:
`
`where
`
`R0, is an etch rate.
`From the concentration and the surface reaction rate, the
`particular etching step can be improved by way of adjusting
`selected etching parameters.
`,
`In an alternative specific embodiment, a method to “tune”
`a plasma source using a loading eifect relationship (or
`equation) is illustrated by the simplified flow diagram 200 of
`FIG. 4. The method includes a step 201 of measuring an etch
`rate against an efiective etchable area AW. The effective
`etchable area changes by varying the number m of wafers in
`the reactor, varying the size of the wafer, or the like. The
`effective area can be changed 209 by altering a gap between
`a wafer and its above surface 211, changing wafer quantity
`in the reactor 213, and varying substrate support member
`dimensions 215. The method preferably occurs at constant
`temperature and pressure. However, the effective etchable
`area may also be varied by way of changing a temperature
`and/or a pressure.
`The method calculates a uniformity value (step 217) from
`the measured values of etch rate vs. effective area in steps
`211, 213, and 215. The uniformity is calculated by, for
`example:
`
`10
`
`15
`
`20
`
`25
`
`30
`
`35
`
`uniformity = 100(1 - *
`
`RMAX - RMIN
`m R;
`m
`2.2 —r=1
`
`Where
`
`Rm is a maximum etch rate;
`RM,” is a minimum etch rate;
`In is a sample number;
`R,- is a general etch rate for an ith sample; uniformity is a
`planarity measurement in percentage.
`In a specific embodiment, a uniformity of about 90% and
`greater or preferably 95% and greater indicates that the
`effective area of the substrate is substantially equal to the
`actual substrate area (step 221) via branch 216. Of course,
`other methods of calculating a uniformity from etch rates
`and effective areas may also be used depending upon the
`particular application. Alternatively, an etching profile is
`measured and the effective area Agiis calculated (step 219)
`by way of, e.g., the loading effect relationship.
`At least two and more different effective etchable areas
`(step 223) are measured, or preferably at least three and
`more different etchable areas are measured. Alternatively,
`the flow diagram returns via branch 224 to step 209, and
`
`45
`
`50
`
`55
`
`65
`
`Page 13 of 19
`
`8
`takes another etch rate measurement at a diiferent effective
`area. The flow diagram then turns to step 203.
`In step 203, a supply of etchant ST in the reactor is
`calculated. Based upon the different etchable areas a slope
`mAef deduces from the loading effect relationship as fol-
`lows.
`
`__1__ = .1—
`Ra:(m)
`ksna
`
`k,A,-+F
`=—-—-— +
`k,ST
`
`
`mAzr
`ST
`
`where Ro,(m) is the etching rate at the boundary between the
`plate stack zone and transport zone when m substrates are
`present in the reactor. The first term includes a recombina-
`tion term proportional to the total effective area A, which
`acts to catalyze loss of etchant on reactor surfaces in the
`reactor plus a convection term F. The second term is the
`loading eifect relation, where the reciprocal etch rate is
`proportional to the amount of efiective etchable substrate
`area AeItimes the number of substrates 111. When the etching
`across a substrate is uniform, Aziis the geometrical substrate
`areaAW. When etching is nonuniform, on the other hand, A4.
`is a function of kWJD and geometrical reactor dimensions.
`The supply of etchant ST may be calculated for a different
`plasma source or plasma source parameters such as
`temperature, pressure. or the like by repetition 207 of steps
`201 and 203. By way of the supply of etchant to the reactor,
`other plasma source parameters may be varied to obtain
`desired etching rates and uniformity for the particular reac-
`tor.
`
`Step 205 provides for the modification of chamber mate—
`rials and the like to reduce slope numerator (k,, A,+F) in
`selecting the desired etching conditions. The chamber mate—
`rials can be modified to reduce, for example, the recombi—
`nation rate in the reactor. The recombination rate is directly
`related to the effective reactor recombination area A,. In step
`205, the recombination rate can be adjusted by changing A,
`via changing chamber material, coating chamber surfaces
`with, for example, a product sold under the trademark
`TEFLONTM or KALREZTM and the like, among others.
`Alternatively, the slope numerator flow term F is reduced
`when F contributes as a substantial loss term. Of course, the
`particular materials used depend upon the application.
`In step 207, the method changes plasma source param—
`eters such as rf power, flow rate, and the like to select desired
`etching conditions. Once one of the aforementioned param—
`eters is adjusted, the method returns to step 201 via branch
`208. At step 201, an etch rate vs. effective etchable area is
`measured and the method continues through the steps until
`desired etching condition are achieved Of course, other
`sequences of the aforementioned step for tuning the plasma
`source may