`Flamm et al.
`
`US00571 1849A
`[11] Patent Number:
`[45] Date of Patent:
`
`5,711,849
`Jan. 27, 1998
`
`[54] PROCESS OPTIMIZATION IN GAS PHASE
`DRY ETCHING
`
`[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
`
`[51] Int. (31.6 ............................................... .. H01L 21/3065
`[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;
`216139, 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 DOCUMENTS
`
`3/1980 Holiike .............................. .. 156/6431
`4,192,706
`4,226,665 10/1980 Mogab
`..
`4,243,506
`1/1981 Ikeda et al. ..
`4,297,162 10/1981 Mundt et al.
`156/345 P
`4,340,461
`7/1982 Hendricks et al.
`204/29832
`5,147,520
`9/1992 Bobbio ....... ..
`156/345 P
`5,330,606
`7/1994 Kubota et a1.
`156/6261
`5,399,229
`3/1995 Stefani et a1.
`5,445,709
`8/1995 Kojima et a1. ..................... .. 156/6221
`
`OTHER PUBLICATIONS
`
`Bird et a1., Transport Phenomena, 1960, John Wiley & Sons,
`p. 510.
`Manos, D. M. and Flamm, D. L., Plasma Etchings, An
`Introduction, 1989, Academic Press, (title page and table of
`contents only).
`
`Thompson et al. “Introduction to Microlithography” @ 1983
`ACS pp. 228-235.
`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 al. Plasma Chem. Plasma Process. 10(2) 207-229
`(1990).
`Elliott “Integrated Circuit Fabrication Technology” © 1982
`pp. 242-243 and 258-271.
`
`Manos et a1. “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 ?rst plasma
`etching apparatus 10 having a substrate 21 therein. The
`substrate includes a top surface and a ?lm overlying the top
`surface, and the ?lm having a top ?lm surface. The present
`reactor design method also includes chemical etching the top
`?lm surface to de?ne a pro?le 27 on the ?lm, and de?ning
`etch rate data from the pro?le 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
`
`LAM Exh 1001-pg 1
`
`
`
`US. Patent
`
`Jan. 27, 1998
`
`Sheet 1 of 8
`
`5,711,849
`
`1. -
`
`13
`\
`Plasma
`Generating
`/
`
`h I l l I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I‘
`
`I I I I l l I I I I I I I I I I I l I l I I I I I I I I I I I I I I I I I I I l l l l I I .11
`
`CONCENTRATIONT
`"00
`
`21
`
`/
`”/////////////////////z
`
`FIG. 1A
`
`LAM Exh 1001-pg 2
`
`
`
`U S. Patent
`
`Jan. 27, 1998
`
`Sheet 2 0f 8
`
`5,711,849
`
`x35
`
`LAM Exh 1001-pg 3
`
`
`
`US. Patent
`
`Jan. 27, 1998
`
`Sheet 3 of 8
`
`5,711,849
`
`Measure etch profile [- 100
`Etch film at constant pressure and preferably
`101
`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.
`
`1
`
`/_.1 03
`
`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 sampledlf
`temperature varies it will be average etch rate.
`
`105
`
`
`
`Fit to model with kvO/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: kvO/D and the etch rate at edge of the plate
`or wafer.
`>
`
`107
`
`New temperatures
`in order to get
`
`ks?z), ks(T3) ‘
`
`Calculate D and with
`it kvo & k5
`Calculate D from Chapman-Enskog kinetic theory
`formulas (see R. B. Bird, W. E. Steward, E. N.
`Llghtfoot, pp. 510-513, Transport Phenomena, Wiley
`(1960). Multiply kvo/D by D(T,P) to obtain
`kvo(T,dgap) : ks(T)(AreaNolume)=kS/dgap
`
`/106
`
`1 O8
`f
`
`S
`eparate
`l pre-exp & Ea
`From kS(T1), kS(T2)... do least square fit to
`extract Ea and preexponential where
`_
`_
`_
`ks(-|')=A(T1"2)Ae Ea/kT or, if Ea '5 known,
`just extract preexponential.
`
`‘l 11
`
`/109
`his; EFKBdQZFKVo no to
`._.>
`uce no, t e atom
`concentration at the edge
`of the wafer.
`
`FIG. 3
`
`LAM Exh 1001-pg 4
`
`
`
`US. Patent
`
`Jan. 27, 1998
`
`Sheet 4 of 8
`
`5,711,849
`
`200
`j 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.
`l
`J 209
`Change Aeff
`
`b
`
`I r211
`
`Alter gap (d) between
`waters and surface
`above
`l
`
`J224
`
`218 No
`
`lr 213
`
`Change number of
`waters in the reactor
`
`(-215
`Vary substrate
`(& simultaneously) support
`member dimensions
`
`is uniformity very high
`(>90-95%)?
`
`217
`
`Yes
`
`Measure etching profile
`and compute Aeff
`(loading eqn)
`
`J219
`
`Aeff = A substr
`
`223
`
`Has data for n Aeff values
`been measured? (n2 3)?
`
`Fit to eqn. 5, & from slope
`(m Aeff) obtain HST, the supply of
`etchant from source to the reactor.
`
`l
`
`Modify chamber materials etc. to
`reduce slope of the numerator,
`(kr Ar + F) or reduce flow if F term is
`major etchant loss.
`
`202
`
`f‘ 207
`Try new plasma source or
`plasma source parameters.
`
`FIG. 4
`
`LAM Exh 1001-pg 5
`
`
`
`US. Patent
`
`Jan. 27, 1998
`
`Sheet 5 of 8
`
`5,711,849
`
`Specify required
`uniformity
`
`/ 301 f 300
`
`input predetermined ks or determine
`ks from uniformity measurements at f 303
`one or more temperatures
`
`l
`
`Compute locus of highest T vs. P and /'3O7
`d; and highest P vs. T and d where
`uniformity meets specification.
`
`1
`
`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 f 309
`statistical and experimetnal error and
`process drift. (PO,TO)
`l
`
`311
`
`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.
`4
`Locate intersection space of P<Pi ,T<Ti
`313
`(uniformity manifold) and maximum
`etch rate or etchant supply at selected /
`RF power (flow) values.
`
`J, .
`lt the resulting etch rates are too
`low, change power and/or reduce
`effective etchable area (example: /' 315
`increase d, decrease number of
`substrates).
`
`FIG. 5
`
`LAM Exh 1001-pg 6
`
`
`
`U.S. Patent
`
`Jan. 27, 1998
`
`Sheet 6 0f 8
`
`5,711,849
`
`
`
`1/Ash Rate
`
`0.0008
`
`0. 0007
`
`0.0004
`
`0.0003
`
`Loading Effect Data
`
`// O
`
`/ /
`//
`
`_ 25
`
`30
`
`5
`
`1O
`
`15
`20
`LCD Plates
`
`FIG. 6
`
`1
`: — dgap
`4‘
`
`FIG. 7
`
`FIG. 8
`
`LAM Exh 1001-pg 7
`
`
`
`US. Patent
`
`Jan. 27, 1998
`
`Sheet 7 of 8
`
`5,711,849
`
`150
`1 00
`50
`Radial Distance from the Wafer Center, millimeters
`
`FIG. 9
`
`Z
`
`0 a
`
`dgnw
`.md
`lull Y
`
`x
`
`FIG. 10
`
`Y
`
`Aln
`
`m m
`b .mu
`
`2 I! a
`
`FIG. 11
`
`LAM Exh 1001-pg 8
`
`
`
`US. Patent
`
`Jan. 27, 1998
`
`Sheet 8 of 8
`
`5,711,849
`
`1201
`
`1200
`
`
`
`
`
`Etching Hate, Almin
`
`FIG. 12
`
`LAM Exh 1001-pg 9
`
`
`
`1
`PROCESS OPTIMIZATION IN GAS PHASE
`DRY ETCHING
`
`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 speci?c embodiment, the present inven
`tion also provides a method of designing a reactor. The
`present method includes providing a ?rst plasma etching
`apparatus having a substrate therein. The substrate has a top
`surface and a ?lm overlying the top surface. The ?lm has a
`top ?lm surface. The present method also includes chemi
`cally etching the top ?lm surface to de?ne an etching pro?le
`on the ?lm, and de?ning etch rate data which has an etch rate
`and a spatial coordinate from the etching pro?le. 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 de?ning 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 bene?ts 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 speci?cation and attached drawings.
`
`BRIEF DESCRIPTION OF THE DRAWINGS
`
`FIG. 1 is a simpli?ed diagram of a plasma etching
`apparatus according to the present invention;
`FIG. 1A is a simpli?ed cross-sectional view of a wafer
`pro?le according to the plasma etching apparatus of FIG. 1;
`FIG. 2 is a simpli?ed diagram of an alternative embodi
`ment of a plasma etching apparatus according to the prevent
`invention;
`FIGS. 3-5 are simpli?ed ?ow 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 simpli?ed 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.
`
`DESCRIPTION OF THE SPECIFIC
`EMBODIMENT
`Plasma Etching Apparatus
`FIG. 1 is a simpli?ed 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 de?ned 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
`
`BACKGROUND OF THE INVENTION
`
`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
`?at 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 di?iCUllI-IO 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.
`
`10
`
`25
`
`30
`
`35
`
`45
`
`SUMMARY OF THE INVENTION
`
`According to the present invention, a plasma etching
`method that includes determining a reaction rate coe?icient
`based upon etch pro?le 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, ?ow rate and the like by way of the etch pro?le data.
`In a speci?c 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 ?lm overlying the top surface. The ?lm
`includes a top ?lm surface. The present method also includes
`chemically etching the top ?lm surface to de?ne an etching
`pro?le on the ?lm, and de?ning etch rate data which
`includes an etch rate and a spatial coordinate from the
`etching pro?le. A step of extracting a reaction rate constant
`
`50
`
`55
`
`65
`
`LAM Exh 1001-pg 10
`
`
`
`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 con?ne 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
`oo-axial reactor also relies upon a chemical etch rate which
`is diffusion limited. In particular, the chemical etch rate is
`generally de?ned as a chemical reaction rate of etchant
`species plus at least a di?usion 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 de?ned 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
`de?ned as no(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.
`
`15
`
`25
`
`In a speci?c 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 ?rst order form:
`
`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 ?rst order etching reaction
`can be de?ned as follows:
`
`45
`
`4
`spatial coordinates such as z and r. The substrate includes a
`bottom surface 23, sides 25, and a top surface ?lm 27. As can
`be seen, the top surface ?lm includes a convex region, or
`etching pro?le. The etching pro?le 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 pro?le n,,(r,z) is also shown where the greatest
`concentration of reactant species exists at the outer periph
`ery of the top surface ?lm. In the present invention, an etch
`rate constant may be obtained by correlation to the etching
`pro?le. 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 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 con?guration 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 ?ow 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 ?uorine 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.
`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
`pro?le 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 di?’usion 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
`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 simpli?ed ?ow diagrams of plasma
`etching methods according to the present invention. The
`
`where
`Ra, de?nes a reaction rate;
`no de?nes a concentration;
`A de?nes a reaction rate constant;
`T de?nes a temperature;
`EACT de?nes an activation energy; and
`R de?nes a gas constant. An example of the ?rst 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 de?ned in
`
`55
`
`65
`
`LAM Exh 1001-pg 11
`
`
`
`5
`present methods provide for improved etching conditions by
`way of a reaction rate constant derived from, for example, an
`etching pro?le. It should be noted that the present methods
`as illustrated should not be construed as limiting the inven
`tion as de?ned in the claims. One of ordinary skill in the art
`would easily recognize other applications of the inventions
`described here.
`In a speci?c 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 ?lm is placed into a plasma
`etching apparatus or the like. The overlying ?lm is de?ned
`as an etching ?lm. In the present embodiment, the overlying
`?lm is a photoresist ?lm, but can also be other ?lms such as
`a silicon ?lm, a polysilicon ?lm, silicon nitride, silicon
`oxide, polyimide, and the like.
`A step of plasma etching the ?lm 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 ?lm stops before the
`endpoint (or etch stop). Alternatively, plasma etching stops
`at a ?rst sign of the endpoint (or etch stop). The plasma
`etching step preferably stops before etching into an etch stop
`layer underlying the ?lm to de?ne a “clean” etching pro?le.
`The substrate including etched ?lm is removed from the
`chamber of the plasma etching apparatus. The etched ?lm
`includes an etching pro?le (step 103) made by way of
`plasma etching (step 101). The etching pro?le 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 de?ned as an etch rate at a selected
`spatial coordinate over an etch rate at the substrate edge. The
`relative concentration ratio is de?ned 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 de?ned in the x-y
`coordinates. The etching pro?le 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 de?ned in the r
`and 9 coordinates. The etching pro?le is characterized as a
`relative etch rate u, a r-location, and a B-location (u, r, 9). An
`45
`array of data points in either the x-y coordinates or r-G
`coordinates de?ne the etching pro?le. The array of data
`points can be de?ned 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 pro?le 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 (kW/D) and an etch rate at an edge is calculated at step
`105. The etch constant over di?’usivity correlates with data
`points representing the etch rate pro?le. In x-y coordinates,
`the relationship between kw/D and the relative etch rate
`u(x,y) is often de?ned as follows:
`
`6
`
`Where
`a and b de?ne substrate leng?is in, respectively, an
`x-direction and a y-direction.
`
`"F1 "m
`
`sin’mt
`2
`
`coshNW x]
`cosh [W -3‘-]
`
`+
`
`coshNW y]
`co
`cosh [W %]
`
`In cylindrical coordinates, the relationship between the etch
`constant over di?usivity kva/D and the relative etch rate u(r)
`is de?ned as follows:
`
`where
`a is an outer radius (or edge) of the substrate and I0 is
`modi?ed Bessel function of the ?rst kind.
`In step 106, a di?’usivity is calculated for the particular
`etchants. The binary diffusivity D A B may be calculated based
`upon the well known Chapman-Enskog kinetic theory equa
`tion:
`
`1
`
`1
`
`dawn)
`
`DAB = 2.2646 X 10-5 W
`
`where
`T is a temperature;
`c is a total molar concentration;
`MA and MB are molecular weights;
`D AB is a binary diffusivity;
`on 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 dilfusivity may also be
`used. The equivalent volumetric reaction rate constant kw, is
`derived from the diifusivity as follows.
`
`Once the reaction rate constant kw is extracted, the surface
`reaction rate constant k_v may be isolated from the previous
`equation as follows.
`
`Repeat steps 101-106 at ditferent temperatures T2,
`T3. . . Tn to calculate additional reaction rate constants k(T2),
`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
`
`5,711,849
`
`20
`
`25
`
`30
`
`35
`
`50
`
`55
`
`65
`
`LAM Exh 1001-pg 12
`
`
`
`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 ?rst order reaction
`from the data k(T2), k(T3) . . . k(T,,) at T2, T3 . . .Tn collected
`via step 109 by way of the following equation:
`
`'Eac:
`
`8
`takes another etch rate measurement at a diiferent effective
`area. The ?ow diagram then turns to step 203.
`In step 203, a supply of etchant ST in the reactor is
`calculated. Based upon the diiferent etchable areas a slope
`mAe? deduces from the loading effect relationship as fol
`lows.
`
`_
`l
`l
`Ras(m) m ksno
`
`krAr + F
`
`Mar
`ST
`
`+
`
`15
`
`20
`
`25
`
`The activation energy is preferably calculated by a least
`square ?t 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:
`HERE/K;
`where
`Ros 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 speci?c embodiment, a method to “tune”
`a plasma source using a loading eifect relationship (or
`equation) is illustrated by the simpli?ed ?ow diagram 200 of
`FIG. 4. The method includes a step 201 of measuring an etch
`rate against an effective 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:
`
`35
`
`uniformity = 100m - *
`
`45
`
`where R0,(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 ?rst 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 etfective etchable substrate
`area Aqftimes the number of substrates m. When the etching
`across a substrate is uniform, Aqris 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 modi?cation of chamber mate
`rials and the like to reduce slope numerator (kr, A,+F) in
`selecting the desired etching conditions. The chamber mate
`rials can be modi?ed 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 Ar
`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 ?ow 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, ?ow 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 also exist depending upon the particular appli
`cation.
`FIG. 5 is a simpli?ed ?ow diagram for a method of
`selecting a desired uniformity and desired etching param
`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