United States Patent
`Flamm et al.
`
`[19]
`
`I IIIII
`
`111111111111111111 IIIII IIIII Ullllllllllllllllll 11111111 1111
`US005711849A
`5,711,849
`[11] Patent Number:
`Jan.27, 1998
`[45] Date of Patent:
`
`[54] PROCESS OPTIMIZATION IN GAS PHASE
`DRY ETCHING
`
`Thompson et al. "Introduction to Microlithography" © 1983
`ACS pp. 228-235.
`
`[75]
`
`Inventors: DanielL. Flamm, 476 Green View Dr.,
`VVrunutcree~ Calif. 94596;JohnP.
`Verboncoeur, Hayward, Calif.
`
`[73] Assignee: Daniel L. Flamm, VVrunut creek, Calif.
`
`[21] Appl. No.: 433,623
`
`May 3, 1995
`
`[22] Filed:
`Int. Cl.6
`................................................. BOlL 21/3065
`[51]
`[52] U.S. Cl ...................................... 156/643.1; 156/625.1;
`156/346 P; 156/626.1; 156/659.11; 156/646.1;
`204/298.31; 204/298.32; 216/58; 216/59
`[58] Field of Search ......................... 204/298.31, 298.32;
`216/39, 58, 74, 79, 246 P, 625.1, 643.1,
`626.1, 646.1, 659.1, 662.1, 659.11
`
`[56]
`
`References Cited
`
`U.S. PATENT DOCUMENfS
`
`4,192,706
`4,226,665
`4,243,506
`4,297,162
`4,340,461
`5,147,520
`5,330,606
`5,399,229
`5,445,709
`
`3/1980 Horiike ................................ 156/643.1
`10/1980 Mogab ................................. 156/643.1
`1/1981 Ikeda et al ........................... 1561345 P
`10/1981 Mundt et al ......................... 1561345 P
`7/1982 Hendricks et al ................... 1561345 P
`9/1992 Bobbio ............................... 204/298.32
`7/1994 Kubota et al ........................ 1561345 P
`3/1995 Stefani et al. ....•..•.••.•...••••••. 156/626.1
`8/1995 Kojima et al. ....................... 156/622.1
`
`aTHER PUBLICATIONS
`
`Bird et al., Transport Phenomena, 1960, John VViley & Sons,
`p. 510.
`Manos, D. M. and Flamm, D. L., Pklsma Etchings, An
`Introduction, 1989, Academic Press, (title page and table of
`contents only).
`
`Giapis et al. Appl. Phys Lett 57(10) 983-985 (Sep. 1990).
`
`Gregus et al. Plasma Chern. Plasma Process. 13(3) 521-537
`(1993).
`
`Babanov et al. Plasma Chern. Plasma Process. 13(1) 37-59
`(1993).
`
`Ha et al. Plasma Chern. Plasma Process. 11(2) 311-321
`(1991).
`
`Rayn et al. Plasma Chern. 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.
`
`Primary Examiner-Martin Angebranndt
`Attorney, Agent, or Firm-Townsend and Townsend and
`crew LLP
`
`[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
`
`s
`
`Page 1 of 19
`
`Samsung Exhibit 1001
`
`

`

`U.S. Patent
`
`Jan.27, 1998
`
`Sheet 1 of 8
`
`5,711,849
`
`17 '-..._Plate
`Stack
`
`10
`
`/
`
`13 "
`
`Plasma
`Generating
`
`F
`
`12
`
`~~
`~"~w
`21
`
`Transport
`~
`15
`
`E
`
`FIG.1
`
`18
`
`8
`
`CONCENTRATION
`
`r
`
`FIG. 1A
`
`Page 2 of 19
`
`

`

`U.S. Patent
`
`Jan. 27, 1998
`
`Sheet 2 of 8
`
`5,711,849
`
`55
`
`53
`
`/·50
`J
`.#./
`
`1
`
`:~lli
`
`1 ~ \ .... :>'·
`. '""·;t.J
`''·-···--::r-·'
`{ r--·MW
`:::::::::::
`6~ I /~"''~"-J ~Ill
`(~, p .,.,\._._ .... J \c.:::::::::::::::::::::::::::::::::::~::::::~:
`~: v,\
`r----... h , 63
`.,
`, ,.
`. E«
`l. /i
`'"<v,,o \.,~
`.,"'!
`!
`... ,
`0A ~~~
`;~ •.>
`
`·.
`
`\
`)
`'•,• ..• , ... ,_,-;/'/.
`/
`f}l
`I
`
`,
`
`,
`
`'-..
`
`'-,
`
`~m~.•n•n:3(9.:•
`
`~
`~
`
`J
`
`6:5
`
`FfGx2
`
`51 i ··~·-·--·­
`HighH:~t
`
`·j(}
`d tnT;1
`....
`• ...... ·}
`
`P. · (·r· hrr)·· 2
`\ ~.· '\ '• .•
`
`240
`
`220
`
`2(}0
`
`TCC)
`
`FIG, SA
`
`Page 3 of 19
`
`

`

`U.S. Patent
`
`Jan. 27, 1998
`
`Sheet 3 of 8
`
`5,711,849
`
`Measure etch profile
`
`,.,r- 100
`
`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.
`
`_____/ 101
`...
`
`.,.---103
`
`Get etch rate profile data as (Etch rate,x,y) or
`{Etch rate, r, a) triads, an n x 3 array where
`n is the number of points sampled.lf
`temperature varies it will be average etch rate.
`
`10~
`
`Fit to model with kv0 /D and
`etch rate as parameters
`
`Run a least squares fit using differences between the
`data array and analytical model for etch rate to
`compute: kv0 /D and the etch rate at edge of the plate
`or wafer.
`
`New temperatures
`in order to get
`ks(T 2). ks(T 3) ...
`
`CalculateD and with
`it kvo & ks
`
`_/106
`
`CalculateD from Chapman-Enskog kinetic theory
`formulas (see R. B. Bird, W. E. Steward, E. N.
`Lightfoot, pp. 510-513, Transport Phenomena, Wiley...._ ______ _.
`(1960). Multiply kv0 /D by D(T,P) to obtain
`kv0 (T,dgap) = ks(T)(AreaNolume)=ksldgap
`
`Separate
`~,. pre-exp & Ea
`From ks(T 1 ), ks(T 2). .. do least square fit to
`extract Ea and preexponential where
`ks(T)=A(T 112)Ae-EalkT Or, if Ea is known,
`just extract preexponential.
`
`109
`
`Use ER(edge)=kvo n0 to
`.,_..., .. M deduce n0 , the atom
`concentration at the edge
`of the wafer.
`
`FIG.3
`
`Page 4 of 19
`
`

`

`U.S. Patent
`
`Jan.27, 1998
`
`Sheet 4 of 8
`
`5,711,849
`
`200
`
`201
`
`)
`
`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 Aett·
`209
`
`ChangeAett
`
`211
`Altergap(d)between
`wafers and surface
`above
`
`213
`
`215
`
`Change number of
`wafers in the reactor
`
`Vary substrate
`(&simultaneously) support
`member dimensions
`
`Yes
`
`208
`
`Fit to eqn. 5, & from slope
`Try new plasma source or
`T
`(m Aett) obtain 1/S , the supply of
`t-----P'tplasma source parameters.
`etch ant from source to the reactor. _j 203
`
`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
`
`

`

`U.S. Patent
`
`Jan. 27, 1998
`
`Sheet 5 of 8
`
`r
`
`uniformity
`
`/
`
`Input predetermined ks or determine
`
`one or more temperatures
`
`5,711,849
`/300
`
`303
`
`Specify required )/301
`..
`ks from uniformity measurements at /
`~
`
`/3
`07
`
`Compute locus of highest T vs. P and
`d; and highest P vs. T and d where
`uniformity meets specification.
`
`l
`values below the calculated manifold v-3
`by a predetermined amount to allow for
`statistical and experimetnal error and
`process drift. (P0 ,T0 )
`~
`Determine max edge etch rate & supply
`of etchant from plasma source (ST) for /3
`11
`
`Specify: uniformity limit manifold. Select
`d values and adjust locus of P and T
`
`09
`
`RF power, flow values and [Pi,Tj](d)
`within uniformity limits manifold.
`
`i
`
`Locate intersection space of P<Pi ,T <Ti
`
`etch rate or etchant supply at selected
`RF power (flow) values.
`
`(uniformity manifold) and maximum /
`i
`
`313
`
`If the resulting etch rates are too
`low, change power and/or reduce
`effective etchable area (example:
`increased, decrease number of
`substrates).
`
`5
`/31
`
`FIG. 5
`
`Page 6 of 19
`
`

`

`U.S. Patent
`
`Jan.27, 1998
`
`Sheet 6 of 8
`
`5,711,849
`
`Loading Effect Data
`v
`
`(~
`
`/
`v
`
`/ v
`
`0.0008
`
`0.0007
`
`2
`~ 0.0006
`.c
`CJ'J
`~ 0.0005
`,.-
`
`0.0004
`
`0.0003
`
`/ vr
`I/
`
`0
`
`5
`
`10
`
`15
`
`20
`
`25
`
`30
`
`LCD Plates
`
`FIG. 6
`
`s
`
`FIG. 7
`
`FIG. 8
`
`Page 7 of 19
`
`

`

`U.S. Patent
`
`Jan.27, 1998
`
`Sheet 7 of 8
`
`5,711,849
`
`1
`
`(fJ
`(fJ
`Q)
`
`0.8
`
`c: 0.9
`0
`(fJ
`c:
`Q)
`E
`0
`0.7
`<li
`1\i 0.6
`a:
`0> c: 0.5
`·a.
`0..
`·;:: 0.4
`.......
`(f)
`"0 0.3
`Q)
`N
`ro 0.2
`E .....
`0
`z
`0.1
`
`0
`
`0
`
`150
`100
`50
`Radial Distance from the Wafer Center, millimeters
`
`FIG. 9
`
`_ld=dgap
`-fd=O
`
`y
`
`b/2
`
`X
`
`X
`
`FIG. 10
`
`-b/2 - - - - -
`a/2
`-a/2
`
`FIG. 11
`
`Page 8 of 19
`
`

`

`U.S. Patent
`
`Jan. 27, 1998
`
`Sheet 8 of 8
`
`5,711,849
`
`1201
`
`(
`
`3000
`
`1209
`
`1200
`
`)
`
`c 2500
`
`E - 2000
`
`o<(
`a)
`-ro 1500
`a:
`Ol c 1000
`E
`u
`iti 500
`
`0
`20
`
`Y-axis em
`
`-1{J
`
`1205
`
`-20
`
`20
`
`x-axis em
`1203
`
`FIG. 12
`
`Page 9 of 19
`
`

`

`5,711,849
`
`1
`PROCESS OPTIMIZATION IN GAS PHASE
`DRY ETCHING
`
`BACKGROUND OF THE INVENTION
`
`2
`from the 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(cid:173)
`tion also provides a method of designing a reactor. The
`5 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(cid:173)
`cally etching the top film surface to define an etching profile
`10 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.
`
`25
`
`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(cid:173)
`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
`fiat 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, 15
`polyimide, 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 20
`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(cid:173)
`nique is obtaining and maintaining etching uniformity
`within selected predetermined limits. In fact, the conven(cid:173)
`tional technique for obtaining and maintaining uniform
`etching relies upon a "trial and error" process. The trial and 30
`error process often cannot anticipate the effects of parameter
`changes for actual wafer production. Accordingly, the con(cid:173)
`ventional technique for obtaining and maintaining etching
`uniformity is often costly, laborious, and difficultto achieve.
`Another limitation with the conventional plasma etching 35
`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 40
`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 45
`etching semiconductor wafers that is easy, reliable, faster,
`predictable, and cost effective is often desired.
`
`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(cid:173)
`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. SA is a plot of uniformity, temperature, pressure, and
`gap for an etching process according to the present inven(cid:173)
`tion;
`FIG. 6 is a simplified plot of i/ash 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.
`
`SUMMARY OF THE INVENITON
`
`50
`
`According to the present invention, a plasma etching
`method that includes determining a reaction rate coefficient
`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 55
`dimensions, temperature, pressure, radio frequency (rl)
`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
`
`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
`60 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
`65 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
`
`Page 10 of 19
`
`

`

`5,711,849
`
`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 5
`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 10
`species plus at least a diffusion 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 descnbed by way of the 15
`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 20
`is often annular, between the plasma generating zone and the
`plate stack zone is defined as no0. As etchant diffuses
`radially from the transport zone into the plate stack zone and
`over surfaces of the substrates, it is consumed by an etching
`reaction. A reactant concentration above the substrate can be 25
`defined as n0 (r,z), where r is the distance from the center of
`the substrate and z is the distance above the substrate. A
`diffusive velocity v o of etchant species in the plate stack
`zone is characterized by Fick' s law.
`
`4
`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(cid:173)
`ent etch rates along the r-direction of the substrate corre(cid:173)
`sponding to different etchant species concentrations. A con-
`centration profile n0 (r,z) is also shown where the greatest
`concentration of reactant species exists at the outer periph(cid:173)
`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(cid:173)
`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 operably 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
`30 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,
`35 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-
`40 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 diffusion effects, rather than direc(cid:173)
`tional bombardment.
`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(cid:173)
`niques. The present invention uses the etching rate constant
`50 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
`55 present invention provides a reaction rate which can be used
`in the design of reactors where diffusion 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 while ion bombardment drives reaction in a ver(cid:173)
`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 different 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
`
`\in,
`v.=-D-(cid:173)
`n.
`
`In a specific embodiment, a gap d8ap above the substrate
`is much less than the lateral extent d8 ap<<r and gas phase
`mass transfer resistance across the small axial distance is
`negligible so that the axial (z-direction) term of the concen(cid:173)
`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---780
`where
`S is a substrate atom (e.g., resist unit ''mer"); and
`0 is the gas-phase etchant (for example oxygen atoms)
`with certain etching kinetics. The first order etching reaction
`can be defined as follows:
`
`45
`
`where
`Ros defines a reaction rate;
`no defines a concentration;
`A defines a reaction rate constant;
`T defines a temperature;
`BACT defines an activation energy; and
`R defines a gas constant An example of the first reaction 60
`is described in D. L. Flamm and D. M. Manos "Plasma
`Etching," (1989), which is hereby inc01porated 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. lA. The substrate 21 is defined in
`
`65
`
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`

`

`5,711,849
`
`6
`
`where
`a and b define substrate lengths in, respectively, an
`x-direction and a y-direction.
`
`cosh[\J k,,, D + (1ttffib 'f
`
`x]
`
`cos~
`
`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(cid:173)
`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 overlying 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 isothermally at
`temperature T 1, but can also be performed with changing 20
`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 25
`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 30
`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 35
`etchant species at a selected spatial coordinate over a con(cid:173)
`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 40 where
`Tis a temperature;
`a relative etch rate u, ax-location, and a y-location u, (x, y).
`c is a total molar concentration;
`In cylindrical coordinates, the relative etch rate is also in the
`MA and MB are molecular weights;
`z-direction, and the spatial coordinates are defined in the r
`and e coordinates. The etching profile is characterized as a
`DAB is a binary diffusivity;
`crAB is a collision diameter; and
`relative etch rate u, a r-location, and a 8-location (u, r, 8). An 45
`QD.AB is a collision integral.
`array of data points in either the x-y coordinates or r-e
`The Chapman-Enskog kinetic theory equation is described
`coordinates define the etching profile. The array of data
`in detail in part Ill of R. B. Bird, W. E. Stewart, and E. N.
`points can be defined as an nx3 array, where n represents the
`Lightfoot, "Transport Phenomena," Wiley (1%0) which is
`number of points sampled and 3 represents the etch rate and
`hereby incorporated by reference for all plll})oses. Of course,
`two spatial dimensions. Of course, the choice of coordinates 50
`other techniques for calculating a diffusivity may also be
`depends upon the particular application.
`used. The equivalent volumetric reaction rate constant k,.0 is
`Optionally, in a non-isothermal condition, an average etch
`derived from the diffusivity as follows.
`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 55
`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 A rate
`constant is appropriately readjusted and the aforementioned
`method is repeated as necessary.
`An etch constant (or a reaction rate constant) over diffu(cid:173)
`sivity (k,.jD) and an etch rate at an edge is calculated at step
`105. The etch constant over diffusivity correlates with data
`points representing the etch rate profile. In x-y coordinates, 65
`the relationship between k,.jD and the relative etch rate
`u(x,y) is often defined as follows:
`
`where
`a is an outer radius (or edge) of the substrate and !0 is
`modified Bessel function of the first kind.
`In step 106, a diffusivity is calculated for the particular
`etchants. The binary diffusivity DAB may be calculated based
`upon the well known Chapman-Enskog kinetic theory equa(cid:173)
`tion:
`
`5 u(x,y) =
`
`l: - 4
`- sin~
`m=1 nm:
`2
`
`10
`
`15
`
`cosh [ \J k,.,,D + (1ttffib)2 n
`
`+
`cosh[\J k,.,,D + (1tt1Tia'f
`cosh [ \J k,.,,D + (1ttffia)2 ~]
`
`y]
`
`m1tX
`cos--
`a
`
`In cylindrical coordinates, the relationship between the etch
`constant over diffusivity k,.jD and the relative etch rate u(r)
`is defined as follows:
`
`u(r)
`
`I.(~ r)
`I.(~~ a)
`
`I T(-1 +-1 )
`~
`MB
`MA
`DAB= 2.2646 X 10-5 - -0,-AB""'2h""'""v.,wC----,,..--
`
`Once the reaction rate constant k,0 is extracted, the surface
`reaction rate constant k.,. may be isolated from the previous
`60 equation as follows.
`
`Repeat steps 101-106 at different temperatures T 2 ,
`T 3 ••• T n to calculate additional reaction rate constants k(f 2),
`k(T 3 ) ••• k(T n). 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
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`

`5,711,849
`
`7
`temperature. Of course, the selection of temperatures and
`trial numbers depend upon the particular application.
`Extract an activation energy Bact for a first order reaction
`from the data k(T 2), k(T 3) ••• k(T ,) at T 2 , T 3 ••• T, collected
`via step 109 by way of the following equation:
`
`8
`takes another etch rate measurement at a different 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
`5 mA'llf deduces from the loading effect relationship as fol(cid:173)
`lows.
`
`mA<if + - -
`sT
`
`where R08(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 Ar which
`acts to catalyze loss of etchant on reactor surfaces in the
`reactor plus a convection term F. The second term is the
`loading effect relation, where the reciprocal etch rate is
`proportional to the amount of effective etchable substrate
`area Aeff times the number of substrates m. When the etching
`across a substrate is uniform, Atffis the geometrical substrate
`areaAw. When etching is nonuniform, on the other hand, AeJf
`is a function of k,jD 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(cid:173)
`rials and the like to reduce slope numerator (k,., Ar+F) in
`selecting the desired etching conditions. The chamber mate(cid:173)
`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 areaAr In step
`205, the recombination rate can be adjusted by changing Ar
`via changing chamber material, coating chamber surfaces
`with, for example, a product sold under the trademark
`TEFLONTM or KALREZ™ 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-
`45 eters such as rf power, flow rate, and the like to select desired
`etching conditions. Once one of the aforementioned param(cid:173)
`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
`50 desired etching condition are achieved. Of course, other
`sequences of the aforementioned step for tuning the plasma
`source may also exist depending upon the particular appli(cid:173)
`cation.
`FIG. 5 is a simplified flow diagram for a method of
`selecting a desired uniformity and desired etching param(cid:173)
`eters within selected ranges to provide a desired etch rate for
`a particular etching process. The etching parameters include
`process variables such as reactor dimensions, a pressure, a
`temperature, and the like for a particular substrate and
`reactants. Other etching parameters may also be used
`depending upon the particular application.
`In step 301, select a uniformity for the selected substrate
`and the reactants. The selected uniformity becomes an upper
`operating limit for the reaction according to the present
`method. The upper operating limit ensures a "worst case"
`uniformity value for an etched substrate according this
`method. Uniformity can be defined by, for example:
`
`The activation energy is preferably calculated by a least 10
`square fit of data collected at step 109 or any other suitable
`statistical technique. By way of the same equation, the
`pr