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A TWO DIMENSIONAL MODEL FOR LPCVD REACTORS HYDRODYNAMICS AND MASS
TRANSFER
C. Vinante, P. Duverneuil, J. Couderc
To cite this version:
C. Vinante, P. Duverneuil, J. Couderc. A TWO DIMENSIONAL MODEL FOR LPCVD REACTORS
HYDRODYNAMICS AND MASS TRANSFER. Journal de Physique Colloques, 1989, 50 (C5), pp.C5-
35-C5-43. �10.1051/jphyscol:1989507�. �jpa-00229530�
A TWO DIMENSIONAL MODEL FOR LPCVD REACTORS HYDRODYNAMICS AND MASS TRANSFER
C. VINANTE, P. DUVERNEUIL and J.P. COUDERC
E.N.S.I.G.C., CNRS UA-192, chemin de la Loge, F-31078 Toulouse Cedex, France
R6sum6.
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Cet article pr6sente un modble bidimensionnel qui analyse, en dbtail, l'hydrodynamique, les ph6nombnes de transport de matyere et de r6actions chimiques au sein des rbacteurs de LPCVD. I1 d6veloppe et discute deux cas particuliers correspondant aux d6p6ts de silicium polycristallin pur et de silicium polycristallin dop6 in situ au phosphore. Les r6sultats mettent en Bvidence la complexit6 des ph6nomtnes impIiqu6s et, tout particulitrement, l'imponance des &actions homogtnes dans la phase gaz.Abstract.
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A two dimensional model analyzing in great details the hydrodynamics, mass transport and chemical reactions inside LPCVD reactors is proposed. Two different applications in the cases of depositions of pure polysilicon a d of phosphorus in situ doDed ~olvsilicon are develo~ed and discussed. The results put in evidence the complex pheiomena involved and,harticularly, the importance of the homogeneous reactions in the gas phase.In spite of a rapid increase of the industrial use of LPCVD reactors, particularly in the microelectronics field, their design and the choice of their operating conditions remain, today, mainly empirical ; of course, this constitutes an approximate, time consuming and, hence, expensive procedure.
However, in the last ten years, a tendency towards a more scientifical engineering analysis developed and a first few mathematical models, able to simulate numerically these equipments, appeared /1,2/. Till, now, the gas flow description in these models has always been very simple, assuming a purely axial convective transport in the annular region between the wall of the reactor and the edge of the wafers and a stagnant zone between two successive wafers. The range of validity of these simulations has been restricted to the simplest cases of deposition of one single element from one pure gas phase, for example the deposition of pure polycrystalline silicon from silane.
This paper presents a new two dimensional model which provides a more detailed and precise description of the hydrodynamical, mass transport and chemical phenomena inside LPCVD reactors. The final results describe accurately the variations of the deposition rate on the wafers and on the hot walls of the reactor.
1. EQUATIONS
The treatment of the problem involves the general hypothesis of isothermicity, constant gas characteristics (density, viscosity and diffusivity), steady state and cylindrical symmetry. The simplified forms of the Navier-Stokes and mass transport equations can then be written as :
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1989507
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avr
avr ap
a2vr 1avr
vrr component, p (vr -
+
vZ -) =-
-+
+-(p -- -
-m az
ar ar2 r ar ,Z + -)+pgr az2avZ avz ap
1avz azVz
z component, p (vr -
+
vZ -) =-
-+
+-(p --
+ -)+pitzar
az az a
r & az21
a ax,
a2xkaxk
axk Rkmass transfer, - Dk [ - - (r -)
+ -1 +
vr ---+
vZ-
--
-r
m m
az2 &az
cFrom a chemical point of view, the two different cases of deposition of pure polysilicon from silane and of in situ phosphorus doped polysilicon from a mixture of silane and phosphine have been considered. The chemical mechanisms invoived by these depositions have been discussed in great details in the literature, for example in /3,4/. For this work, the following system of five different reactions has been selected,
kl
SiH4 I- SiH2 + HZ
.thegas
{
k3phase
SiH4 + Si H2 => k2 Si2H6
t
SiH2+ Si + H2 on the
silicon
{
SiH4+ Si + 2H2surface
Si2H6 + 2Si + 3 H2
The kinetics of these reactions can be found in the literature. For this analysis, the following data have been selected :
3950
For the kg = 7.58
lo6
exp (-
-) m3/mol/s R T5400
k2 = 106.7 exp (-
-
j m3/mol/s RTOn the solid surfaces, reaction (3) has been supposed infinitely rapid and reaction (5) has been neglected. For reaction (4) the following equation has been selected I61
1.6 l g e x P (- 18 500/T).P.xsa4
R4 = mol de ~ i , , m ~ / s .
1
+
60+
70 o O o . P . x ~ ; ~ 4For the boundary conditions, the usual hypotheses of no slip for the velocity and of mass flux equal to the rate of consumption or production by heterogeneous chemical reactions have been used on the solid surfaces.
For the entrance and exit sections of the system (see figure 1) a general hypothesis of stationarity has been adopted. As a consequence the velocity profile has
for the mean silylene concentration, corresponding to different previous gas phase histories, that is to say different conditions upstream in the reactor.
The complete set of equations has been solved using a finite differences method and an implicit Gauss Seidel algorithm.
The geometrical and operating parameters corresponding to the case treated here are indicated on figure 1. The physical properties of gases, density, viscosity and diffusivity have been determined using classical methods /I/.
2. FLOW FIELD
The chemical conversion between two successive wafers remains weak enough to support the hypothesis of a constant volumemc flow rate in the integration region (see figure 1). Hence, the Navier-Stokes equations can be solved independently of the mass transport and chemical reaction phenomena.
The axial and radial velocity components distributions are presented respectively on figures 2 and 3.
It must first be observed that these results are noticeably different from those presented by us at the last european CVD conference, in Jerusalem /8/. The reasons for this disagreement are first the use of a convergence criterium much more severe in the present work and, secondly, a much more realistic hypothesis for the width of the wafers which is no longer supposed negligible (see figure 1).
In the annular region, the axial component profile presents a maximum approximately at mid distance between the reactor wall and the wafer edge while the radial component remains quite everywhere negligible (care must be taken of the scale changes in figure 3).
Just immediately at the wafer edge level, the radial component takes non negligible values, corresponding to an important .entrance flow fate between two successive wafers. iust immediatelv downstream the first wafer, and to the corresponding exit flow-rate upstre&of the second wafer. These radial movements decrease in intensity very rapidly when the radial coordinate decreases.
It can be observed that the hypothesis of a purely axial movement in the annular region and'of a motionless gas in the interwafers space, which are generally used in simplified models are not very far from the real situation. The most important difference appears in the wafers edge region ; unfortunately this is the region where particular phenomena are often observed (see, in the following, the case of the deposition of in situ phosphorus doped polysilicon which results in the famous bull's eye effect).
3. CONCENTRATION DISTRIBUTION AND DEPOSITION RATE PROFILE FOR THE CASE OF PURE POLYSILICON
The model provides a very great number of informations which will not all be described and discussed here in details.
For concentrations distributions, it can be said, first, that silane remains approximately constant everywhere in the system. The slight variations which have been observed can be neglected in the calculation of the deposition rate.
Hydrogen and disilane demonstrate more important and interesting variations. By lack of place, they willnot be discussed here.
In fact, we consider only the distribution of silylene, by far the most significant for LPCVD purposes. Radial and axial profrtes are presented on figures 4, 5, 6 and 7, for two entrance concentration conditions for silylene, namely x = 7.4.10-~ for figures 4 and 5, which represents approximate1 the equilibrium condition for these temperature and pressure, then x = 1.4.107{ approximately 5 times less for figures 6 and 7.
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All these figures demonstrate clearly the existence of variations in silylene concentration, from high values in the annular region to much lower values in the interwafers space, with a transition region just at the edge of the wafers. From a qualitative point of view, these variations can be linked to differences in the ratio A/V of the deposition surface area A to the volume of gas V. In the annular region, where A/V is low, the gas phase silylene production overcomes its surface consumption : the resulting equilibrium concentration is high. On the contrary, in the interwafers regions, where A/V is high, the consumption overcomes the production, resulting in a weak equilibrium concentration value.
Figures 8 and 9 show the radial variations of the film growth rate on the wafer. It appears clearly that silane constitutes the major reactant ; its concentration in the system being quite perfectly uniform, a constant film growth rate results on the major part of the wafer. However, the contribution of silylene produces an increase of the growth rate in the wafer edge region, important when the entrance conentration of silylene is high (fig. 8) and weaker in the other case (fig. 9).
An example of the growth rate dismbution on the hot wall of the reactor is presented on figure 10 : the deposition rate decreases from the entrance to the exit. It must be observed that the role played by silylene in this high concentration region is much more important than for the deposition on the wafer. As a consequence, the growth rate is higher on the reactor wall than on the wafer ; the difference will decrease with the entrance silylene concentration.
From a scientifical point of view, it is interesting to observe, on figure 11 the particular phenomena at the edge and on the width of the wafer which, to our knowledge, are presented for the first time..
From an engineering point of view, it is necessary to add that the deposition rates calculated with this two dimensional model are in close agreement with the results obtained with simpler previous models and with experimental data /I/.
4. CONCENTRATION DISTRIBUTION AND DEPOSITION RATE PROFILE FOR THE CASE OF IN SITU PHOSPHORUS DOPED POLYSILICON
When even a very small fraction of phosphine is added to silane, many troublesome phenomena appear suddenly. They have been discussed in &tail in the literature 191. It is useful, here, to recall only that
1
-
the growth rate is markedly decreased2
-
radial heterogeneities appear producing the so called bull's eye deposit organization.The main reason for these changes is that phosphine adsorbs preferentially on the silicon surfaces and inhibits quite completely reaction 4, of deposition from silane
.
The exact inhibiting action being still unknown, it has been arbitrarily decided to model the case of complete inhibition for which reaction 4 is completely suppressed. Deposition is then only produced by silylene adsorption and reaction.The silylene concentration distributions are not presented here. They are approximately similar to the one corresponding to pure polysilicon.
The growth rates, on the contrary, are markedly decreased, the main deposition mechanism, from silane, being now suppressed. At the same time, the radial variations due to the silylene concenkation h;&rogeneities become much more abrupt, producing the famous bull's eye configuration (see figures 12 and 13).
Figure 14 presents the growth rate variations on the reactor hot wall and figure 15 the results at the wafer edge.
From a scientific point of view, it is interesting to observe that the model reproduces numerically the particular characteristics that have been experimentally observed in the deposition of phosphorus in situ doped polysilicon. From an engineering point of view, additional data on the inhibition effect by phosphine would be necessary to become able to predict accurately the exact value of the growth rate.
the entrance concentration of silylene (the exact value of which is qnknown).
5. COMMENTS
The results presented in this paper are the first few obtained with the new two dimensional model which is under development in our laboratory.
Nevertheless, it is yet perfectly clear that, from a scientific point of view, it provides a much more detailed and precise description of the complex phenomena involved in a LPCVD process than previously. In particular, it demonstrates the importance of gas phase reactions and their tight connection with the gas flow structure, This model will, undoubtedly, be of help to explain many of the complex facts that have been observed experimentally.
From a practical point of view, this model can and will be used to design new and more efficient industrial reactors, first in the difficult case of in situ phosphorus doped polysilicon, then for boron doped, polysilicon, low temperature oxide, Sipos or other deposition cases of practical interest.
The corresponding economical goals seem of sufficient importance and the first results presented here encouraging enough to support the development of additional researches in that general field of the detailed modeling-of LPCVD equipments.
SYMBOLS concentration mass diffusivity pressure
acceleration of gravity radial coordinate
volumetric rate of consumption (or production) in the gas phase temperature
velocity molar fraction axial coordinate REFERENCES
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f 3
3 2 %
"b
P )oe c c
,
I
I V
J 3
Axial and radial distributions of silylene molar fraction: figs 4 and 6 for the annular region, figs 5 and 7 for interwafers spac
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PolysDkon film growth rate : figs 8 and 9 on a wafer, fig 10 on the reactor hot wall and fig 11 on the wafer edg
