Gas-to-Particle Conversion Mechanism in Chemical Vapor Deposition

A gas-to-particle conversion mechanism is proposed for producing silicon carbide ultrafine particles by a SiH4/C2H2 chemical vapor deposition reaction...
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Ind. Eng. Chem. Res. 1998, 37, 3602-3609

MATERIALS AND INTERFACES Gas-to-Particle Conversion Mechanism in Chemical Vapor Deposition of Silicon Carbide by SiH4 and C2H2 Lu-Sheng Hong* and Zh-Liang Liu Department of Chemical Engineering, National Taiwan University of Science and Technology, 43 Keelung Road, Section 4, Taipei 10672, Taiwan

A gas-to-particle conversion mechanism is proposed for producing silicon carbide ultrafine particles by a SiH4/C2H2 chemical vapor deposition reaction system. The reaction was performed in a horizontal hot-wall tubular reactor at a temperature range of 1123-1373 K, where SiC was formed as an aerosol in the gas phase and deposited to form porous SiC films. An analysis of the deposition growth rate profile along the longitudinal direction of the reactor shows that the depositing process is controlled by a gas-phase reaction with an activation of 23 kcal/mol. Also, the composition ratio of carbon to silicon of the deposited films was found to change gradually from 1 at the inlet of the reactor to 2 downstream. The results imply that a gaseous polymerization reaction between C2H2 and SiH2 plays an important role in the formation of the particles. Introduction Chemical vapor deposition (CVD) is one of the most important techniques for preparation of particles with size in the range of nanometers. CVD has the advantage because it starts from gaseous molecules. Fineparticle (1-100 nm) preparation by CVD has been proven to be successful in many fields, e.g., TiO2 as pigments from TiCl4/O21 and metal ultrafine particles from reduction of metal chlorides.2,3 Besides, CVD has a lot of potential applications in membrane technology4,5 because of its ability to control the microstructure of an inorganic porous support. For convenience, particle formation in CVD can be thought to be composed of two parts. First is the process of solid formation from gaseous molecules. Second is the process of particle growth. The first process, in a wide scope, can be esteemed as formation of the initial nucleus. This may result from homogeneous gas-phase processes, either physical or chemical, to produce a supersaturated state which then collapses by nucleus formation.6 The second process, i.e., growth of the initial nucleus into a cluster or particle with bigger size, may result from physical condensation of a monomer molecule into nuclei, heterogeneous reaction between unreacted molecules and nuclei, or Brownian coagulation.7,8 The mechanism of particle formation, involved in the real CVD process, may be more complex than the scenario described above. It could be a mixing of every elementary process mentioned above together with effects such as flow, diffusion, and heat transfer in the reaction field. Therefore, a detailed mechanism concerning particle formation in CVD, especially the early stage of nucleation, is usually difficult to describe. Early * To whom correspondence should be addressed. Telephone: 886-2-2737-6650. Fax: 886-2-2737-6644. E-mail: [email protected].

research was done by Ulrich et al.9-11 They prepared silica particles by a flame combustion method (a hightemperature process). George et al.12 produced a TiO2 particle using TiCl4 and O2. They discussed the effects of inlet reactant concentration, temperature, and residence time in the reactor on the particle size and showed that the final particle size can be well-explained solely by Brownian collision theory. It is found that the chemical reaction, at high temperatures, is extremely fast and the nucleation time of nuclei is too short to cause a barrier to particle formation. The rate of particle formation is therefore controlled by the physical process afterward. Recently, Hong and Komiyama13 suggested a CVD particle forming process that is controlled by homogeneous nucleation. They used CuI2 and O2 to form copper oxide deposits in a hot-wall tubular reactor and found a sudden change of film morphology which is ascribable to the formation of particles in the gas phase. Their data strongly suggested that homogeneous nucleation dominated particle formation in such a CVD reaction system. However, largely because of the complexity of the reaction, no report was made about the particle formation mechanism that is controlled by the gas-phase reaction. In this paper, we report a CVD reaction system using SiH4 and C2H2 as the reactant gases that forms SiC particles even at moderate temperatures of less than 1273 K. Emphasis is placed on understanding the detailed chemical reaction mechanism involved in the gas-to-particle conversion process. By using a tubular reactor which has well-defined volume and temperature, the film growth phenomena related to the particle formation are investigated. This includes a kinetic analysis to the growth rate and the property changes of the deposits along the longitudinal direction of the reactor. A mechanism based on a gas-phase polymerization reaction is proposed and has been verified by

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Ind. Eng. Chem. Res., Vol. 37, No. 9, 1998 3603

after deposition were weighed. Also, silicon, 5 mm in width, was placed in the reactor and used as a substrate. The properties of the deposits on the substrate were investigated by the following techniques. The morphology of the deposited films was investigated using a scanning electron microscope (SEM) technique. The crystalline structure of the film was analyzed using an X-ray diffraction technique (XRD). The composition of the deposited films was investigated by using X-ray photoelectron spectroscopy (XPS). The particles formed at the first heating zone of the reactor were cold-trapped and observed by using a transmission electron microscope (TEM) technique. The specific surface area of the particles was determined by a single-point RunauerEmmet-Teller (BET) method at the boiling temperature of N2. Growth Rate Profile along a Tubular Reactor Figure 1. (a) Schematic diagram of the CVD reactor system: (1) mass flow controller; (2) pressure gauge; (3) reactor; (4) bypass line; (5) pressure regulating valve; (6) rotary pump. (b) Temperature profiles of the reaction zone at various setting temperatures.

investigating the effects of reaction temperature, inlet reactant concentration, and reaction atmosphere gas on the final particle size. Experimental Section The experimental setup of a low-pressure CVD reactor is illustrated in Figure 1a. A horizontal hot-wall tubular CVD reactor (quartz tube) was used because it provides a simple and well-characterized reaction zone for deposition.14 The diameter of the reactor was varied from 7 to 18 mm inner diameter. The reactor was heated by a three-zone resistance furnace, and the temperature of each zone was controlled independently by a temperature controller with a thermocouple inserted on the inner surface of the heater at the center. Figure 1b shows the temperature profiles, which were measured at the experimental volumetric flow rate and normal pressure. The results show that the uniform temperature profile in the reaction zone is about 35 cm in length. Also, an estimation was made to find the wallto-gas heat transfer, which shows that the gas temperature is essentially the same as the wall temperature. The silicon and carbon source gases were silane (SiH4, 99.9%) and acetylene (C2H2, 99.6%), respectively. Mass flow controllers were used to regulate the flow of gases. Argon (Ar, 5 N) or hydrogen (H2, 5 N) was added to adjust the total volumetric flow rate to keep a constant residence time of 100 ms in the reactor. The residence time here is defined as the ratio of the volume of the quartz tube to the volumetric flow rate at the reaction temperature and pressure. Experiments were all performed under a reduced pressure of 20 Torr. Typical flow rates for SiH4, C2H2, and Ar in a reactor of 12.0 mm in diameter at 1223 K were 8.6, 17.2, and 133.2 sccm, respectively. In this range of conditions, the gaseous flow was laminar with Reynolds numbers in the range of 7-10. The entrance length required for a fully developed velocity profile was estimated to be less than 1 cm. During reaction, solid deposits directly formed on the wall of the reactor. To measure the growth rate profile of the deposits along the longitudinal direction of the reactor, quartz rings, 1.5-2.0 cm/section, were put into the reactor and their mass changes before and

In this work, CVD reaction was performed in a tubular quartz reactor with a uniform temperature profile. Such a reaction field is characterized by its simplicity and ease of definition. First of all, an attempt was made to model the film growth rate profile along the flow direction (x) of a tubular reactor as a function of operating conditions including reactor diameter and reactant concentration, etc. It demands understanding what the rate-determining step is. Among the possible rate processes, gas-phase reaction of the reactant to form an active growth species, surface reaction of a film growth species, and gas-to-surface diffusion (mass transfer) of a growth species are the most probable candidates. When a first-order rate process assumption is used, film growth rate can be derived as follows. (i) Gas-phase reaction is the rate-determining step: Under this situation, the mass conservation equation is given by

u

dC ) -kgC dx

(1)

where u is the gas linear velocity, C is the reactant concentration, and kg is the gas-phase reaction constant in reciprocal seconds. Then, the concentration profile for a major reacting species is given by

x C ) C0 exp -kg u

(

)

(2)

where C0 is the initial concentration. The film growth, being formed due to consumption of a gaseous growth species on the surface eventually, is derived as

(

)

d2 /(dx πd)kgC 4

GR ) F dx π

d x ) FC0 kg exp -kg 4 u

(

)

(3)

where GR is the film growth rate in meters per second, F is the volume of solid product produced from 1 mol of reactant, and d is the reactor diameter. The film growth rate here is characterized by two features. First, the film growth rate is proportional to the reactor diameter. Second, the growth rate profile will show strong dependence on temperature because of a change of kg in the exponential term. (ii) Surface reaction is the rate-determining step:

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Figure 2. Variation of silicon carbide film growth rate along the longitudinal direction of the reactor at various reactor diameters.

Figure 3. Dependence of the film growth rate in the uniform temperature zone at various reactor diameters.

Under this situation, the mass conservation equation is given by

4 dC ) -ks C dx d

u

(4)

where ks is the surface reaction rate constant in meters per second. The film growth rate can be derived aswhich is characterized by a reverse proportion relation

GR ) C0Fks exp(-4ks(x/u)(1/d))

(5)

with respect to reactor diameter d in the exponential term. (iii) Gas-to surface diffusion is the rate-determining step: Under this situation, the mass conservation equation is given by

u

4 dC ) -kd C dx d

(6)

where kd is the mass-transfer coefficient related to the Sherwood number (Sh) as kd ) (Sh)D/d, where Sh approximates 3.66 in a tubular reactor and D is the gas diffusivity. The film growth rate is derived as

GR ) C0Fkd exp(-4(Sh)D(x/u)(1/d2))

(7)

which is characterized by a second-order reverse proportion relation with respect to reactor diameter d in the exponential term. Then, when the experimental data of the film growth rate profile at various reactor diameters or reaction temperatures are compared, the possible rate-determining steps in the film growth process can be argued. Results and Discussion 1. Deposition Rate Profiles at Various Reactor Diameters. Figure 2 shows the growth rate profile of the deposits along the longitudinal direction of the reactor at various reactor diameters (7, 12, and 18 mm inner diameter) at 1273 K. Considering the film growth rate profile in the uniform temperature zone which starts from 5 cm from the inlet of the reactor, two important features are observed. First, despite the same reactant concentrations at the inlet of the reactor, the deposition rate increases when the reactor size is enlarged. Second, all the profiles decline sharply along the flow direction. Figure 3 shows the relation of the

Figure 4. Growth rate profiles along the longitudinal direction of the reactor at various reaction temperatures.

deposition rate profiles, plotted on a logarithmic scale, and the longitudinal axial position in the reactor. The slope of the line, which represents the rate constant of a rate process, shows no dependence on the reactor diameter. Comparing this experimental result with the model relationship of GR and the exponential terms on reactor diameter d, we conclude that the gas-phase reaction is the most possible rate-controlling step. 2. Deposition Rate Profiles at Various Reactor Temperatures. Another attempt was made to examine the growth rate profile of the deposits at various reaction temperatures. The result is shown in Figure 4, in which the growth rate is plotted as a function of the axial position of the reactor. When the inlet part of the nonuniform temperature region is neglected, the film growth rate profile, plotted on logarithmic scale, is shown in Figure 5. A good linear relationship is obtained, indicating that first-order assumption is modest. The slope increases evidently when the reaction temperature is raised, which indicates a chemical reaction, i.e., a gas-phase reaction here, controls the solid depositing process. The axial position also can be represented by the residence time in the reactor. Therefore, the slope in Figure 5, having a dimension of reciprocal seconds, represents the first-order gas-phase reaction rate constant. From the slopes of the lines at various temperatures, the Arrhenius plot of this reaction can be determined and is shown in Figure 6. The relation between ln kg and 1/T is linear and gives an activation of 23.5 kcal/mol (Ea). 3. Morphology of the Deposits. Figure 7 shows six examples of SEM photographs, showing the cross section of the deposited films on a silicon substrate taken at different axial positions for runs at 1223 and

Ind. Eng. Chem. Res., Vol. 37, No. 9, 1998 3605

Figure 5. Growth rate profiles (in logarithmic scale) along the longitudinal direction of the reactor at various reaction temperatures.

Figure 6. Arrhenius plot of the gas-phase reaction rates.

1273 K. It is found that the deposits formed at the inlet part of the reactor are dense, e.g., parts a (1223 K) and d (1273 K) of Figure 7 taken at 9 cm from the inlet of the reactor. The morphology changes gradually from dense to porous with an increase in the reaction residence time as shown in the sequence parts a-c of Figure 7. The morphology change of the films, most plausibly, is caused by the gradual size increase of the gaseous depositing species, from molecules to clusters and then into fine particles, along the longitudinal direction of the reactor. Comparing the deposits at various reaction temperatures, we found that the morphology of the deposits at 1273 K is more porous than that at 1223 K (Figure 7e vs Figure 7b and Figure 7f vs Figure 7c). This indicates that the tendency of film morphology change, from dense to porous, shifts to the upstream of the reactor when the reaction temperature is raised. We attribute this phenomenon to the earlier occurrence of large particles at higher reaction temperatures. Also, the same tendency was observed when the reactant concentration was increased. These experimental facts imply that the gas-phase reaction, which is favored by high reactant concentration and high temperature, did present a barrier to the gas-to-particle conversion in this reaction system. That is, the higher the temperature and reactant concentration, the earlier the condensing species will turn to particles. 4. Composition Variation of the Deposits (SiCx, x ) 1-2) along the Longitudinal Direction of the Reactor. Another attempt was made to investigate the chemical composition of the deposits, i.e., the ratio of carbon to silicon content in the deposits, by an XPS technique. Figure 8 shows the results of XPS, where the content ratio of carbon to silicon (C/Si) of the

Figure 7. SEM photographs showing the fracture surface of films deposited on silicon substrate: (a) T ) 1223 K, taken at 9 cm from inlet; (b) T ) 1223 K, taken at 15 cm from inlet; (c) T ) 1223 K, taken at 25 cm from inlet; (d) T ) 1273 K, taken at 9 cm from inlet; (e) T ) 1273 K, taken at 15 cm from inlet; (f) T ) 1273 K, taken at 25 cm from inlet.

deposits is plotted as a function of the axial position of the reactor. The result is characterized by a gradual increase of the carbon content with an increase in the reaction residence time, from the stoichiometric composition of SiC to the carbon-rich composition of SiC2. According to the above experimental results, a plausible film formation mechanism, schematically shown in Figure 9, is proposed as follows. (1) SiH4 decomposes in the gas phase to form SiH2, an active intermediate with two free radicals15 (Coltrin et al., 1984), which is likely to react with C2H2.16,17 (2) With an increase of the reaction time along the flow direction of the reactor, an addition polymerization reaction occurs between SiH2 and C2H2. The polymerization reaction results in a series of complex gaseous species that accounts for the variation of the composition

3606 Ind. Eng. Chem. Res., Vol. 37, No. 9, 1998 Scheme 1

Figure 8. Content ratio of carbon to silicon (C/Si) of the deposits along the longitudinal direction of the reactor.

Figure 9. Schematic illustration of the reaction model showing the gas-to-particle conversion due to gas-phase polymerization of SiH4 and C2H2.

of the deposits. A detailed reaction mechanism is constructed as follows. (i) Initiation: SiH4 thermodecomposes to generate SiH2 as a primary radical, which then combines with C2H2 to form a monomer (AB)18,19 as shown in Scheme 1. (ii) Propagation: The monomer continues to join with radical SiH2 and π-electron donor C2H2 according to eqs c and d of Scheme 1. Repeating eqs c and d of Scheme 1, the propagation reaction can be written as eq e of Scheme 1. (iii) Termination: The termination reaction can occur when a polymer radical reacts with another one or when it meets the reactor wall. Focusing on the deposits formed on the wall, two types of termination, considering the relation of film composition and reaction residence time, are proposed as follows. (a) At low degree of polymerization, the content ratio of C to Si of the deposits is near 1, an example of which is given by eq f of Scheme 1. (b) At high degree of polymerization, the content ratio of C to Si of the deposits approaches 2, as shown in eq g of Scheme 1. The content ratio C/Si of the deposits as a function of the degree of polymerization (n) can be derived as

C/Si ) (2n - 2)/n,

ng2

(8)

The polymerization reaction described here is thought to be directly related to the gas-to-particle conversion in this reaction system. That is, gas species of low degree of polymerization are molecular, while they increase in size with an increase in the degree of polymerization and eventually nucleate to form particles. The gradual change of the morphology of the deposits with respect to residence time (as shown in

Figure 7) reflects the gradual size increase of the gas species along the axial direction of the reactor. The deposited films turn porous because sintering becomes more and more difficult when the size of the depositing species is increasing. To understand the size of the depositing species in the gas phase, a TEM technique was applied. Experiments were contrived to trap the gas species produced at the first zone of the reactor by using only first zone heating. Effects of reaction temperature, reactant concentration, and reaction atmosphere gas on the size of the trapped particles were investigated to justify the proposed gas-to-particle conversion mechanism. 5. Particle Sizes at Various Reaction Parameters. Figure 10 shows TEM micrographs of the deposits trapped at various reaction temperatures. The deposits are in the form of a rough sphere, which we specify as “particle” here. XRD measurements show the diffraction pattern of SiC polycrystalline. The particles may stick together by van der Waals force or electrostatic force which may make particle size determination difficult. Nevertheless, the average size of the particles was measured by direct sampling from TEM micrographs. Table 1 shows the values of the particle average

Ind. Eng. Chem. Res., Vol. 37, No. 9, 1998 3607 Table 1. Average Size of the Particles Trapped in the Gas Phase at Various Reaction Temperatures (Reaction Conditions: Partial Pressure of SiH4 ) 1.1 Torr and That of C2H2 ) 2.2 Torr; Total Pressure ) 20 Torr)

reaction temp (K)

average particle diameter from TEM observation (nm)

specific surface area from BET measurement (m2/g)

theoretical specific surface area by hard sphere assumption (m2/g)

1223 1323 1373

8.7 9.7 10.6

185 181 166

214 192 176

Figure 11. Effect of reactor temperature on the average particle diameter (dp).

Figure 12. Effect of inlet SiH4 concentration on the average particle diameter (dp).

Figure 10. Typical transmission electron micrographs showing the particulate trapped on the wall of the reactor at a place 12 cm from the reactor inlet when only the first heating zone is applied. Reaction temperature is (a) 1223, (b) 1273, and (c) 1323 K, respectively.

diameter together with a series of specific surface area data obtained from BET measurement. Assuming the particles as spherical and independent elements, the outer surface area of the particles was calculated, which is also shown in Table 1. The specific surface value calculated, based on the average particle diameter directly measured from TEM, is almost the same as that obtained from BET measurement. From this result, we can conclude that the hard-sphere assumption is true; that is, the effect of particle sticking in Figure 10 is almost negligible. In the reaction temperature range investigated, particle diameter increases with temperature, from 8.7 nm at 1123 K to 10.6 nm at 1373 K. Figure 11 shows the exponent relationship of particle size with respect to reaction temperature which gives a value of 1.7. The effect of the inlet reactant concentration on the particle size was also investigated. Since the reactivity of C2H2 is conceived to be much smaller than that of SiH4, only the SiH4 concentration was varied. Figure 12 shows the average particle size as a function of the inlet concentration of SiH4. The result shows an exponent of concentration to be 0.15 at 1323 K. Another reaction parameter that supports our mechanism is the effect of reaction atmosphere gas on

3608 Ind. Eng. Chem. Res., Vol. 37, No. 9, 1998

Figure 13. Average particle diameter as a function of the hydrogen replacement ratio (H2/(H2 + Ar)).

the particle size. H2 was introduced instead of Ar. Figure 13 shows the average particle diameter as a function of the hydrogen replacement ratio (H2/(H2 + Ar)) at 1223 K at a constant reactant concentration ratio of [SiH4/C2H2] ) 2. The average particle diameter decreases with an increase in the H2 replacement ratio, from 9.3 nm in a pure Ar atmosphere down to 6.4 nm in a pure H2 atmosphere. A discussion of the experimental results of the particle size is given as follows. First, the positive exponent (1.7) of the reaction temperature on average particle diameter (dp) is completely different from the value of -0.2 predicted by a correlation equation of the final particle size derived by Ulrich,9 who developed the particle growth model according to the Brownian coalescence theory as

dp ) A(η0.4T-0.2C00.4t0.4)

(9)

where A is a constant, η is the sticking coefficient, and t is the residence time. The departure of the temperature dependence indicates that collision and coalescence should not be the dominating phenomenon that affects the particle size in the present reaction system, though it is very likely to occur after initial nuclei are formed. Second, the small dependence of the SiH4 concentration (0.15) on the particle size compared with that of the reaction temperature (1.7) strongly indicates that the effect of chemical reaction is much larger than that of collision and coalescence. Therefore, we believe the gaseous polymerization reactions proposed above dominate the particle formation process. The proposed reaction mechanism predicts a high degree of polymerization of the gaseous species at high reaction temperature due to high reaction rate. That is, the higher the reaction temperature, the bigger the gaseous species that will form. This is reflected in the size variation of the particles trapped in Figure 10. Also, the effect of the reaction atmosphere gas on the particle size can be well-explained because introducing H2 will retard the formation of SiH2 and the propagation reaction, which results in a decrease in the degree of polymerization and the particle size eventually. The trapped particles observed here, mainly by the driving force of thermophoresis due to the sharp temperature gradient at the boundary between the first heating zone and the second one, could be larger than the real gaseous species at the same reaction residence time. Despite this, the variation tendencies of the particle size on every reaction parameter still reflect the information about the particle formation process.

In this reaction system, the critical nucleus that can stably exist in the gas phase remains unknown. A single SiC molecule cannot stably exist in the gas phase because of its high melting temperature and low vapor pressure at the reaction temperatures. However, it is reasonable to claim that the intermediate species, especially the compounds with low degrees of polymerization as described in eqs d and e of Scheme 1, may still remain molecular even though their sizes are large. This can be ascribed to the surrounding organic groups that make the surface energy stable compared with that of the bulk SiC. Emphasis should be placed on the experimental fact that the whole process concerning the particle formation is controlled by the gas-phase reaction. This is quite different from high-temperature CVD systems in which chemical reaction is usually instantaneous and the particle deposition is always a diffusion-controlled process. The proposed reaction mechanism here seems realistic for it explains well all the experimental data, though it cannot easily be justified. For a more detailed understanding, in situ detecting techniques are necessary and will be the future work. Conclusions In conclusion, the gas-to-particle conversion mechanism in a CVD reaction system using SiH4 and C2H2 to synthesize SiC fine particles was investigated. By analyzing the growth rate profile and chemical composition of the solid deposits along the longitudinal direction of a tubular reactor, the controlling step related to the gas-to-particle conversion was determined. The results indicate that a gaseous polymerization reaction between SiH4 and C2H2 dominates the formation of SiC particles in this CVD reaction system. A detailed reaction mechanism was constructed, considering an addition reaction between SiH2 and C2H2, by inserting the free radicals of SiH2 into the π-bonding of C2H2. Also, particles formed in the gas phase were cold-trapped and observed by TEM. The effects of the reaction temperature, inlet reactant concentration, and atmosphere reaction gas on the particle size were experimentally investigated to justify the proposed reaction mechanism. Among them, a positive exponent of the reaction temperature on the particle size (1.7) was obtained which departed from the value (-0.2) predicted from the Brownian coalescence theory. This indicates a different mechanism that controls the particle growth which we ascribe to the chemical reaction that occurred in the gas phase. The proposed reaction mechanism predicts the size of the particles in the gas phase as a function of polymerization degree. A more detailed mathematical analysis with respect to the growth mechanism is under way. Acknowledgment The authors thank National Science Council of Taiwan for the financial support under the Contract NSC85-2214-E-011-007. Literature Cited (1) Suyama, Y.; Kato, A. TiO2 Produced by Vapor-Phase Oxygenolysis of TiCl4. J. Am. Ceram. Soc. 1976, 59, 146. (2) Lamprey, H.; Ripley, R. L. Ultrafine Tungsten and Molybdenum Powders. J. Electrochem. Soc. 1962, 109, 713.

Ind. Eng. Chem. Res., Vol. 37, No. 9, 1998 3609 (3) Saeki, Y.; Matsuzaki, R.; Nishihara, H.; Aoyama, N. Preparation of Cobalt Powder by Hydrogen Reduction of Cobalt Dichloride. Denki Kagaku 1978, 46, 643. (4) Xomeritakis, G.; Lin, Y. S. Chemical Vapor Deposition of Solid Oxides in Porous Media for Ceramic Membrane Preparation. Comparison of Experimental Results with Semianalytical Solutions. Ind. Eng. Chem. Res. 1994, 33, 2607. (5) Yan, S.; Maeda, H.; Kusakabe, K.; Morooka, S. Thin Palladium Membrane Formed in Support Pores by Meta-Organic Chemical Vapor Deposition Method and Application to Hydrogen Separation. Ind. Eng. Chem. Res. 1994, 33, 616. (6) Hiddy, G. M. Aerosols; Academic Press: New York, 1984. (7) Friedlander, S. K. Smoke, Dust and HazesFundamentals of Aerosol Behavior; Wiley: New York, 1987. (8) Kirkbir, F.; Komiyana, H. Formation and Growth Mechanism of Porous, Amorphous, and Fine Particles Prepared by Chemical Vapor Deposition. Can. J. Chem. Eng. 1987, 65, 50. (9) Ulrich, G. D. Theory of Particle Formation and Growth in Oxide Synthesis Flames. Combust. Sci. Technol. 1971, 4, 47. (10) Ulrich, G. D.; Nilnes, B. A.; Subramanian, N. S. Particle Growth in Flames. II: Experimental Results for Silica Particles. Combust. Sci. Technol. 1976, 14, 243. (11) Ulrich, G. D.; Subramanian, N. S. Particle Growth in Flames. III: Coalescence as a Rate-Controlling Process. Combust. Sci. Technol. 1977, 17, 119. (12) George, A. D.; Nurley, R. D.; Place, E. R. Formation of TiO2 Aerosol from the Combustion Supported Reaction of TiCl4 and O2. Faraday Symp. Chem. Soc. 1973, 7, 63. (13) Hong, L. S.; Komiyama, H. Chemical Vapor Deposition of CuOx Films by CuI and O2: Role of Cluster Formation on Film Morphology. J. Am. Ceram. Soc. 1991, 74, 1597.

(14) Breiland, W. G.; Coltrin, M. E. Si Deposition Rates in a Two-Dimensional CVD Reactor and Comparisons with Model Calculations. J. Electrochem. Soc. 1990, 137, 2313. (15) Coltrin, M. E.; Kee, R. J.; Miller, J. A. A Mathematical Model of the Coupled Fluid Mechanics and Chemical Kinetics in a Chemical Vapor Deposition Reactor. J. Electrochem. Soc. 1984, 131, 425. (16) Hong, L. S.; Shimogaki, Y.; Egashira, Y.; Komiyama, H. Study of the Reaction of Si2H6 in the Presence of C2H2 in Synthesis of SiC Films by LPCVD Using a Macro/microcavity Method. J. Electrochem. Soc. 1992, 139, 3652. (17) Becerra, R.; Walsh, R. Gas-Phase Kinetic Study of the Silylene Addition Reaction to Acetylene and Acetylene-d2 over the Temperature Range 291-613 K. Int. J. Chem. Kinet. 1994, 26, 45. (18) Erwin, J. W.; Ring, M. A.; O’Neal, H. E. Mechanism and Kinetics of the Silane Decomposition in the Presence of Acetylene and in the Presence of Olefins. Int. J. Chem. Kinet. 1985, 17, 1067. (19) Rogers, D. S.; O’Neal, H. E.; Ring, M. A. Comparative Trapping Kinetics of Silylene. 1. Silylene Reactions with 1,3Butadiene and Acetylene and with 1,3-Butadiene and Methanol. Organometallics 1986, 5, 1467.

Received for review March 24, 1998 Revised manuscript received May 14, 1998 Accepted May 16, 1998 IE9801812