Computer simulation of a CF4 plasma etching silicon
`David Edelson and Daniel L. Flamm
`AT&T Bell Laboratories, �Murray Hill, New Jersey 07974
`(Received 28 December 1983; accepted for publication 30 March 1984)
`A CF4 plasma etching silicon has been simulated to identify dominant chemical processes and to
`quantify the effects of various reaction and transport parameters. The model was a one­
`dimensional plug-flow reactor in which a packet of gas is followed through the plasma and into
`the afterglow region, allowing the simulation to be performed as an initial value problem in
`ordinary differential equations. Two temperature zones were used with all known significant
`reactions incorporated into the chemical mechanism with the best available rate constants.
`Adjustable parameters were included only for certain sticking coefficients, surface recombination
`rates, and surface polymerization rates. Appropriate adjustment of these parameters gives
`satisfactory agreement between the simulations and experimental measurements of downstream
`gas-phase composition. The model unambiguously shows that fluorine atoms are the main
`reactive species in the plasma, that gas phase chemistry is clearly dominated by neutral reactions,
`and that formation of surface polymer has a strong effect on the composition of the gas phase. A
`full sensitivity analysis of the mechanism reveals that transport processes, surface chemistry, and
`the formation of fluorocarbon polymer on the walls are among the dominant components of the
`mechanism, but adequate data for these are unavailable. It is concluded that improvements in the
`model will require the inclusion of three-dimensional spatial dependencies and better information
`on surface processes.
`
`I. INTRODUCTION
`At the present time, control of the many factors affect­
`ing plasma processing (e.g., gas composition, pressure, tem­
`perature, discharge frequency, power, reactor geometry, and
`flow pattern) is largely empirical. 1 The chemistry of the plas­
`ma itself is incompletely understood and our knowledge of
`surface interactions is poor. However, we have long held that
`the total description of a process need not be a prerequisite
`for the construction and study of a detailed model, and that
`even in rudimentary form, a model can show the extent to
`which current knowledge is consistent with experiment, and
`can often pinpoint specific gaps which must be filled in order
`to complete the picture. 2
`With this philosophy in mind, we have assembled a de­
`tailed chemical and flow model of a relatively simple plasma
`processing system: CF4 etching silicon. There is a consider­
`able literature on the chemistry of ions and molecular frag­
`ments in this gas, or for analogous compounds from which
`behavior can be extrapolated. By using a simplified flow field
`and parameterizing unknown quantities, a preliminary
`model can be built which shows most features of the real
`system. Sensitivity analysis can then provide information on
`the relative importance of various components of the mecha­
`nism and can indicate the refinements needed to improve the
`model for use in prediction and process control.
`
`II. THE MODEL
`
`A. Flow model
`As a first approximation to the complicated geometry
`and flow pattern of a production plasma reactor, we have
`assumed plug flow in a cylindrical tube. This configuration
`has been used in laboratory studies of plasma chemistry3 and
`to generate reactive species for "downstream etching." A
`cylindrical packet of gas (a "plug") of length .Jx flows axiaJly
`J. Appl. Phys. 56 (5), 1 September 1984
`
`1522
`
`along the tube, and is considered to be well mixed across its
`diameter. The gas enters the plasma region at time 0 and
`exits at time tf =I /v, where I is the length of the plasma
`region and v the flow velocity. Thus time and space coordi­
`nates can be interchanged, and the simulation reduced to an
`initial-value problem in ordinary differential equations with
`time the only independent variable. The space beyond the
`plasma region (the "afterglow") may also be included in the
`computation so that the decay of reactive species toward
`equilibrium is observed downstream.
`The numerical solution is stopped at a time correspond­
`ing to the exit from the plasma region; parameter values are
`reset to those appropriate to the afterglow and the computa­
`tion is resumed. This effectively imposes an abrupt change in
`conditions, especially temperature, at the edge of the plasma
`zone, rather than a gradual transition. However, charged
`species concentrations and electron temperature do in fact
`decay rapidly in this zone and this approximation should be
`good for the present purposes.
`
`B. Plasma model
`The plasma is assumed to be a source of ionization that
`produces electrons and ions in the region according to the
`equation
`CF4---+CF3+ + F +e-.
`( 1)
`Other ions are neglected because CF 3+ is by far the predomi­
`nant ion in CF4 (Refs. 4 and 5) and CF4/02 (Ref. 6) and
`homologous fluorocarbon discharges7 and the mole fraction
`of silicon-containing compounds in the gas phase is low.
`Loss of the charged species proceeds by homogeneous reac­
`tion (e.g., R11, R16) and ambipolar diffusion to the walls,
`and subsequent surface recombination according to reac­
`tions R34-38 in Table I (see Sec. II C); the source intensity is
`adjusted to maintain the plasma density at a preset value.
`
`0021-8979/84/171522-10$02.40
`
`@ 1984 American Institute of Physics
`
`1522
`
`Exhibit 2001
`IPR2017-0392
`
`

`

`U1
`1\) CN
`
`rn <D -a m 3
`
`�
`
`TABLE I. CF4 Plasma etching mechanism.
`
`No.
`
`Reaction
`
`Rate expression
`
`k l'la�mn
`
`ki\ficrglow
`
`Ref.
`
`Flow-7 cm3 min-1
`
`Relative sensitivity ratings
`
`Flow- 25 cm3 min-1
`
`Flow- 70 cm3 min-1
`
`Gas phase reactions
`
`e-+ CF4-+CF3 + F + e-
`2CF r-�C2F ,.( •)
`
`CF3 + F + M-CF4 + M
`
`Parameter
`
`Parameter
`2.002X 10-14T-3.462X 10-n
`
`7.3x 10-32r-1.0334
`
`l.OOX 10-10
`
`3.5ox 10-32
`5.92x w-12
`
`1.30X 1Q4
`t.7ox 10-lo
`5.oox w-9
`t.92x 10-34
`
`T� <0.67 k = 6.0X 10-9
`Te > 0.67 k = 3.27 X 10-9T ,,- 312
`2.92X w-10
`1.2 x w-10T ,�·5(2. + 3.45/T .. )e- 3'451r. 1.81 x w-9
`
`e- + p--F + 2e­
`CFJ-+ + p--CF3 + F
`
`2
`3
`
`4
`
`5
`
`6
`
`7
`
`8
`
`9
`
`10
`11
`
`0.0
`3.5ox w-32
`5.62X w-12
`
`1.66x w-lo
`
`0.0
`
`2.02X 10-H
`
`0.0
`
`6.oox 10-9
`
`0.0
`4.oox 10-7
`
`a
`
`b
`
`b
`
`b
`
`a
`
`c
`
`d
`
`e
`
`d
`f
`
`7
`9
`
`I
`7
`
`8
`4
`
`5
`10
`I
`
`7
`6
`
`6 5 I 10
`8 2
`6 5
`
`10
`10
`1
`9
`5
`I
`I
`5 8
`
`7 8
`6 9
`4
`
`10 9
`1
`8 9
`
`I
`7 8
`2
`6
`8 7
`5 8
`I
`3
`
`10
`10
`3
`5
`
`10
`
`8
`8
`
`7
`
`3 2
`
`5 5
`
`9 8
`6 5
`
`2
`
`7 7
`7 7
`2 2
`
`9
`5
`
`2 9
`9 9
`2 I
`2 I
`7 7
`
`2 7
`3
`6
`
`I
`
`9
`8
`
`5
`
`9
`7
`2
`
`10
`10
`8 8
`
`4
`
`6 5
`7 7
`2 2
`
`9
`6
`
`4
`
`9
`6
`
`7 3
`
`2
`
`F+ p--F2+e-
`p-+ M-F+e- +M
`
`CF3 + F2-+CF4 + F
`
`Estimate based on other systems
`1.4X l0-10e-1.9/T,
`l.l X 10_10e -42'140/(1.16x H,.T,J
`
`Estimate based on similar reactions
`
`Estimate
`
`Heterogeneous reactions
`CF3-CF3(S)
`
`F-F(S)
`
`876 ScF, T0·5 /r
`0.167ro·s /r
`4.17 X w-131JF T0·�
`
`F + Si-SiF(Si)
`
`193.96T�t /r se-
`
`125R017�'1i(Note q)
`
`F + SiF(Si)-SiF2(Si)
`F + SiF2(Si)-SiF3(Si)
`F + SiF3(Si)-SiF.1(Si)
`
`Fast
`Fast
`Fast
`
`4.00X 10-7
`9.73x w-32
`0.0
`3.32x w-12
`5.oox w-lo
`
`g
`h
`
`0.0
`0.0
`
`3.32x w-12
`
`s.oox w-w
`
`4.53x1o-s
`
`9.60x10-7
`
`k
`
`3.26X 101
`
`3.18X 101
`
`3.11
`
`3.69X 10-14
`3.87X 10-IS
`
`3.03
`3.60X 10-14
`
`3.78X 10-IS
`
`46.1
`
`1.00
`1.00
`1.00
`
`0.0
`
`1.00
`1.00
`1.00
`
`m
`
`n
`
`0
`
`12
`13
`14
`
`15
`
`16
`
`17
`
`18
`
`19
`
`20
`
`21
`
`22
`23
`24
`
`7 6
`3
`6
`
`7 7
`6 3
`4 5
`
`10
`
`5 3
`3 I
`
`4 3
`10 5
`7 3
`
`8
`
`6 2
`3 5
`
`5
`6
`10 3
`7 6
`
`10
`
`8 8
`3 4
`
`7 7
`4 2
`3 4
`I
`8
`
`6 7
`3 2
`
`4 4
`8 7
`7
`6
`
`7 6
`3
`
`7
`6
`9
`6
`6 5
`
`10
`
`10
`
`7
`3
`
`5
`4
`6
`
`9
`
`8 9
`4 4
`
`7 7
`2 I
`3 3 1 2
`7
`
`7 4
`4
`
`7 3
`6 10
`
`6
`
`6
`
`3
`
`6
`3
`6
`
`9
`
`9 9
`9 9
`1 1
`1 1 1
`5
`5
`6 2
`5 5
`I
`
`2 7
`2 2
`
`6
`6
`6 5
`5 5
`I
`8
`
`9
`7
`2
`
`7
`4
`
`3
`3
`5
`
`10
`
`�
`
`m a. <D r.n 0 :J Ill :J a. � r
`
`11 Cil 3 3
`�
`U1 1\) CN
`
`Exhibit 2001
`IPR2017-0392
`
`

`

`.... 01 1\) �
`� )> "0 �
`""0 ::r '< J> < l2-01
`
`.m
`z p
`_01
`
`en a> ¥ 3 0"" �
`
`co CXI �
`
`TABLE I. continued .
`
`No.
`
`Reaction
`
`Rate expression
`
`k Jllu.ma
`
`kAfierglL>W
`
`Ref.
`
`Flow-7 cm3 min- 1
`
`C2Ft. F
`
`F2
`
`Relative sensitivity ratings
`
`Flow-25 cm3 min- 1
`
`Flow -70 cmJ min-1
`
`SiF4 C2Fc, F
`
`F1
`
`SiF4 C2Fc, F
`
`F2
`
`SiF4
`
`Surface Reactions
`2F(S)-F2(S)
`CF3(S) + F(S)-CF4(S)
`2CF3(S)-C2F 6(S)
`Desorption
`CF4(S)-CF4
`C2F6(S)-C2F6
`F2(S)-F2
`F(S)-F
`CF2(S)-CF3
`SiF4(Si)-SiF4
`Simulated diffusion
`
`e--e-(S)
`
`Very fast
`
`Parameter
`Parameter
`Parameter
`Parameter
`Parameter
`Parameter
`
`1.oox 1020
`0.0
`0.0
`
`I.OOX 1010
`l.OOX 1010
`l.OOX 1010
`0.0
`0.0
`l.OOX 1010
`
`l.OOX 1020
`0.0
`0.0
`
`l.OOX 1010
`l.OOX 1010
`l.OOX 1010
`0.0
`0.0
`l.OOX 1010
`
`Ambipolar diffusion
`
`3.28X 105
`
`2.44X 103
`
`CF/�F/(S)
`
`Ambipolar diffusion
`
`2.44X 103
`
`25
`26
`27
`
`28
`29
`30
`31
`32
`33
`
`34
`
`35
`
`36
`
`p
`
`p
`
`10
`
`10
`
`10
`
`10
`
`3
`
`10
`
`10
`
`3
`
`7
`
`5
`
`10
`
`10
`
`4
`
`10
`
`10
`
`4
`
`10
`
`10
`
`9
`
`9
`
`/0
`10
`
`10
`
`10
`
`4
`
`p---F-(S)
`
`Ambipolar diffusion
`
`Surface recombination
`
`e-(S) + CF3+(S)-CF3(S)
`CF3(S)-CF2(P) + F(S)
`
`F-(S) + CF3+(S)-CF4(S)
`Polymerization
`
`Very fast
`Very fa'>t
`
`Parameter
`
`3.28X 105
`3.28X H!s
`
`2.44X 103
`
`p
`
`l.OOX 1020
`l.OOX 1020
`
`l.OOX 1020
`l.OOX 1020
`
`l.OOX 102
`
`l.OOX lQl
`
`CF2(P) + F(S)-CF_,(S)
`
`Parameter
`
`0.0
`
`0.0
`
`37
`38
`
`39
`
`40
`
`10
`/0
`2
`
`6
`6
`6
`
`9
`9
`3
`
`3
`
`7
`7
`4
`
`/0
`10
`3
`
`9
`9
`3
`
`9
`9
`4
`
`10
`10
`4
`
`/0
`/0
`I
`
`7
`7
`2
`
`4
`
`9
`9
`4
`
`2
`
`9
`
`10
`
`10
`
`8
`
`10
`
`10
`
`10
`
`9
`
`10
`
`10
`
`10
`
`10
`
`10
`
`10
`
`10
`
`10
`
`10
`
`7
`
`10
`
`/0
`
`10
`
`Note: Sensitivity entries in roman type are for systems with no silicon pres-
`ent. Sensitivity entries in italic type are for systems with silicon present.
`aS. R. Hunter and L. G. Christophorou, J. Chern. Phys. (in press).
`hi Reformulated from M. Rossi and D. M. Golden, Int. J. Chern. Kinet. 11,
`775(1979).
`hl M. Rossi (private communication).
`cl R. K. Boyd and G. Burns, J. Phys. Chern. 83, 88 (1979).
`c2W. D. Breshears and R. F. Bird, J. Chern. Phys. 58, 5176 (1971).
`d J. S. Whittier, M. L. Lundquist, A. Ching, G. E. Thornton, and R. Ho-
`ftand, Jr., J. Appl. Phys. 47, 3542 (1976).
`�1 D. W. Trainor, J. H. Jacob, and M. Rokni, J. Chern. Phys. 72, 3646(1980).
`D. W. Trainor and J. H. Jacob, Appl. Phys. Lett. 35, 920 (1979).
`dB. Schneider and C. Brau, Appl. Phys. Lett. 33, 569 ( 1978).
`n W. L. Nighan and W. J. Wiegand, Phys. Rev. A 10, 992 (1974).
`f2 H. L. Chen, R. E. Center, D. W. Trainor, and W. I. Fyfe, J. Appl. Phys.
`48, 2297 (1977).
`81 A. Mandl, J. Chern. Phys. 64, 903 (1976).
`V. Shui and J. C. Keck, J. Chern. Phys. 59, 5242 (1975).
`•3 A. Mandl, J. Chern. Phys. 59, 3423 (1973).
`
`2
`8
`
`2
`
`�
`
`9
`
`m a. a> fii 0 ::J Q) ::J a. 9 r
`
`"TI ii) 3 3
`
`01 1\) :...
`
`(1979).
`
`hR. Hofland, Jr. and A. Mandl, J. Chern. Phys. 54, 4129(1971).
`i M. J. Rossi, J. R. Barker, and D. M. Golden, J. Chern. Phys. 71, 3722
`il W. L. Nighan and W. J. Wiegand, Phys. Rev. A 10,992 (1974).
`jl V. Cermak, A. Dalgarno, E. E. Ferguson, and L. Friedman, /on-Molecule
`Reactions (Wiley-1 nterscience, New York, 1970).
`k M. A. Biondi, in Principles�� Laser Plasmas, edited by G. Bekefi (Wiley,
`New York, 1976), p. 125ff.
`1 Thermal impact times a sticking coefficient.
`m P. C. Nordine and J.D. LeGrange, AIAA 1. 14, 644(1976).
`" Thermal impact (for F) times fractional coverage.
`''D. L. Flamm, V. M. Donnelly, and J. A. Mucha, J. Appl. Phys. 52,3633
`(1 98 1).
`piS. C. Brown, Introduction to Electrical Discharges in Gases (Wiley, New
`�'2K. P. Suleebka and J.D. Craggs, Vacuum 24,557 (1974).
`York, 1966).
`P3M. S. Naidu and A. N. Prasad, J. Phys. D. 5, 983 (1972).
`q Unirnolecular rate constant, [Si] = 1.
`
`Exhibit 2001
`IPR2017-0392
`
`

`

`Equation ( 1) is not explicitly in the chemistry, but is simulat­
`ed by source and sink terms that maintain electrons and
`CF 3+ ions constant throughout the plasma zone.
`It is implicitly assumed that charged species are main­
`tained by the tail of a high-energy electron energy distribu­
`tion function (Vriens ModelS-10) while electron molecule dis­
`sociation to major neutral radical channels can be attributed
`to electrons distributed about a lower energy. By analogy to
`drift tube Defile data, we assume the that the average energy
`of electrons participating in reactions other than Eq. ( 1) is
`::::::5 eV.
`
`C. Chemistry model
`Inasmuch as possible, the chemistry model is assembled
`from reactions which have been reported in the literature,
`together with others that are assumed to occur by compari­
`son with reactions of homologous compounds. This model is
`given in Table I. Note that diffusion, mentioned below, has
`been reformulated in terms of "chemical'' rate expressions
`for convenience in handling by the BEL LCHEM Simulation
`Program.11
`The chemical reaction rate expressions which are in­
`cluded in Table I are gathered from many sources, as indicat­
`ed in the accompanying references. In some instances these
`do not pertain to the cited reaction, but to a related homolog.
`In other cases, the references may give only a functional
`form for a generic class of reaction to which we have as­
`signed numerical values based on other information. Elec­
`tron temperature is difficult to define in a plasma system and
`the energy distribution function is almost surely non-Max­
`wellian, while the electron-molecule rate expressions may
`come from experiments done under completely unrelated
`conditions. These values have been used nonetheless, since
`the purpose of this work was to see whether such a model,
`however crude, bears any resemblance to real experience.
`The major dissociation channel for CF4 is taken to be
`e + CF4�CF3 + F + e,
`(2)
`2
`proceeds only at
`which, according to Winters and Inokuti, 1
`high electron energies (12.5 eV threshold). However, recent
`data show that the alternative dissociative attachment reac­
`tion
`e + CF4�CF3 + p-
`(3)
`is fast (ka ;::; 10-10 cm
`/sec) at 5-6 eV (Refs. 13 and 14).
`3
`Hence Eq. (3) combined with the rapid detachment reaction
`e+F-�+e+F
`(4)
`is equivalent to R1, Table I, and can proceed at t�e lower
`characteristic electron energies ( ;::::: 5-6 e V) observed in drift
`tube experiments. 15 Dissociation of C2F 6 is assumed to pro­
`ceed similarly and the rate is based on data from Ref. 14. CF2
`and its unsaturated derivatives are neglected as gas phase
`species since small amounts ofCF2 which may be formed by
`dissociation of CF3 (which a posteriori is itself found to be
`present only at very low concentrations in the model) are
`rapidly saturated by the F atoms and F2 which are present. 16
`D. Diffusion model
`Transport of active species from the gas phase to the
`reacting surface is treated as an averaged loss over the entire
`J. Appl. Phys., Vol. 56, No. 5, 1 September 1984
`
`1525
`
`volume. This is derived from the standard solution to the
`'radial diffusion problem 17 and is formulated as a "residence
`time'' (inverse of the rate constant)
`A2
`(s)
`r=n·
`where the "diffusion length" A for the lowest mode of diffu­
`sion is
`A=-r-.
`2.405
`The diffusion constant (cm2 /sec) for charged species is
`estimated from the ambipolar diffusion formula
`
`(6)
`
`(7)
`where Te and T +are the electron and positive ion tempera­
`tures, respectively.18 The diffusion constant for the domi­
`nant positive charge carrier CFt is estimated as
`D+ = 0.00146[T +t75 /p,
`(8)
`where the ion temperature T + is in Kelvin, and the gas pres­
`surep is in torr. The dominant negative charge carrier in the
`plasma is the electron, with a diffusion constant given by
`JL.,kTe
`D .. =---,
`(9)
`e
`where,ue ·is the electron mobility, k is Boltzmann's constant
`and e is the electronic charge. The effective diffusion con­
`(De +A 2ac/Eo)
`stant is given by
`_
`•
`Ds- DA
`DA +A ac/Eo
`2
`The term in parentheses is a conductivity correction term;
`ac = nee(j.L+ + .Ucl
`u0 the plasma conductivity, is given by
`where ,u + is the positive ion mobility, ne the electron den­
`sity, and Eo is the permittivity of free space. Under the condi­
`tions assumed for this study the correction is small and
`DszDA.
`In the afterglow, the same formulation is used, even
`though the simulation shows that negative ions rather than
`electrons may be the predominant negative carrier under
`some conditions. In addition, at the lower densities and tem­
`peratures there may be ch3rge separation and spatially ex­
`tended sheaths may form so that the assumed model is no
`longer applicable. However, the charged species decay
`quickly in this region so that these inaccuracies have little
`effect on the behavior of observable neutral species.
`
`(10)
`
`E. Surface interaction model
`Gas phase species are adsorbed on the inert reactor
`wall, and these adsorbed species can react further with im­
`pinging gaseous species or with other adsorbed species and
`can desorb and return to the gas phase. Rates used for these
`processes are given in Table I. These expressions combine a
`surface adsorption or reaction rate with the radial diffusion
`estimate, and in addition contain a scaling factor that per­
`mits surface concentrations to be expressed as equivalent
`D. Edelson and D. L. Flamm
`
`1525
`
`Exhibit 2001
`IPR2017-0392
`
`

`

`TABLE II. CF4 plasma on silicon; parameters and initial conditions .
`
`Temperature
`
`Ts Tt T,
`Ts;
`
`Plasma
`
`313 K
`453 K
`5.0eV
`500K
`
`Afterglow
`
`2 98 K
`2 98 K
`0.025 eV
`
`·Flow
`Tube radius
`
`1 -8 0 cm3 min-1 (STP)
`0.95 em
`
`Plasma
`
`parameters
`
`Reaction
`
`parameters
`
`Plasma length
`
`5 .0cm
`
`Sampling distance
`5, Si surface fraction
`
`15.0cm
`0.125
`
`ScF,, sticking coefficient 0.002
`
`1/cF,, reaction efficiency 0.001
`
`1/F, reaction efficiency
`
`0.005
`
`Initial conditions
`
`[e]o
`(CFt ]o
`[F]o CF4
`
`l.OOX 1010 cm-3
`l.OOX 1010 cm-3
`
`l.OOX 1010 cm-3
`0.50 Torr
`
`volume concentrations. For reactions that are characterized
`in Table I as "parameter," the rate constant used is an order­
`of-magnitude estimate. Those marked "fast" have been set
`sufficiently high so that they never become the rate limiting
`step in their reaction chain.
`The reactions used to model the silicon etching process
`have been constructed as a sequence of single F -atom pro­
`cesses ultimately resulting in the formation of SiF4 on the
`surface that subsequently desorbs to the gas phase. The first
`F -atom reaction is chosen to be the rate limiting step, in
`order to emulate the published rate of silicon gasification by
`F atoms.1 This makes the process first order in F, maintains
`the proper stoichiometry, and agrees with observation. De­
`sorption of partially fluorinated species has not been includ­
`ed in the model, even though gaseous SiF2 is produced in this
`system. 19•20 Such species would be quickly fluorinated in the
`gas phase19 so that their effect on the overall product yield is
`the same as that of desorbed SiF4• Silicon, when present, was
`assumed to be uniformly distributed along the walls of the
`plasma zone, covering a fraction s of the total surface.
`A computational problem encountered in matching
`wall chemistry with the gas phase flow model is that the gas
`"plug" advances in both space and time, while the wall re­
`mains stationary. In reality, the flowing gas mixture en­
`counters a wall that has previously been exposed to reactive
`gas, and the surface concentrations of adsorbed species are
`determined by this history. This is not serious in the plasma
`region, since the wall species rapidly come to a steady state
`with the gas. However, in preliminary trials the afterglow
`region displayed an anomalous behavior where radicals re­
`combined too rapidly, and continuously removed material
`from the wall. An experimental parallel exists in that a reac­
`tor must be "conditioned" for a certain time before repro­
`ducible data are obtained; this is symptomatic of the buildup
`of adsorbed species concentrations which thereafter remain
`J. Appl. Phys., Vol. 56, No. 5, 1 September 1984
`
`1526
`
`[CF3(S)] =
`
`essentially constant. These effects were modeled by setting
`the concentration for the major wall species, CF3(S), to that
`given by the steady-state relationship between reactions
`R17, R19, and R20 of Table I.
`kl7[CF3]
`kt9[CF3] + k2o[F]
`The concentration of CF3(S) is then constrained to this
`steady-state approximation value at each step of the simula­
`tion. The mass balance error caused by this open system
`model is less than 0.1 %.
`
`(11)
`
`F. Polymerization model
`Under some conditions of operation, a film of highly
`fluorinated organic material is known to form on the surface.
`The model allows for this occurrence and characterizes the
`material as CF2(P). The amount of material removed from
`the system in this way can be adjusted by assigning suitable
`values for the forward and reverse reaction rates correspond­
`ing to this process.
`
`/
`
`Ill. SIMULATION
`The behavior of the model was calculated for the flow,
`pressure, and geometry in the experimental work of Smo­
`linsky and Flamm. 3 The initial conditions and parameters
`selected are given in Table II. Note that temperatures are
`necessarily estimated. The silicon surface temperature T si
`was not measured and may have been much higher than the
`assumed value; for instance, a similar thermally-isolated
`sample in a stream of fluorine atoms was sometimes heated
`to incandescence. 21 The gas phase temperature estimate is
`probably reasonable, but the effective electron temperature
`T ..
`is somewhat uncertain. However, parametric studies
`show that the computation is insensitive to Te because the
`rate of the dissociation reaction, Eq. ( 1), is set by the assumed
`plasma density, and the overall effect of the composite of
`16�------------------------------------�
`15-
`14-
`pt)
`E: 13-
`(,) >- 12-
`� 11 -
`.lcF�
`...,.... """
`010��-·-·��--------�--�----��
`w
`-
`(J) w u 9-w a.. (J) 8-(!) 0 ...J7-
`.,....-·- ............
`6-
`5 _
`ELECTRON-\
`I /
`4�--�AL· ----�� --��----�J----����--· �L-1---J
`- 3
`-5
`-7
`-2
`-4
`-1
`-6
`0
`FIG. 1 . Results of computer simulation of the mechanism of Table I for a
`CF4 plasma with no silicon present. Pressure= 0.5 Torr, flow rate= 24.73
`
`.,...·
`
`/
`
`LOG TIME SEC
`
`cc STP/min.
`
`D. Edelson and D. L. Flamm
`
`1526
`
`Exhibit 2001
`IPR2017-0392
`
`

`

`17
`
`,., I
`E r--------------------------------CF4
`u 16
`>-�
`(/) z w a 15
`(/) w
`(.) w g, 14
`(!) 0 ....J
`
`-6
`
`-5
`
`-4
`
`-3
`
`-2
`
`0
`
`FIG. 2. Results of computer simulation (continued) of the mechanism of
`Table I for a CF4 plasma with no silicon present. Pressure= 0.5 Torr, flow
`rate = 24.73 cc STP /min .
`
`LOG TIME SEC.
`
`18
`
`17
`
`,., I E u 16
`�-------------------------------CF4
`>-�
`(/) z w 15
`a
`(/) � (.) w Q. 14
`(/)
`(!) 0 ....J
`
`----- -CF3 (S)---..._
`
`/
`/
`/
`/
`
`......
`'
`'
`F
`'--
`A---SiF4
`, ,, ...... c F.
`·-· , .. ...... - 2 6
`,,
`/ x"!) •.
`./ �'
`/ /G I
`,,
`\
`.
`/ '/
`,,
`I
`�ti, �
`/
`,,
`i
`,,
`.
`j;..
`\
`.�
`/
`I
`/
`
`-6
`
`-5
`
`-3
`
`-2
`
`-1
`
`0
`
`-4
`LOG TIME SEC.
`FIG. 4. Results of computer simulation (continued) of the mechanism of
`
`Table I for a CF� plasma with silicon present. Pressure= 0.5 Torr, flow
`rate= 27.16 cc STP/min.
`
`13
`
`13
`
`Eqs. (2) and (3), expressed as Rl, is reported to be a weak
`function of electron energy. The plasma density was selected
`so that product yields approximated experimental values,
`and is of the same order of magnitude as that observed in
`several systems. 22-24
`Chemical rate expressions not available from the litera­
`ture were estimated a priori and remain fixed. Sticking coef­
`ficient Si and reaction efficiency 17 parameters, as well as
`
`rates for the polymerization model R39, R40, were chosen
`empirically so that modeling results agree reasonably well
`with experiment. Since there are many remaining uncertain­
`ties in the model, no attempt was made to optimize the fit.
`The parameter selections were made on the basis of experi­
`ments performed in the absence of silicon; this single set of
`
`parameters was then used without change in all simulations
`including those where silicon was present.
`
`IV. BEHAVIOR OF THE MODEL
`
`Species concentrations computed under a typical set of
`conditions, with and without silicon present, are given ver­
`sus time in Figs. 1-4. In Figs. 5-8 concentrations are given as
`linear time t = d lv). While the latter is easier to compare
`a function of lineal·distance along the reactor (equivalent to
`
`with experimental data, the logarithmic plots are more ap­
`propriate for displaying the time scales of the reaction kinet­
`ics.
`
`Since the plasma is constrained to have constant density
`of charged species, the continual dissociation of the feed gas
`
`16�--------------------------------------,
`
`15-
`
`14 1-
`
`'? 13 I­
`
`E u 121->-� u; 11 r­
`z � 10 =-··-
`(/) w 9-u w Q. 8-(/)
`(!) 0 7 -....J
`
`.. / /
`
`/ /
`
`F.:
`
`/ /
`
`........ -·-·�
`
`/
`
`� �
`ELECTRON-�
`
`I
`
`6-
`
`5-
`
`4
`-7
`
`1527
`
`i
`
`-6
`
`I
`-5
`
`\1
`
`I
`-2
`
`0
`
`I
`I
`I
`-1
`-3
`-4
`LOG
`TIME SEC.
`CF4 plasma with silicon present. Pressure= 0.5 Torr, How rate= 27.16
`FIG . 3 . Results of computer simulation of the mechanism of Table I for a
`cc STP/min.
`J. Appl. Phys., Vol. 56, No. 5, 1 September 1984
`
`, ......... -.. -.. --_ .. -.. -··-�-F .. -.. _ .. _.,_.,_ .. _.,_,._, __ ..
`/
`
`15
`
`14
`
`,.,
`
`13
`
`I E (j 12
`>-1-U) 11
`z w a
`(/) w
`(.) w Q. (/)
`(!) 0 ...J
`
`10
`
`9
`
`8
`
`7
`
`6
`
`5
`
`4
`0.00
`
`3.00
`
`12.00
`
`15.00
`
`9.00
`6.00
`DISTANCE em
`FIG. 5. Same results as Fig. I plotted against the longitudinal distance coor­
`
`dinate of the reactor.
`
`D. Edelson and D. L. Flamm
`
`1527
`
`Exhibit 2001
`IPR2017-0392
`
`

`

`18
`
`17
`
`16
`
`15
`
`14
`
`13
`
`.., I E u
`>-1::: U) z w a
`U) w
`u w a.. U)
`
`(!)
`0 _J
`
`�----------------c�------------------�
`
`----------F----------------�
`CF"
`-·-. 3 :��:�<" ........... C2 Fs • ·�·-·�·.··· •••••••••••••••••••••
`\ '
`.---·Fz·
`.... --�.
`..... ___ .�
`'/
`.. ····
`',',
`.....
`...... '
`:
`'c�',,
`!
`.J' ........
`!
`....
`
`.
`12
`0.00
`
`3.00
`
`FIG. 6. Same results as Fig. 2 plotted against the logitudinal distance coor­
`
`dinate of the reactor.
`
`6.00
`9.00
`DISTANCE em
`
`12.00
`
`15.00
`
`18
`
`17
`
`.., I E u 16
`>-� (f) z w a 15
`(f) w
`u w a.. 14
`
`(f)
`(!)
`0
`_J
`
`13
`
`DISTANCE em
`
`FIG. 8. Same results as Fig. 4 plotted against the longitudinal distance coor­
`dinate of the reactor.
`
`CF4 by ionization [Eq. (1)], and by Rl, initially leads to an
`increase in F-atom concentration. Eventually a quasisteady
`state is reached by the balance of this production rate with
`those of various removal processes. R 1 is the predominant
`source of F atoms, contributing at least 75% of those radi­
`cals. The value of this steady state atom concentration de­
`pends strongly on the surface concentration ofCF3 radicals,
`since heterogeneous removal of F atoms by adsorbed CF3( S)
`dominates F-atom loss in the absence of silicon. The gas
`phase concentration ofCF3 in steady state with the adsorbed
`CF3 is governed by the fast two-body removal process, R3-
`R5, which is close to its high pressure limit under the present
`conditions. The rate of this reaction has only recently be­
`come available and it was not recognized that two-body ho­
`mogeneous recombination of this radical could be dorni-
`
`nant. 25 A further ramification of this sequence is that the
`magnitude of the F-atom concentration is sensitive to as­
`sumed values controlling the rates of the heterogeneous
`chemistry ( sticking coefficients S; and reaction efficiencies
`'1/).
`The major stable products formed in this process are F2
`and C2F6, and SiF4 when Si is present. F-atom concentra­
`tions remain high downstream, since recombination to F 2 is
`slow. In the gas phase, CF 3 can dimerize to C2F 6 or react
`with F or F 2 to regenerate the feed CF4• The surface reaction
`parameters again influence this through their effect on gas
`phase densities.
`The rates for polymerization and depolymerization
`control the amount of CF 2(P) removed from the system, and
`thus also the C/F ratio of the gaseous products. Since only a
`few percent of the gas feed is reacted at the simulated resi­
`dence times, formation of polymer has a strong effect on the
`16�------------------------------------�
`composition of the gaseous products. With the parameters
`used in these simulations, less feed is converted to polymer
`than to gaseous products (C2F6, SiF4, F2, F).
`
`15
`
`14
`
`-··- .. - .. -:---.. -- .. --F- . . - .. --.. --··-
`
`V. COMPARISON WITH EXPERIMENT
`
`In Figs. 9-11 the simulations are compared with data
`from Ref. 3. Product mole fractions were calculated at a
`downstream distance corresponding to the location of the
`mass spectrometer sampling orifice.
`Figure 9 compares model and experiments as a function
`of flow rate at constant pressure. The agreement is gratifying
`in that the results are better than order-of-magnitude correct
`and the trends agree with experiment. The yield of F2 is
`somewhat low in relationship to the other products and
`could have been brought into better conformity by adjust­
`ment of parameters, but this is unwarranted because of the
`uncertainties in several rate constants. At very low flow rates
`( $5 seem) the simulation predicts a substantial increase in
`conversion as well as a peak in F-atom mole fraction. This is
`not consistent with the two lowest data points; however it
`
`D. Edelson and D. L. Flamm
`
`1528
`
`6
`
`5
`
`3.00
`
`FIG . 7. Same results as Fig. 3 plotted against the longitudinal distance coor­
`
`6.00
`9.00
`DISTANCE em
`
`12.00
`
`15.00
`
`dinate of the reactor.
`
`1528
`
`J. Appl. Phys., Vol. 56, No.5, 1 September 1984
`
`Exhibit 2001
`IPR2017-0392
`
`

`

`CF4 PLASMA
`
`CF4 PLASMA
`
`5.0
`
`4.0
`
`1--r;j 3.0
`u a:: w 0.
`
`. .
`',
`'
`.
`'
`
`'
`.
`. .
`'
`
`\
`. ' . ' . \ ' '
`
`6
`
`'
`
`'
`
`'
`
`'
`
`6
`
`6
`
`' ... ' ' ' ... ... ' 6" ... ,
`
`.....
`
`6
`....... ..... ...... 6
`...................
`
`6
`
`-···
`
`o F2
`
`5.0
`
`4.0
`
`I-� 3.0 u a:: w (l.
`w ...J � 2.0
`
`1.0
`
`0
`
`0
`
`0
`0
`0
`0.0 �...--. ___ _,__ ___ �-----'---------J
`
`0.0
`
`PRESSURE TORR
`
`1.0
`
`O.OL-----------------------'
`FIG. 1 1. Comparison of simulation results with the experimental data of
`as a function of pressure at a constant flow rate of 13 cc STP /min.
`
`Ref. 3 for a CF4 plasma with no silicon present. The experiments were done
`
`sharp increase in conversion at low flows (conversion against
`flow without Si present were not reported in this latter
`study).
`The simulation at constant flow rate and varying pres­
`sure shows some disagreement with the experimental trends.
`In this case, however, there is serious doubt that the experi­
`ments were done at a constant power input to the plasma and
`there may have been a change in the charge density as pres­
`sure was varied. In fact, recent experimental data23 suggest
`that charge density decreases with increasing pressure at
`constant power. The trends predicted by our model would
`then agree with experiments performed in such a way as to
`maintain a constant charge density over the pressure range.
`Moreover, this data was near the low flow regime and may
`be subject to the experimental error mentioned above.
`
`VI. SENSITIVITY ANALYSIS
`
`Recently sensitivity analysis has become a powerful
`tool for identifying the controlling components of a complex
`chemical mechanism. Originally a tedious and expensive
`procedure, advances have reduced it to a practical and inex­
`pensive aid to reaction simulation in chemical kinetics. 27
`The technique requires evaluation of the derivatives of
`the concentrations c of the ith chemical species at time t to
`the parameters a of the k th rate expression a In c i I ,I a In a k •
`Using the Green's Function Method28 we have evaluated
`these quantities for the observed effluent gas species, at the
`time corresponding to the downstream sampling distance. A
`sensitivity rating for each c; was then assigned to each reac­
`tion by ranking the results in order of decreasing absolute
`sensitivity values, assigning a rating of 10 to the highest, and
`decreasing it by one point for each decrease by half a power
`of I 0 on a logarithmic scale. These ratings are tabulated in
`the rightmost columns of Table I for the systems with (italic
`type) and without (roman type) silicon present. Three differ-
`D. Edelson and D. L. Flamm
`
`1 529
`
`0.0
`
`20.0
`
`60.0
`40.0
`FLOW RATE SCCM
`FIG. 9. Comparison of simulation results with the experimental data of Ref.
`3 for a CF4 plasma with no silicon present. The experiments were done as a
`function of the flow rate of the feed gas, at a constant pressure of0.50 Torr.
`
`may be that the flow rate measurements (using an extreme of
`a rotameter scale) were in error, or that contamination sput­
`tered from the alumina tube ( e.g., oxygen) was significant at
`this low flow