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Flow and reaction simulation of a tungsten CVD reactor
370
Applied Surface Science38 (1989) Y't0-385 North-Holland, Amsterdanl
F L O W AND R E A C T I O N S~IV~.ILATION O F A T U N G S T E N CVD ~ C T O R J.I. U L A C I A F., S. HOWELL, H. K O R N E R * and Ch. W E R N E R Corporate Research and Development (EL P T 33), and * Semiconductor Devices, Siemens AG, 8000 Munich 83, Fed. Rep. of Germany
Received 21 March 1989; accepted for publication l0 April 1989 This work presents the physical and chemical simulation of a tungsten CVD reactor using fluid-dynamicsequations. Numerical results are computed solving for the mass-, chemical-spceies-, momentum- and energy-conservation equations with appropriate boundary conditions in the reactor. The deposition rate at the surface is modeled by kinetically- and ~ transport-bruited regimes that depend on the surface reaction kinetics and diffusivities of the reacting species. The calculation provide~ three-dimensional contours for flow, temperature, pressure, concentrations for various chemical species, and deposition rates as a function of process parameters. In addition, a model for selective-tungsten deposition on silicon has been included to obtain the loss of selectivity as a function of time. I. I n t r ~ u c f i o n To understand the problems and minimize the variabihty of a C V D process, it is necessary to investigate the effect of temperature, flow, pressure, and reaction kinetics on the deposition rate. Process simulation provides a fast and cost-effective alternative because it identifies the physical and chemical environments at the wafer surface, allows optimization for higher deposition rates, and determines the conditions to obtain better uniformity. In addition, it provides visual feedback in space and time on the variables that control the reaction and the effect that equipment settings have on deposition rate [1,2]. The main problems in these simulations are the low pressures used, where the validity of the fluid equations is questionable because the mean free path has the same order of magnitude as the reactor dimensions, and the non-linearity of the surface kinetics. This work presents the two-dimensional flow, temperature, pressuce, and kinetics simulation of a cold-wall tungsten C V D reactor with models that determine the selectivity to silicon dioxide. The results detail the two- and three-dimensional distributions of the previously mentioned variables as a function of space and time. From the kinetic data, it was possible to determine the deposition rates and the concentration profiles for H 2, W F 6, and H F for different operating conditions. 0169-4332/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
J.L Ulacia F. et aL / Flowand reaction simulation of a tungsten CVD reactor
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2. Mathematical model The physical interpretation of a CVD reactor requires the solution of a relatively large set of coupled partial differential equationt. These equations are solved using a finite volume scheme by the program PHOENICS [3] with several modifications to include a more realistic physical description of the gas mixture and the boundary conditions in the reactor. The variables are solved self-consistently until a steady-state solution is reached within are error of less than one percent of the total input and output fluxes in the system. 2.1. Partial differential equations
The simulations are based on the solution of the mass-, chemical-species-, momentum-, and energy-continuity equations. The mass-continuity equation is expressed as ~p a~ + v - ( p ~ ) = o, (1) where p is the density of the media, t is time, and u is the velocity vector. The conservation of chemical species considers the effect of both convection and diffusion for every particle i in the reactor as -~t (pro,) 4- V -(p~,m,) = V °(/), Win,) = G.,
(2)
where m~ is the mass fraction of particle i, D, is the diffusion coefficient, and G, is the generation term in the bulk. Momentum continuity is described by the Navier-Stokes equation as 0 ~-(pu) + v .(puu) = v .(~vu)
0P - 7~, + B + v,
(a)
where Pm is viscosity of the mixture, P is pressure, B is the body force per unit volume, and V represents unit viscous terms in addition to those expressed by/~m" The energy conservation is
~ ( p u ) + v - ( p u ~ ) = v "(~m V T ) + Sh,
(4)
where H is the specific enthalpy that is related to the temperature through heat capacity Cp as d H = C~,dT, ~,,, is the thermal conductivity of the mixture, T is temperature, and S h is the volumetric rate of heat generation. The ideal gas law P-~ p R T closes the equation s~:t and must be included to describe the variations of pressure and veloci,y along the reactor. For the previous equations, the density, viscosity, diffusion coefficients, and heat conduction are a function of temperature and the composition of the mixture [4]. The viscosity is a function of temperature using the Chapman-
372
J.L Ulacia F. et al. / Flowand reaction simulation o/ a tungsten CVD react,r
Enskog theory for the pure compounds and a fonction of composition using the method of Wilke with the Herning and Zipperer approximation. The diffusion coefficients were computed using the Chapman-Enskog theory for two species and Blanc's law for the m/xture only at one composition. The value obtained was used to compute a unique diffusion-Prandtl number that was used in all the simulations. The heat conductivity of pure I12 as a function of temperature was used because there is little information on heat transport properties of W}~.,.A full description of the computatim~ of these variables can be found in the appendix. 2.2. Boundary conditions
For the mass-balance equatioL, the boundary conditions were specified at the inlet with the gas-flow rites for each of the gases fed into the reactor. At the outlet, mass losses for I-I:, HF, and WF6 depend on the relative tool fraction of the gas. The generation of HF at the wafer surface depends or., the reaction stoichiometry imposed as a boundary condition. In the chemical-species equations, the generation terms tJ~ were neglected because there are no reactions in the bulk. The generation of HF and the loss of WF6 at the wafer surface are computed according to the thermal reduction of tungsten hexafluoride and hydrogen through the reaction w ~ ( ~ ) + ~ H:(~) --, w(~) + 6 H~(~) The deposition rat{,' Rw is described by mass-transfer- and reaction-kineticslimited regimes, R d and Rk respectively, through a mechanism that consldcrs a sequential transport and reaction processes as 1
1
Rw
Rd
+
1
Rk "
(5)
In general, the slower mechanism is the one that limits the overall reaction. The mass-transfer-limited regime R d is determined by the maximum possible diffusive flux Ja near the wafer within the first discretization grid point. Here, the concentration of WF6 is given by the diffusion equation and is zero at the wafer surface as Jd 1 N~vt%~. R~ = ~ - p~Z~w~ ,
(6)
where Pw is the density of CVD tungsten, DWF0 is an estimation of the diffusion coefficient of WF6 in H E [4] at the operating conditions, N~vF~is the concentration of WF6 at the first grid center, and 6 is the distance from the cell ('enter cr~ ~'he xvafer The tran~fnrm~llon from rn~q fraefion~ to n~wahor
density is done by N~= m~PNA/Mi, where N A iS Avogadro's number, and M, is the molecular weight of the species.
J.L Ulacia F. et aL / Flow and reaction sinwlatton of a tungsten C VD reactor
373
The kinetics.limited regime is described by an Arrherfius equation proportional to the square root of the partial pressure of H 2 [5,6] as Rk= ko
, .
)
,
(7)
where k0 = 4.08 x 106 nm rain- ~ P a - t/2, the activation energy E~, = 0.75 eV, and k is Boltzmann's constant. For the momentum.balance equation, the velocity is zero parallel and perpendicular to the reactor walls. The initial condition of velocity is calculated self..consistently from the mass-flux at the inlet under steady-state conditions. The energy equation was solved with known ~emperamres at outer walls, which are water cooled, and the wafer holder at the desired deposition temperature. In all the other parts of the reactor, the gas in thermal equilibrium with the walls and the boundaries do not contribute to heat generation or loss. 2. 3. H e a t c o n d u c t i v i t y m o d e l
Because the deposition rate in the kinetics-limited regime depends exponen. tially on the local wafer temperature, the computation of realistic temperature profiles is a key issue for these simulations. In the pres.mre range investigated, it is necessary to account for the reductton of the heat-transport coefficient in the Knudsen-regime because the. wafer is separated by a small gap and has a poor thermal contact with the susceptor. A descriptio~ of the heat transport model can be found in fig. 1. Sm
I
111111111
1
111 11111 Sr~
KGa,
Fi B. 1. Heat sources applied to the wafer, susceptor, and gas. Sm is the incomin 8 heat from the lamps (independent of T), SL i~ the lateral heat loss through mechanical susceptor suspension ar,d i~ ~c.l;,~,;dto ff,c v,,A!",,.,.w,,,,t.,,. ",~, Sra,) to ,,~di,~ti~,.h,;a~ l,.,~ t,J d~ ~,~l;.~,Jq i~ ,.,~.d.,.d..
heat transfer between wafer and susccptor, and Jrad is radiative heat transfer between wafer and susceptor,
J.l. Ulacia F.. et al. / Flow and reaction simulation of a tungsten CVD reactor
374
For a gas, it is possible to identify two distinctive regions for heat conduction as a function of pressure [7]. At high pressures, where the mean-free path of the gas is small ,~'ompared with the distance between the ~vafer and the suseeptor, the heat conductivity is independent of pressure. This is true for 10 Torr and above, and a negligible temperature drop across the gap is calculated. However, at low pressures, the heat conduction is proportion',d to the mean-free path and, therefore, on pressure. The equation that describes the heat-conduction flux Yc in both limits is K m ( T h -- T~) d.4. 2 c ~ , / / p ,
Jq=
(8)
where tcm is heat conductivity of the gas, Th - T~ is the temperature difference between the hot (Th) and cold (To) surfaces, d is distance between the sources, c is proportional to the mean free path, and fl' is a constant of the order of unity, which was adjusted to get good correlation with measurement. This mechanism is important for the conductive and convective heat transfer to the gas that is calculated exactly by solving the full energy conservation equation (eq. (4)) using known heat conductivities for each medium. Radiative heat exchange between wafer and susceptor is considered by the addition of a second heat flux Jrad as J,od
=
c~:( r~ -
r:),
(9)
where Cws is the radiation exchange coefficient (approximately 0.2 for tungsten/graphite), and o is the Stefan-Boltzmann constant. Several heat sources Sr~d were included at the wafer and susceptor open surfaces to account for the energy exchange with cold reactor walls and the heating lamps. In addition, the graphite susceptor has a heat loss through the mechanical support. This loss depends on the temperature difference between the holder and the reactor wall Tw as
sL = A ( r - rw),
(10)
where A is a constant that describes the heat transport efficiency.
2.4. Selectivity model This model only considers the nucleation process and neglects the growth of tungsten nuclei; therefore, the contribution of area coverage caused by the lateral growth of nuclei is not included. The kinetic process is briefly described by the mechanism in fig. 2. In the following description, the exponent in parenthesis for a variable AI) represents the phase as tungsten (W), or silicon dioxide (SLOE), or the gas (g). Here, WF~g) is transported to the surface by convection and diffusion identified by the double arrow labeled (1) in fig. 2. The concentration of WF~g) in the gas is computed from a steady state
37s
Fig. 2. Renction mechnnism for the loss OF selectivity. The double arrows show the main FBBCIIOR path and the letters represent (1) adsorption of WF, on the surface. (2) the chemical reaction to form the tungsten fluorinated compound WF,, (3) fragmentation reaction to form tungsten. (4) dcsorption of Wp’, into the gas. (5) diffusion and convectionin lhe gas ghase.(6) adsorptionof WF, on silicon dioxide. and (7) chemical reaction lo form W on SKI*.
solution at the operating conclitio
most important reactio sumes tlxa! one interme
previously, and
atthesurface
tationprocess, themoael
as-
se nature of thetungsten Com~Q~~~ is ~e~e~~te~ in in thecomputation of the mass- and reticle-1:ontinuity equations. To avoid the kk%ic description for the reduction of Wq and because thereaction is ~~etic~~y bitter by some e&W Q*ep.it will be assumed that the co~~~~t~~tio~ Of the ~~~~~~t on the tungsten is pscportion generated, it &sorbs thro centration on the tungsten on the heatof sub~m~tion. other gaseous species (5X a species-continuity equation with a boun deposition on both tungst I the F~~~rn~~t&posits on tes moee selective tu~~ste~; tungsten, the reaction procee ~is~~o~oetio~~tes creating however, of it deposits in s theme of chnnpaf the tu~~sten nucleates (7). The tungsten area ns a Function o to theB-lltF Of ~~~~~~tio~ on SD,. The equations in ~~~~erne~t with this m~~~Rism are
376
d.I. Ulacia F et aL / Flow and reaction simulation of a tungsten C,teD reactor
~t (pmwF~) + V "(#umwF.) = V "(DwF. VmwF.),
(12)
(siOz)a Iv 0 w +k40sio2], Jwv(0,. t) = -t,.wFywV retw)a + k 2N wF. " s i o : - Ntg) writ,.3
(13)
N~b° ~ = kdm~)~ ,
(14)
Rw=k~N~g°~'Os.o~,. ,
(15)
aOw
at
= k~Rw,
(16)
0w + 0sio~ = 1,
(17)
that represent, the equilibrium of the intermediate from the main reaction through kf, the continuity equation for WF, in the gas, the sublimation and deposition fluxes at the boundary, the adsorption equilibrium of WFx on $iO2 with constant k d, the deposition rate for tungsten nucleates through kw, the rate of selectivity loss by the constant k s, and the conservation of area. In the flux equation (eq. (13)), kt arid k 3 represent the sublimation and deposition of WFx on tungsten respectively and, k2 and k4 shows the same phenomena but on silicon dioxide. In the present computation, k 2 = 0 and K b = k 3 = 1% to simplify the number of fitting parameters. With some algebraic mmipulations of the previous identities, eqs. (13) and (15) reduce to J W F ,•( O , t ) -
O0W at
-- g a N ~( 0) w
- KbNwF (g) ,,
= K c N ~ (1 - 0w),
(18) (19)
where K~ = k t k I and K c = kok~k w. The boundary conditions required to solve eqs. (12) and (19) are, at the wafer interface, eq. (18) and N~g~ W F, ~ I, w , t) = 0
(20)
and the initial conditions are N(g) WFI,~'~ ~ , 0) = 0,
(21)
0 w (0) = O° ,
(22)
where 0 ° is the initial exposed area to be coated selectively. With this model, the reactor has been simulated in two dimensions assuming quasi-equilibrium flow at each timestep so that time dependent terms in eqs. (1)-(4) are neglected and only considered in eq. (19) to calculate the gradual decrease in selectivity. This approximation intrinsically implies that diffusion is a faster process than nucleation.
J.L Ulacia F. et aL / Flow and reaction simulation of a tungsten CFD reactor
377
3. Reactor desc~ptio,a In the reactor simulated, the wafer faces down into the gas flow and is heated from the back side with halogen lamps. The gas is introduced at the bottom of the reactor and is e~tracted at the top through four pumping ports. The relevant chamber dimensions can be observed in fig. 4. The left hand side of the figure presents the axis of symmetry on which the reactor can be mirrored. The gas temperature increases from the inlet (at T~) up to the deposition conditions near the wafer, and decreases to the water-cooled temperature of the walls. The reactor is incorporated in two- and three-dimensional simulation in cylindrical-polar coordinates to take advantage of the symmetry of the problem. From many three-dimensional simulatiors, a uniform flow along the wafer surface was observed, iadicat~'~g fl~at two-dk..~sional simulations are sufficient for future work. Typically the simulation consisted of a couple hundred grid points in 2D and few thousand in 3D. A larger amount of grid lines has been introduced near the wafer because this region contains the largest gradients of temperature and velocity, and is of most interest for deposition.
4. Results The range of conditions simulated are for pressure 0.1-9.0 Ton', for temperature 650-850 K, H2 flow 100-2000 standard cm3 rain-i (seem), and WF6 flow 0-50 seem. The large difference of molecular size and weight from WF6 to H 2 has strong influence on the viscosity of the mixture even at 2 percent composition. This happens because the viscosity of the mixture is scaled by the square root of the ratio of molecular weights, which is a large number for WF6 and a very small number for H 2, and both contributions have the same order of magnitude. Comparing computations that consider the viscous effect for pure H: and those for the mixture as a function of temperature, the velocity field was not greatly modified; however the dynamic pressure was changed substantially as a result of an increase in viscosity. The effect of thermal diffusion has been completely neglected in tiffs computation and should not modify the calculated deposition rates on most of simulated conditions because the reaction is far from being mass-transporb limited and depends only on the partial pressure of H,; howexer, ~he concentration of WF6 should change as a function of position. In most of the simulations, the deposition rate was determined by the kindieally-limited regime, and only entered the mass-transporblimited regime at high temperatures and small flows of WF0. At low pressures, the diffusion flux is larger than the convective flux making the HF concentration on the
378
J.L Ulacia F. et al. / Flow and reaction simulation of a tungsten CVD reactor
Fig. 3. Gas flow vectors inside the CVD reactor. The gas enters the reactor at the bottom and exits at the top through four pumping ports. The flow is laminar even at 2000 sccm.
Fig. 4. Temperature contours inside the CVD reactor. The temperature increases as the gas approaches the hot wafer.
J.L Ulacia F et al. / Flow and reaction simulation of a tungsten CVD reacter
379
Fig. 5. Dynamic pressure inside the CVD reactor. The real pressure is cemputed adding the nominal pressure at the outlet with the dynamic pressure.
Fig. 6, Concentration contours of tun~ten hexafluofide near the wafer. The reaction does not enter into mass-transport-limited conditions near the wafer.
380
J.l. Ulacia F. et al. / Flow and re,,ction simulation of a tungsten CVD reactor
Fig. 7. Concentration contours of hydrogen fluoride near the wafer. The concentration of HF is somewhat independent of total flow rate. wafer independent of the flow rate and only dependent on the deposition rate. At higher pressures, the convective flux is larger than the diffusion flux and the hydrogen fluoride contours depend on the total flow in the reactor. These observations are in agreement with the Peeler number Pc = Q / ( 4 ~ r L D m ) where Q is the total flow, and L is the characteristic reactor dimension, that varies from 10 -5 to 1. From all the simulations performed, a set was selected to illustrate the advantages of using this simulation technique and the value of the data obtained. This analysis shows the two-dimensional results of a blanket deposition at 900 mTorr at 700 E that are comparable to many experimental setups reported in the literature. The gas flow vectors inside the CVD reactor are presented in fig. 3. Here the gas enters with a high velocity and expands in the main body of the reactor near the hot wafer and is cooled at the outlet. The flow was found to be laminar even at 2000 sccm total flow, which is explained by the small Reynolds number in the system (Re < 50). The temperature and dynamic-pressure contours are illustrated in figs. 4 and 5 respectively. The dynamic pressure is the difference between the pressure in any location in the chamber and the outlet (900 mTorr) and is maximum at the inlet port. The pressure gradient is not linear because the viscosity changes as a function of both temperature and
J.]. Ulacia F. et al. / Flow at~d reaction simulation of a tungsten C V D reactor
381
composition. Figs. 6 and 7 illustrate a close up near the wafer for the mol-fraction profiles of W F6 and HF. In this example, the concentration of W F6 at the surface is larger than zero and the reaction is still kinetically limited. The concentration of H F is uniform along the wafer because both, the wafer and the holder, contribute to its generation. The e×perintental and simulated results produced by the heat-conduct;vity model are illustrated in fig. 8 for different pressures. These results also agree with uniformity measurements obtained from deposited wafers; ho~v,ver, the error bars are larger with this teelmique because the results depend on the resistivity of CVD tungsten. Depending on the deposition process, selective or blanket, the concept of selectivity has different meanings, in the first case, low selectivity is undesirable because it destroys the process, while in the second it is a requirement for a fast and uniform coverage. To have a consistent definition for both processes, selectivity S is defined as the reciprocal of the rate of tungsten area coverage with respect to time (reciprocal of eq. (19)) as S = Ot/OOw; therefore, a selective process should have a high value for selectivity, while a blanket process should have a low number. This definition is only valid for wafers with a ,,mgsten-area coverage of less than 0.5 because the value of selectivity increases when 0 w tends to one and considers the problem of time-dependent nucleation because, eventually, even the best selective process becomes nonselective at large deposition times. Analyzing the equations that represent the loss of selectivity, it is observed ti~at generation of nuclei is an auto-catalytic reaction and S is an inverse function of the WF~S); therefore, any additional modification in the process ~ha~ reduces this concentration will increase the overall selectivity. For exam4flO,O
~3 0.3 Ton 460.0 440,0
~ ~ ~
A 0.9 Tort 0 3.0Tort ~ Su~cpior
~I,4;0.0, 3g0.0
1
~..,.,...~ ~ ~ ~
~
O
~
o
~
,
1,0
2,0
3.0
4.0
360.0
3,~0.0
~ 0.0
~ 5,0
6.0
7,0
~.0
9,0
t0.0 I tO;
Position (cm) Fig. 8. Experimental and calculated temperature profiles on the graphite susceptor and the wafer at different pressures.
382
J.l. Ulacia F. et aL / Flow and reaction simulation of a tungsten C V D reactor
pie, to obtain high selectivities, it is desirable to work at the lowest possible partial pressure of \~,F6 without entering the mass-transport-limited regime, and the lowest temperature without compromising deposition rate. The effect of pressure presents a trade-off. On one hand, lower pressures decrease the overall concentration of WF~ g>, but on the other hand, the deposition rate is reduced when the p:~: i.'tl pressure of H 2 decreases and the temperature of the wafer is lower as a ~sult of the smaller heat conduction. The effect of total flow in the system st~ ,uld be regar~,ed with care because at low pressures the transport is dominat~ 1 by diffusion and its effect should not be significant; however, at higher pressures convection dominates and could be used to effectively remove the intermediate. Fig. 9 illustrates the fractional area of tungsten on the wafer as a function of time, for two wafers under identical deposition conditions but with different holder reactivities. Initially, the wafer with the non-reactive holder begins with a one percent tungsten area while the other wafer is pure SiO 2. The maximum coverage line was obtained integrating eq. (19) with the steady-state concentration of ,'WF~ ~r~g) in a fully covered tungsten wafer. It can be seen from thiS figure that the rate of tungsten area increase is much larger for the reactive than the non-reactive holder because WF~ is generated outside the wafer and diffuses inwards creating nucleates. Therefore, a larger rate of coverage means a faster loss of selectivity. For the non-reactive holder, the tungsten area coverage grows exponentially in the early stages. This increase imposes a condition on the initial silicon area to be selectivity coated to a value of 5 to 10 percent maximum. Overall, a wafer with less exposed silicon will have a better selectivity at the end of the process than one with large exposed areas. For the reactive hol~. :r, the radial increase of nucleates on the wafer is
-o L~
"~ u r,~
i.t 1.0 o.9 o.8 o3 0.0 o~ o.4 o3 O.2 O.I
0,0 0.~
0.05
0.10 0.15 0.20 0.25 0.30 ReducedTime (Kc'q) Fig. 9. Fractional area of t ~sten as a function of reduced time. The upper line correspondsto a wafer with a reactiveholdc: hile the lowercurve to a wafer in a non-reactiveholder initiallywith an area coverageol 7e percent. Reducedtime is the product of K d from eq. (19).
J.L Ulacia F.. et al. / Flow and reaction simulation o f a tun,?sten CVD reactor
383
I.l 0.9 0.8 0,51'0~ C.~ 0.7 0.6 .~
0,4
03
.
~
..... ~
.
~
.
~
.
_._ ~..~'""".
_ * 5 Time
t
0.1
0.0 0.0 1.0 2.0 3,0 ,~.0 5,0 6.0 7.0 8.0 9.0 10,0 Radius (cm) Fig. 10, Fraction iI area of tungsten as a function of radius at different deposition times for a blanket deposition. The wafer gets covered from the edge to the center because the intermediate is generated on the reactive holder. non-uniform, starting at the edges and moving to the center. This effect is best illustrated in fig. 10 that shows the fractional area covered by tungsten as a function of radius at 700 I(~ and different deposition times. The rate of radial increase in deposition is a strong function of the diffusion coefficient used for WF~ (lower values produce less uniform films) and on temperature. It should be noted that the tungsten fractional area defined by eq. (19) considers nucleates of all sizes distributed over the surface that contribute to coverage while measured data considers the amount of nuclei of onty one size [9] or the total number of nuclei regardless of their dimension [10]; however, the exponential increase of tungsten deposition is well described by this model. In summary, it can be said that a process is selective if the value of S does not fall below an arbitrary So for a constant value of film thickness d o. Here the process lime must be measured in a constant unit (seconds), the value of do can be assigned to the typical deposition thickness of one nficrometer (1 t~m) while SO depends on the specific requirements (typically 1 < So < 1OO). This definition allows the comparison of different processes and presents a consistent figure of merit. 5. ConeRusions This work characterized the CVD deposition of tungsten by solving several fluid-dynan~c equations that describe this phenomena. This exercise provided a better understanding of the CVE' process, identifying the variables that control the chemical reaction and the way in which their magnitude affect deposition rate and film uniformity. The heat transport model identified the
384
J.l. Ulacia F. et al. / Flowattd reaction simulation of a ttmgsten CVD reactor
main cause for temperature difference5 in the wafer and the susceptor, and a selectivity model predicted the conditions on which higher or lower values of selectivity can be obtained. These results have a strong impact on process optimization and equipment setup to obtain better, faster and more uniform depositions using computer simulation instead of the traditional trial-and-error experimental designs.
Aeknowledgemen~ We would like to acknowledge Ms. C. Wieczorek for providing data on blanket depositions, Mr. U. Seidel for taking the dimensions of the reactor, and Dr. C. Aldham of IKOSS for discussion on how to adapt P H O E N I C S to our needs.
At~endlx The viscosity and the diffusion coefficients are a function of temperature using the C h a p m a n - E n s k o g theory for the pure compound as (23)
5 (~rM, R T ) t/2
#
16
~-o 2,Q~,
'
where M, is the average molecular weight, R is the gas constant, o is the molecular cross section, and Ol, is the collision integral described by 12,, = A ( T * ) - • + C [exp( - D T * )] + E [exp( - F T * )],
(24)
where T* = k T / ~ , A = 1.16145, B = 0.14874, C = 0.52487, D = 0.77320, E = 2.16178, and F = 2.43787. Values for o and c for the different chemical species are found in table 1. Table 1 Lennard-Jones potential values for collision diameter and charact~rstic energy for different molecules determined from viscosity data [4]. Substance H2 HF WF6
o (A) 2.827 3.148 5.210
t / k (K) 59.7 330 338
.LL Ulacia F. et at.. / Flow and eeaction simulation of a tungsten C V D reactor
385
The gas viscosity in the mbtture depends on the composition using the method of Wilke as 5"
Y'/~'
(25)
Z7=139 % '
where y, is the tool fraction in the gas. The Herning and Zipperer appro~dmation is used for q~,j as
¢k,i= ( MI/Mi)I/2 ,=q~;I.
(26)
For the diffusion coefficients, the C h a p m a n - E n s k o g theory predicts
3 (4~rkT/MaB) wz
DaB= ~
N~o~B~,
A,,
(27)
where N is the n u m b e r of molecules in the mixture, oaB = (o a + % ) / 2 , fD iS a correction factor of the order of unity, and MAB is the reduced mass defined as MAn = 2 [ ( 1 / M a ) + (1/MB)]-~. Here the collision integral is repre.~cnted as ~2t~ = A
+
C
E
(T*) z exp(Dr*--------~+ e x p ( F T where T* = kT/¢a~, ~AB = (~a%) 1/2, A =
G + exp(r4T*---------~'
(28)
1.06036, B = 0.15610, C = 0.193@3, D = 0.47635, E = 1.03587, F = 1.52996, G ~ 1.76474, and H = 3.89411. According to Blanc's law, the diffusion coefficient for the mixture becomes
~ ~-' Oim=(j~l.j,iDu )
(29)
that is only valid for dilute mixtures. This equation has been used because hydrogen is the main component in the reaction; nevertheless, the large size and weight of W F 6 compared to H 2 has strong influences. References [l] G. Wahl. Thin Solid Films 40 (1977) 13 [2] G. Wahl and P. Batzies. in: Proc. 4th In;era. Conf. on CVD, 1973. Eds. ,?F. Wakefield and LM. Blocher, p. 425. [3] H.I. Rosten and D.B. Spaldin8, The PHOENICS ~e~inner's Guide (CHAM TR/100, Wimbledon. 1987). [4] R.C. Reid. J.M. prausnitz and B,E. Poilu8, The Properties of Gases and Liquids, 4th ed. (McGraw-Hill. New York. 1986). [5] E,K. Broadbenl and C.L. Rmp,iller. L El¢ctrochem. Soc. 131 (1984) 1427. [6] C.M. McConica and K. Krishnamani. J. Electrochem. Soc. 133 (1986) 2542. [7] J.M. Lafferty. Ed., Scientific Fonndalions of Vacuum Techp,:que, 2nd ed. (Wiley, New York. 1965). [8] J.R. Creighton. J. Electrochem Soc. 136 (1989) 271. [9] C.M. McConica and K. Cooper, J. Electrochem.$oc. 135 (1988) 1003. [10] D.R. Bradbury and T. Kamins. L Electrochem, Soc. 133 (1986) 1214.
Applied Surface Science38 (1989) Y't0-385 North-Holland, Amsterdanl
F L O W AND R E A C T I O N S~IV~.ILATION O F A T U N G S T E N CVD ~ C T O R J.I. U L A C I A F., S. HOWELL, H. K O R N E R * and Ch. W E R N E R Corporate Research and Development (EL P T 33), and * Semiconductor Devices, Siemens AG, 8000 Munich 83, Fed. Rep. of Germany
Received 21 March 1989; accepted for publication l0 April 1989 This work presents the physical and chemical simulation of a tungsten CVD reactor using fluid-dynamicsequations. Numerical results are computed solving for the mass-, chemical-spceies-, momentum- and energy-conservation equations with appropriate boundary conditions in the reactor. The deposition rate at the surface is modeled by kinetically- and ~ transport-bruited regimes that depend on the surface reaction kinetics and diffusivities of the reacting species. The calculation provide~ three-dimensional contours for flow, temperature, pressure, concentrations for various chemical species, and deposition rates as a function of process parameters. In addition, a model for selective-tungsten deposition on silicon has been included to obtain the loss of selectivity as a function of time. I. I n t r ~ u c f i o n To understand the problems and minimize the variabihty of a C V D process, it is necessary to investigate the effect of temperature, flow, pressure, and reaction kinetics on the deposition rate. Process simulation provides a fast and cost-effective alternative because it identifies the physical and chemical environments at the wafer surface, allows optimization for higher deposition rates, and determines the conditions to obtain better uniformity. In addition, it provides visual feedback in space and time on the variables that control the reaction and the effect that equipment settings have on deposition rate [1,2]. The main problems in these simulations are the low pressures used, where the validity of the fluid equations is questionable because the mean free path has the same order of magnitude as the reactor dimensions, and the non-linearity of the surface kinetics. This work presents the two-dimensional flow, temperature, pressuce, and kinetics simulation of a cold-wall tungsten C V D reactor with models that determine the selectivity to silicon dioxide. The results detail the two- and three-dimensional distributions of the previously mentioned variables as a function of space and time. From the kinetic data, it was possible to determine the deposition rates and the concentration profiles for H 2, W F 6, and H F for different operating conditions. 0169-4332/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
J.L Ulacia F. et aL / Flowand reaction simulation of a tungsten CVD reactor
371
2. Mathematical model The physical interpretation of a CVD reactor requires the solution of a relatively large set of coupled partial differential equationt. These equations are solved using a finite volume scheme by the program PHOENICS [3] with several modifications to include a more realistic physical description of the gas mixture and the boundary conditions in the reactor. The variables are solved self-consistently until a steady-state solution is reached within are error of less than one percent of the total input and output fluxes in the system. 2.1. Partial differential equations
The simulations are based on the solution of the mass-, chemical-species-, momentum-, and energy-continuity equations. The mass-continuity equation is expressed as ~p a~ + v - ( p ~ ) = o, (1) where p is the density of the media, t is time, and u is the velocity vector. The conservation of chemical species considers the effect of both convection and diffusion for every particle i in the reactor as -~t (pro,) 4- V -(p~,m,) = V °(/), Win,) = G.,
(2)
where m~ is the mass fraction of particle i, D, is the diffusion coefficient, and G, is the generation term in the bulk. Momentum continuity is described by the Navier-Stokes equation as 0 ~-(pu) + v .(puu) = v .(~vu)
0P - 7~, + B + v,
(a)
where Pm is viscosity of the mixture, P is pressure, B is the body force per unit volume, and V represents unit viscous terms in addition to those expressed by/~m" The energy conservation is
~ ( p u ) + v - ( p u ~ ) = v "(~m V T ) + Sh,
(4)
where H is the specific enthalpy that is related to the temperature through heat capacity Cp as d H = C~,dT, ~,,, is the thermal conductivity of the mixture, T is temperature, and S h is the volumetric rate of heat generation. The ideal gas law P-~ p R T closes the equation s~:t and must be included to describe the variations of pressure and veloci,y along the reactor. For the previous equations, the density, viscosity, diffusion coefficients, and heat conduction are a function of temperature and the composition of the mixture [4]. The viscosity is a function of temperature using the Chapman-
372
J.L Ulacia F. et al. / Flowand reaction simulation o/ a tungsten CVD react,r
Enskog theory for the pure compounds and a fonction of composition using the method of Wilke with the Herning and Zipperer approximation. The diffusion coefficients were computed using the Chapman-Enskog theory for two species and Blanc's law for the m/xture only at one composition. The value obtained was used to compute a unique diffusion-Prandtl number that was used in all the simulations. The heat conductivity of pure I12 as a function of temperature was used because there is little information on heat transport properties of W}~.,.A full description of the computatim~ of these variables can be found in the appendix. 2.2. Boundary conditions
For the mass-balance equatioL, the boundary conditions were specified at the inlet with the gas-flow rites for each of the gases fed into the reactor. At the outlet, mass losses for I-I:, HF, and WF6 depend on the relative tool fraction of the gas. The generation of HF at the wafer surface depends or., the reaction stoichiometry imposed as a boundary condition. In the chemical-species equations, the generation terms tJ~ were neglected because there are no reactions in the bulk. The generation of HF and the loss of WF6 at the wafer surface are computed according to the thermal reduction of tungsten hexafluoride and hydrogen through the reaction w ~ ( ~ ) + ~ H:(~) --, w(~) + 6 H~(~) The deposition rat{,' Rw is described by mass-transfer- and reaction-kineticslimited regimes, R d and Rk respectively, through a mechanism that consldcrs a sequential transport and reaction processes as 1
1
Rw
Rd
+
1
Rk "
(5)
In general, the slower mechanism is the one that limits the overall reaction. The mass-transfer-limited regime R d is determined by the maximum possible diffusive flux Ja near the wafer within the first discretization grid point. Here, the concentration of WF6 is given by the diffusion equation and is zero at the wafer surface as Jd 1 N~vt%~. R~ = ~ - p~Z~w~ ,
(6)
where Pw is the density of CVD tungsten, DWF0 is an estimation of the diffusion coefficient of WF6 in H E [4] at the operating conditions, N~vF~is the concentration of WF6 at the first grid center, and 6 is the distance from the cell ('enter cr~ ~'he xvafer The tran~fnrm~llon from rn~q fraefion~ to n~wahor
density is done by N~= m~PNA/Mi, where N A iS Avogadro's number, and M, is the molecular weight of the species.
J.L Ulacia F. et aL / Flow and reaction sinwlatton of a tungsten C VD reactor
373
The kinetics.limited regime is described by an Arrherfius equation proportional to the square root of the partial pressure of H 2 [5,6] as Rk= ko
, .
)
,
(7)
where k0 = 4.08 x 106 nm rain- ~ P a - t/2, the activation energy E~, = 0.75 eV, and k is Boltzmann's constant. For the momentum.balance equation, the velocity is zero parallel and perpendicular to the reactor walls. The initial condition of velocity is calculated self..consistently from the mass-flux at the inlet under steady-state conditions. The energy equation was solved with known ~emperamres at outer walls, which are water cooled, and the wafer holder at the desired deposition temperature. In all the other parts of the reactor, the gas in thermal equilibrium with the walls and the boundaries do not contribute to heat generation or loss. 2. 3. H e a t c o n d u c t i v i t y m o d e l
Because the deposition rate in the kinetics-limited regime depends exponen. tially on the local wafer temperature, the computation of realistic temperature profiles is a key issue for these simulations. In the pres.mre range investigated, it is necessary to account for the reductton of the heat-transport coefficient in the Knudsen-regime because the. wafer is separated by a small gap and has a poor thermal contact with the susceptor. A descriptio~ of the heat transport model can be found in fig. 1. Sm
I
111111111
1
111 11111 Sr~
KGa,
Fi B. 1. Heat sources applied to the wafer, susceptor, and gas. Sm is the incomin 8 heat from the lamps (independent of T), SL i~ the lateral heat loss through mechanical susceptor suspension ar,d i~ ~c.l;,~,;dto ff,c v,,A!",,.,.w,,,,t.,,. ",~, Sra,) to ,,~di,~ti~,.h,;a~ l,.,~ t,J d~ ~,~l;.~,Jq i~ ,.,~.d.,.d..
heat transfer between wafer and susccptor, and Jrad is radiative heat transfer between wafer and susceptor,
J.l. Ulacia F.. et al. / Flow and reaction simulation of a tungsten CVD reactor
374
For a gas, it is possible to identify two distinctive regions for heat conduction as a function of pressure [7]. At high pressures, where the mean-free path of the gas is small ,~'ompared with the distance between the ~vafer and the suseeptor, the heat conductivity is independent of pressure. This is true for 10 Torr and above, and a negligible temperature drop across the gap is calculated. However, at low pressures, the heat conduction is proportion',d to the mean-free path and, therefore, on pressure. The equation that describes the heat-conduction flux Yc in both limits is K m ( T h -- T~) d.4. 2 c ~ , / / p ,
Jq=
(8)
where tcm is heat conductivity of the gas, Th - T~ is the temperature difference between the hot (Th) and cold (To) surfaces, d is distance between the sources, c is proportional to the mean free path, and fl' is a constant of the order of unity, which was adjusted to get good correlation with measurement. This mechanism is important for the conductive and convective heat transfer to the gas that is calculated exactly by solving the full energy conservation equation (eq. (4)) using known heat conductivities for each medium. Radiative heat exchange between wafer and susceptor is considered by the addition of a second heat flux Jrad as J,od
=
c~:( r~ -
r:),
(9)
where Cws is the radiation exchange coefficient (approximately 0.2 for tungsten/graphite), and o is the Stefan-Boltzmann constant. Several heat sources Sr~d were included at the wafer and susceptor open surfaces to account for the energy exchange with cold reactor walls and the heating lamps. In addition, the graphite susceptor has a heat loss through the mechanical support. This loss depends on the temperature difference between the holder and the reactor wall Tw as
sL = A ( r - rw),
(10)
where A is a constant that describes the heat transport efficiency.
2.4. Selectivity model This model only considers the nucleation process and neglects the growth of tungsten nuclei; therefore, the contribution of area coverage caused by the lateral growth of nuclei is not included. The kinetic process is briefly described by the mechanism in fig. 2. In the following description, the exponent in parenthesis for a variable AI) represents the phase as tungsten (W), or silicon dioxide (SLOE), or the gas (g). Here, WF~g) is transported to the surface by convection and diffusion identified by the double arrow labeled (1) in fig. 2. The concentration of WF~g) in the gas is computed from a steady state
37s
Fig. 2. Renction mechnnism for the loss OF selectivity. The double arrows show the main FBBCIIOR path and the letters represent (1) adsorption of WF, on the surface. (2) the chemical reaction to form the tungsten fluorinated compound WF,, (3) fragmentation reaction to form tungsten. (4) dcsorption of Wp’, into the gas. (5) diffusion and convectionin lhe gas ghase.(6) adsorptionof WF, on silicon dioxide. and (7) chemical reaction lo form W on SKI*.
solution at the operating conclitio
most important reactio sumes tlxa! one interme
previously, and
atthesurface
tationprocess, themoael
as-
se nature of thetungsten Com~Q~~~ is ~e~e~~te~ in in thecomputation of the mass- and reticle-1:ontinuity equations. To avoid the kk%ic description for the reduction of Wq and because thereaction is ~~etic~~y bitter by some e&W Q*ep.it will be assumed that the co~~~~t~~tio~ Of the ~~~~~~t on the tungsten is pscportion generated, it &sorbs thro centration on the tungsten on the heatof sub~m~tion. other gaseous species (5X a species-continuity equation with a boun deposition on both tungst I the F~~~rn~~t&posits on tes moee selective tu~~ste~; tungsten, the reaction procee ~is~~o~oetio~~tes creating however, of it deposits in s theme of chnnpaf the tu~~sten nucleates (7). The tungsten area ns a Function o to theB-lltF Of ~~~~~~tio~ on SD,. The equations in ~~~~erne~t with this m~~~Rism are
376
d.I. Ulacia F et aL / Flow and reaction simulation of a tungsten C,teD reactor
~t (pmwF~) + V "(#umwF.) = V "(DwF. VmwF.),
(12)
(siOz)a Iv 0 w +k40sio2], Jwv(0,. t) = -t,.wFywV retw)a + k 2N wF. " s i o : - Ntg) writ,.3
(13)
N~b° ~ = kdm~)~ ,
(14)
Rw=k~N~g°~'Os.o~,. ,
(15)
aOw
at
= k~Rw,
(16)
0w + 0sio~ = 1,
(17)
that represent, the equilibrium of the intermediate from the main reaction through kf, the continuity equation for WF, in the gas, the sublimation and deposition fluxes at the boundary, the adsorption equilibrium of WFx on $iO2 with constant k d, the deposition rate for tungsten nucleates through kw, the rate of selectivity loss by the constant k s, and the conservation of area. In the flux equation (eq. (13)), kt arid k 3 represent the sublimation and deposition of WFx on tungsten respectively and, k2 and k4 shows the same phenomena but on silicon dioxide. In the present computation, k 2 = 0 and K b = k 3 = 1% to simplify the number of fitting parameters. With some algebraic mmipulations of the previous identities, eqs. (13) and (15) reduce to J W F ,•( O , t ) -
O0W at
-- g a N ~( 0) w
- KbNwF (g) ,,
= K c N ~ (1 - 0w),
(18) (19)
where K~ = k t k I and K c = kok~k w. The boundary conditions required to solve eqs. (12) and (19) are, at the wafer interface, eq. (18) and N~g~ W F, ~ I, w , t) = 0
(20)
and the initial conditions are N(g) WFI,~'~ ~ , 0) = 0,
(21)
0 w (0) = O° ,
(22)
where 0 ° is the initial exposed area to be coated selectively. With this model, the reactor has been simulated in two dimensions assuming quasi-equilibrium flow at each timestep so that time dependent terms in eqs. (1)-(4) are neglected and only considered in eq. (19) to calculate the gradual decrease in selectivity. This approximation intrinsically implies that diffusion is a faster process than nucleation.
J.L Ulacia F. et aL / Flow and reaction simulation of a tungsten CFD reactor
377
3. Reactor desc~ptio,a In the reactor simulated, the wafer faces down into the gas flow and is heated from the back side with halogen lamps. The gas is introduced at the bottom of the reactor and is e~tracted at the top through four pumping ports. The relevant chamber dimensions can be observed in fig. 4. The left hand side of the figure presents the axis of symmetry on which the reactor can be mirrored. The gas temperature increases from the inlet (at T~) up to the deposition conditions near the wafer, and decreases to the water-cooled temperature of the walls. The reactor is incorporated in two- and three-dimensional simulation in cylindrical-polar coordinates to take advantage of the symmetry of the problem. From many three-dimensional simulatiors, a uniform flow along the wafer surface was observed, iadicat~'~g fl~at two-dk..~sional simulations are sufficient for future work. Typically the simulation consisted of a couple hundred grid points in 2D and few thousand in 3D. A larger amount of grid lines has been introduced near the wafer because this region contains the largest gradients of temperature and velocity, and is of most interest for deposition.
4. Results The range of conditions simulated are for pressure 0.1-9.0 Ton', for temperature 650-850 K, H2 flow 100-2000 standard cm3 rain-i (seem), and WF6 flow 0-50 seem. The large difference of molecular size and weight from WF6 to H 2 has strong influence on the viscosity of the mixture even at 2 percent composition. This happens because the viscosity of the mixture is scaled by the square root of the ratio of molecular weights, which is a large number for WF6 and a very small number for H 2, and both contributions have the same order of magnitude. Comparing computations that consider the viscous effect for pure H: and those for the mixture as a function of temperature, the velocity field was not greatly modified; however the dynamic pressure was changed substantially as a result of an increase in viscosity. The effect of thermal diffusion has been completely neglected in tiffs computation and should not modify the calculated deposition rates on most of simulated conditions because the reaction is far from being mass-transporb limited and depends only on the partial pressure of H,; howexer, ~he concentration of WF6 should change as a function of position. In most of the simulations, the deposition rate was determined by the kindieally-limited regime, and only entered the mass-transporblimited regime at high temperatures and small flows of WF0. At low pressures, the diffusion flux is larger than the convective flux making the HF concentration on the
378
J.L Ulacia F. et al. / Flow and reaction simulation of a tungsten CVD reactor
Fig. 3. Gas flow vectors inside the CVD reactor. The gas enters the reactor at the bottom and exits at the top through four pumping ports. The flow is laminar even at 2000 sccm.
Fig. 4. Temperature contours inside the CVD reactor. The temperature increases as the gas approaches the hot wafer.
J.L Ulacia F et al. / Flow and reaction simulation of a tungsten CVD reacter
379
Fig. 5. Dynamic pressure inside the CVD reactor. The real pressure is cemputed adding the nominal pressure at the outlet with the dynamic pressure.
Fig. 6, Concentration contours of tun~ten hexafluofide near the wafer. The reaction does not enter into mass-transport-limited conditions near the wafer.
380
J.l. Ulacia F. et al. / Flow and re,,ction simulation of a tungsten CVD reactor
Fig. 7. Concentration contours of hydrogen fluoride near the wafer. The concentration of HF is somewhat independent of total flow rate. wafer independent of the flow rate and only dependent on the deposition rate. At higher pressures, the convective flux is larger than the diffusion flux and the hydrogen fluoride contours depend on the total flow in the reactor. These observations are in agreement with the Peeler number Pc = Q / ( 4 ~ r L D m ) where Q is the total flow, and L is the characteristic reactor dimension, that varies from 10 -5 to 1. From all the simulations performed, a set was selected to illustrate the advantages of using this simulation technique and the value of the data obtained. This analysis shows the two-dimensional results of a blanket deposition at 900 mTorr at 700 E that are comparable to many experimental setups reported in the literature. The gas flow vectors inside the CVD reactor are presented in fig. 3. Here the gas enters with a high velocity and expands in the main body of the reactor near the hot wafer and is cooled at the outlet. The flow was found to be laminar even at 2000 sccm total flow, which is explained by the small Reynolds number in the system (Re < 50). The temperature and dynamic-pressure contours are illustrated in figs. 4 and 5 respectively. The dynamic pressure is the difference between the pressure in any location in the chamber and the outlet (900 mTorr) and is maximum at the inlet port. The pressure gradient is not linear because the viscosity changes as a function of both temperature and
J.]. Ulacia F. et al. / Flow at~d reaction simulation of a tungsten C V D reactor
381
composition. Figs. 6 and 7 illustrate a close up near the wafer for the mol-fraction profiles of W F6 and HF. In this example, the concentration of W F6 at the surface is larger than zero and the reaction is still kinetically limited. The concentration of H F is uniform along the wafer because both, the wafer and the holder, contribute to its generation. The e×perintental and simulated results produced by the heat-conduct;vity model are illustrated in fig. 8 for different pressures. These results also agree with uniformity measurements obtained from deposited wafers; ho~v,ver, the error bars are larger with this teelmique because the results depend on the resistivity of CVD tungsten. Depending on the deposition process, selective or blanket, the concept of selectivity has different meanings, in the first case, low selectivity is undesirable because it destroys the process, while in the second it is a requirement for a fast and uniform coverage. To have a consistent definition for both processes, selectivity S is defined as the reciprocal of the rate of tungsten area coverage with respect to time (reciprocal of eq. (19)) as S = Ot/OOw; therefore, a selective process should have a high value for selectivity, while a blanket process should have a low number. This definition is only valid for wafers with a ,,mgsten-area coverage of less than 0.5 because the value of selectivity increases when 0 w tends to one and considers the problem of time-dependent nucleation because, eventually, even the best selective process becomes nonselective at large deposition times. Analyzing the equations that represent the loss of selectivity, it is observed ti~at generation of nuclei is an auto-catalytic reaction and S is an inverse function of the WF~S); therefore, any additional modification in the process ~ha~ reduces this concentration will increase the overall selectivity. For exam4flO,O
~3 0.3 Ton 460.0 440,0
~ ~ ~
A 0.9 Tort 0 3.0Tort ~ Su~cpior
~I,4;0.0, 3g0.0
1
~..,.,...~ ~ ~ ~
~
O
~
o
~
,
1,0
2,0
3.0
4.0
360.0
3,~0.0
~ 0.0
~ 5,0
6.0
7,0
~.0
9,0
t0.0 I tO;
Position (cm) Fig. 8. Experimental and calculated temperature profiles on the graphite susceptor and the wafer at different pressures.
382
J.l. Ulacia F. et aL / Flow and reaction simulation of a tungsten C V D reactor
pie, to obtain high selectivities, it is desirable to work at the lowest possible partial pressure of \~,F6 without entering the mass-transport-limited regime, and the lowest temperature without compromising deposition rate. The effect of pressure presents a trade-off. On one hand, lower pressures decrease the overall concentration of WF~ g>, but on the other hand, the deposition rate is reduced when the p:~: i.'tl pressure of H 2 decreases and the temperature of the wafer is lower as a ~sult of the smaller heat conduction. The effect of total flow in the system st~ ,uld be regar~,ed with care because at low pressures the transport is dominat~ 1 by diffusion and its effect should not be significant; however, at higher pressures convection dominates and could be used to effectively remove the intermediate. Fig. 9 illustrates the fractional area of tungsten on the wafer as a function of time, for two wafers under identical deposition conditions but with different holder reactivities. Initially, the wafer with the non-reactive holder begins with a one percent tungsten area while the other wafer is pure SiO 2. The maximum coverage line was obtained integrating eq. (19) with the steady-state concentration of ,'WF~ ~r~g) in a fully covered tungsten wafer. It can be seen from thiS figure that the rate of tungsten area increase is much larger for the reactive than the non-reactive holder because WF~ is generated outside the wafer and diffuses inwards creating nucleates. Therefore, a larger rate of coverage means a faster loss of selectivity. For the non-reactive holder, the tungsten area coverage grows exponentially in the early stages. This increase imposes a condition on the initial silicon area to be selectivity coated to a value of 5 to 10 percent maximum. Overall, a wafer with less exposed silicon will have a better selectivity at the end of the process than one with large exposed areas. For the reactive hol~. :r, the radial increase of nucleates on the wafer is
-o L~
"~ u r,~
i.t 1.0 o.9 o.8 o3 0.0 o~ o.4 o3 O.2 O.I
0,0 0.~
0.05
0.10 0.15 0.20 0.25 0.30 ReducedTime (Kc'q) Fig. 9. Fractional area of t ~sten as a function of reduced time. The upper line correspondsto a wafer with a reactiveholdc: hile the lowercurve to a wafer in a non-reactiveholder initiallywith an area coverageol 7e percent. Reducedtime is the product of K d from eq. (19).
J.L Ulacia F.. et al. / Flow and reaction simulation o f a tun,?sten CVD reactor
383
I.l 0.9 0.8 0,51'0~ C.~ 0.7 0.6 .~
0,4
03
.
~
..... ~
.
~
.
~
.
_._ ~..~'""".
_ * 5 Time
t
0.1
0.0 0.0 1.0 2.0 3,0 ,~.0 5,0 6.0 7.0 8.0 9.0 10,0 Radius (cm) Fig. 10, Fraction iI area of tungsten as a function of radius at different deposition times for a blanket deposition. The wafer gets covered from the edge to the center because the intermediate is generated on the reactive holder. non-uniform, starting at the edges and moving to the center. This effect is best illustrated in fig. 10 that shows the fractional area covered by tungsten as a function of radius at 700 I(~ and different deposition times. The rate of radial increase in deposition is a strong function of the diffusion coefficient used for WF~ (lower values produce less uniform films) and on temperature. It should be noted that the tungsten fractional area defined by eq. (19) considers nucleates of all sizes distributed over the surface that contribute to coverage while measured data considers the amount of nuclei of onty one size [9] or the total number of nuclei regardless of their dimension [10]; however, the exponential increase of tungsten deposition is well described by this model. In summary, it can be said that a process is selective if the value of S does not fall below an arbitrary So for a constant value of film thickness d o. Here the process lime must be measured in a constant unit (seconds), the value of do can be assigned to the typical deposition thickness of one nficrometer (1 t~m) while SO depends on the specific requirements (typically 1 < So < 1OO). This definition allows the comparison of different processes and presents a consistent figure of merit. 5. ConeRusions This work characterized the CVD deposition of tungsten by solving several fluid-dynan~c equations that describe this phenomena. This exercise provided a better understanding of the CVE' process, identifying the variables that control the chemical reaction and the way in which their magnitude affect deposition rate and film uniformity. The heat transport model identified the
384
J.l. Ulacia F. et al. / Flowattd reaction simulation of a ttmgsten CVD reactor
main cause for temperature difference5 in the wafer and the susceptor, and a selectivity model predicted the conditions on which higher or lower values of selectivity can be obtained. These results have a strong impact on process optimization and equipment setup to obtain better, faster and more uniform depositions using computer simulation instead of the traditional trial-and-error experimental designs.
Aeknowledgemen~ We would like to acknowledge Ms. C. Wieczorek for providing data on blanket depositions, Mr. U. Seidel for taking the dimensions of the reactor, and Dr. C. Aldham of IKOSS for discussion on how to adapt P H O E N I C S to our needs.
At~endlx The viscosity and the diffusion coefficients are a function of temperature using the C h a p m a n - E n s k o g theory for the pure compound as (23)
5 (~rM, R T ) t/2
#
16
~-o 2,Q~,
'
where M, is the average molecular weight, R is the gas constant, o is the molecular cross section, and Ol, is the collision integral described by 12,, = A ( T * ) - • + C [exp( - D T * )] + E [exp( - F T * )],
(24)
where T* = k T / ~ , A = 1.16145, B = 0.14874, C = 0.52487, D = 0.77320, E = 2.16178, and F = 2.43787. Values for o and c for the different chemical species are found in table 1. Table 1 Lennard-Jones potential values for collision diameter and charact~rstic energy for different molecules determined from viscosity data [4]. Substance H2 HF WF6
o (A) 2.827 3.148 5.210
t / k (K) 59.7 330 338
.LL Ulacia F. et at.. / Flow and eeaction simulation of a tungsten C V D reactor
385
The gas viscosity in the mbtture depends on the composition using the method of Wilke as 5"
Y'/~'
(25)
Z7=139 % '
where y, is the tool fraction in the gas. The Herning and Zipperer appro~dmation is used for q~,j as
¢k,i= ( MI/Mi)I/2 ,=q~;I.
(26)
For the diffusion coefficients, the C h a p m a n - E n s k o g theory predicts
3 (4~rkT/MaB) wz
DaB= ~
N~o~B~,
A,,
(27)
where N is the n u m b e r of molecules in the mixture, oaB = (o a + % ) / 2 , fD iS a correction factor of the order of unity, and MAB is the reduced mass defined as MAn = 2 [ ( 1 / M a ) + (1/MB)]-~. Here the collision integral is repre.~cnted as ~2t~ = A
+
C
E
(T*) z exp(Dr*--------~+ e x p ( F T where T* = kT/¢a~, ~AB = (~a%) 1/2, A =
G + exp(r4T*---------~'
(28)
1.06036, B = 0.15610, C = 0.193@3, D = 0.47635, E = 1.03587, F = 1.52996, G ~ 1.76474, and H = 3.89411. According to Blanc's law, the diffusion coefficient for the mixture becomes
~ ~-' Oim=(j~l.j,iDu )
(29)
that is only valid for dilute mixtures. This equation has been used because hydrogen is the main component in the reaction; nevertheless, the large size and weight of W F 6 compared to H 2 has strong influences. References [l] G. Wahl. Thin Solid Films 40 (1977) 13 [2] G. Wahl and P. Batzies. in: Proc. 4th In;era. Conf. on CVD, 1973. Eds. ,?F. Wakefield and LM. Blocher, p. 425. [3] H.I. Rosten and D.B. Spaldin8, The PHOENICS ~e~inner's Guide (CHAM TR/100, Wimbledon. 1987). [4] R.C. Reid. J.M. prausnitz and B,E. Poilu8, The Properties of Gases and Liquids, 4th ed. (McGraw-Hill. New York. 1986). [5] E,K. Broadbenl and C.L. Rmp,iller. L El¢ctrochem. Soc. 131 (1984) 1427. [6] C.M. McConica and K. Krishnamani. J. Electrochem. Soc. 133 (1986) 2542. [7] J.M. Lafferty. Ed., Scientific Fonndalions of Vacuum Techp,:que, 2nd ed. (Wiley, New York. 1965). [8] J.R. Creighton. J. Electrochem Soc. 136 (1989) 271. [9] C.M. McConica and K. Cooper, J. Electrochem.$oc. 135 (1988) 1003. [10] D.R. Bradbury and T. Kamins. L Electrochem, Soc. 133 (1986) 1214.