Mechanism and Product Branching Ratios of the SiH3+ SiH3 Reaction

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8796

J. Phys. Chem. 1996, 100, 8796-8801

Mechanism and Product Branching Ratios of the SiH3 + SiH3 Reaction K. Matsumoto, M. Koshi,* K. Okawa, and H. Matsui Department of Chemical System Engineering, The UniVersity of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113, Japan ReceiVed: September 13, 1995; In Final Form: February 28, 1996X

The mechanism of the SiH3 + SiH3 reaction was studied by means of time resolved mass spectrometry. SiH3 radical was generated by the ArF laser photolysis of C2Cl4 in SiH4/He mixtures, and the products were detected by a low-energy electron impact ionization mass spectrometer. The rate constant derived from the decay rate of SiH3 agreed well with that obtained from the rise rate of Si2H6. The overall rate constant of the reaction at 297 ( 2 K was determined to be (9.5 ( 3.5) × 10-11 cm3 molecule-1 s-1. H2 could also be detected as a product of the SiH3 + SiH3 reaction, and the yield of H2 was measured to be 11 ( 4%. The other major product of the SiH3 + SiH3 reaction was SiH2, which rapidly reacts with SiH4 to form Si2H6. It was confirmed by the addition of a large amount of H2 as a SiH2-trapping reagent that Si2H6 detected at p ) 5 Torr was exclusively produced via the SiH2 + SiH4 reaction. On the basis of these observations, the branching ratios for the decomposition of vibrationally excited Si2H6 produced by the SiH3 + SiH3 reaction were estimated. These results were compared with conventional RRKM calculations.

1. Introduction The silyl radical is thought to play the central role in silane plasma chemical vapor deposition (CVD) processes.1,2 Because of the lack of rapid reaction of the silyl radical with most closed shell molecules at room temperature, the kinetic lifetime of the silyl radical in many systems is mainly determined by the radical-radical self reaction, SiH3 + SiH3. The details of this important reaction have been recently reviewed by Jasinski et al.3 Although the rate constant of this reaction has been measured by four groups with four different methods,4-7 the results are not in good agreement with each other. In the first report of the rate constant, Itabashi et al.4 produced SiH3 by a pulsed discharge in SiH4/H2 mixtures, and its concentration was monitored by infrared laser absorption. It is noted that the absolute concentration of SiH3 is required to determine the rate constant of the SiH3 + SiH3 reaction. In their analysis of the data, an absorption coefficient calculated from an ab-initio value for the Einstein A-coefficient was used to determine the absolute concentration of SiH3, and the rate constant of (1.5 ( 0.6) × 10-10 cm3 molecule-1 s-1 was obtained at the total pressure of p ) 0.9 Torr (H2 buffer gas). The time-resolved IR diode laser absorption spectroscopy was also used by Jasinski et al.5 to monitor SiH3. In their experiment, SiH3 was generated by the very fast reaction of

Cl + SiH4 f SiH3 + HCl

(1)

Cl atom was produced by laser photolysis of CCl4 at 193 nm, and the absolute yield of HCl was measured by using IR diode laser absorption spectroscopy to determine the initial concentration of SiH3. The value of (7.9 ( 2.9) × 10-11 cm3 molecule-1 s-1 at p ) 9.5 Torr (He) was obtained. Koshi et al.6 also used ArF laser photolysis of CCl4 in SiH4/He mixtures at p ) 5 Torr to produce SiH3. They monitored SiH3 by using near threshold ionization mass spectrometry. SiH3 could be detected with high sensitivity (≈1010 cm-3), and its initial concentration was * Author to whom correspondence should be addressed. FAX: (+81)3-5684-3644. E-mail: [email protected]. X Abstract published in AdVance ACS Abstracts, April 15, 1996.

S0022-3654(95)02693-1 CCC: $12.00

determined by measuring the amount of HCl produced by reaction 1. Their value of (1.2 ( 0.4) × 10-10 cm3 molecule-1 s-1 is in between the value of Itabashi et al. and of Loh and Jasinski. The most recent determination of the rate constant was reported by Baklanov and Chichinin.7 They used photolysis of phosgene at 248 nm to produce Cl atoms, and SiH3 was monitored by LMR. The initial Cl atom concentration was estimated on the basis of the rise rate of the SiH3 signal and the known rate constant of the Cl + SiH4 reaction. Their rate constant of (1.6 ( 0.5) × 10-11 cm3 molecule-1 s-1 is much lower than the previous determinations. In the present study, the rate constant was remeasured with a different precursor molecule (C2Cl4) for the generation of Cl atom. The mechanism of the SiH3 + SiH3 reaction is more complicated than a simple three-body recombination. Becerra and Walsh8 proposed the following mechanism in their kinetic modeling for the Hg(3P1) photosensitized reactions in H2/SiH4 mixtures.

SiH3 + SiH3 f SiH2 + SiH4

(2)

SiH3 + SiH3 f Si2H6**

(3)

Si2H6** f SiH2 + SiH4

(4)

Si2H6** f HSiSiH3 + H2

(5)

SiH2 + SiH4 f Si2H6*

(6)

Si2H6* + M f Si2H6 + M

(7)

Reaction 2 is a direct disproportionation reaction proposed by Reimann et al.9 based on the isotope scrambling experiments. Reaction 3 is a recombination to form vibrationally hot disilane, Si2H6**, which decomposes irreversibly to products via reactions 4 and 5. Silylene formed by reactions 2 and 4 is readily converted to Si2H6*, which contains less excess energy than Si2H6**. This mechanism explains the pressure independence of the measured rate constants for the SiH3 decay. However, the branching ratio for reactions 4 and 5 has not been well established. Becerra and Walsh9 have estimated a value of k5/ k4 ) 0.18 by means of complex kinetic simulations for the end © 1996 American Chemical Society

Mechanism of the SiH3 + SiH3 Reaction

J. Phys. Chem., Vol. 100, No. 21, 1996 8797

products in the Hg-sensitized photolysis of SiH4. Loh and Jasinski5b measured the Si2H6 yield under the steady state photolysis condition by using IR diode laser absorption spectroscopy and suggested that reaction 4 dominates by more than 90%. On the other hand, Koshi et al.6 reported a Si2H6 yield of 60%. Since the value of this branching ratio might have great influence on the modeling calculations of the CVD reactions, especially on the yields of higher silanes such as Si3H8 and Si4H10, further experimental measurements of the reaction products are desirable for the determination of the branching fraction of this reaction. In the present study, H2 produced by the reaction 5 could be detected, and the determination of H2 yield has been performed. Results of the experiments of H2 addition to confirm the mechanism for the Si2H6 formation are compared with the results of RRKM calculations. 2. Experimental Section The apparatus used in the present study is essentially the same as that used in the previous study.6 The only difference is the new quadrupole mass spectrometer (Anelva AQA-200). The reactant gas mixtures were slowly flowed in a Pyrex cell, and the contents of the cell were continuously sampled through a pinhole into an electron impact ionization chamber of the mass spectrometer. Mass-selected ion signal was detected by a twostage multichannel plate (MCP), which was operated under pulse-counting conditions. The pulse signal was sent to a gated counter, and the time dependence at a fixed mass number was obtained by scanning the delay time of the gate with a fixed gate width of 100 µs. Signals were averaged over appropriate laser shots (500 to 10 000, depending on the S/N ratio of the signal) for each waveform. The reactant gas mixture was irradiated by the unfocused output of an ArF laser (Questek 2220). Typical laser fluence ranged from 5 to 20 mJ/cm2. The repetition rate of the laser and the flow rate of the gas mixture were determined so that the reactant gas was irradiated by only one pulse of the ArF laser. Partial pressures of the reactants and the total pressures were measured with a capacitance manometer (MKS Baratron 122A). Experiments were carried out at room temperature (297 ( 2 K) with total pressures of p ) 2-5 Torr (He buffer). Since there is no clean source for the photolysis to generate SiH3, almost all of the direct kinetic studies of SiH3 radical have been performed by using rapid abstraction reactions of H atoms from SiH4 to produce SiH3. The ArF laser photolysis of CCl4 to generate Cl atom is a widely used method. Cl atom produced by the photolysis is effectively converted to SiH3 and HCl via the fast reaction 1. The yield of Cl atom in the 193 nm photolysis of CCl4 is 1.2, and CCl3 and CCl2 radicals are produced.5 Although there is no evidence that these CCl3 and CCl2 radicals interfere with SiH3 kinetic measurement,5 CCl4 itself might react with SiH2, as was pointed out by Koshi et al.6 The reaction of SiH2 with CCl4 will reduce the yield of Si2H6. To avoid such complications in the determination of Si2H6 yield, C2Cl4 was used in the present work for the photolysis source of Cl atom. Because of the large absorption cross section of C2Cl4 at 193 nm (1.8 × 10-17 cm2), the condition of [C2Cl4] , [SiH4] is easily achieved so that SiH2 exclusively reacts with SiH4 to produce Si2H6. In the present experiments, the partial pressures of C2Cl4 and SiH4 ranged from 0.02 to 0.5 mTorr and from 2 to 10 mTorr, respectively. The silyl radicals were detected by using a near threshold ionization technique with the nominal ionization energy of 11 eV.6 Other product species were detected with ionization energies as low as possible to prevent fragmentation, i.e., 14

Figure 1. Time profiles of SiH3 (a) and Si2H6 (b) after the ArF laser photolysis of C2Cl4/SiH4/He mixtures: C2Cl4 ) 0.26 mTorr, SiH4 ) 2.3 mTorr, p ) 4.9 Torr.

eV for HCl at m/z ) 36, 16 eV for Si2H6 at m/z ) 62, and 17.5 eV for H2 at m/z ) 2. 3. Results and Discussion 3.1. Rate Constant of the SiH3 + SiH3 Reaction. For the experimental determination of the rate constant of the SiH3 + SiH3 reaction, the absolute concentration of SiH3 has to be measured. The method for the determination of the initial concentration of SiH3 and the method for the data analysis are the same as those employed by Koshi et al.6 That is, it is assumed that the initial concentration of SiH3 is equal to the concentration of HCl produced by the photolysis of C2Cl4/SiH4 mixtures, and the measured intensity of the HCl signal was calibrated against its absolute concentration. This assumption is valid if SiH3 and HCl are produced only by reaction 1 and if the rate of this reaction is much faster than the rates of any other SiH3 loss processes. These conditions can be satisfied with the concentration of SiH4 in large excess over the concentration of the precursor molecule. An example of the time profile of SiH3 is shown in Figure 1a. The rate of reaction 1 evaluated from the known rate constant is much faster than the rise rate of the SiH3 signal in Figure 1a. This rise rate is controlled by the time constant of the detection system, which is mainly determined by the traveling time of the molecules from the reaction zone in the cell to the ionization region in the vacuum chamber. The decay rate of SiH3 is controlled not only by the rates of reactions 2 and 3 but also by the rate of heterogeneous loss at the cell wall, which is kinetically first order:

SiH3 9 8 products wall

(8)

The rate constants of this process ranged from 70 to 205 s-1, depending on the condition of the surface of the reaction cell. By taking into account reactions 2, 3, and 8, the time profile of SiH3 is expressed as follows:6

[SiH3] [SiH3]0 where

)

exp(k8t) 1 + β(1 - exp(-k8t))

(9)

8798 J. Phys. Chem., Vol. 100, No. 21, 1996

β)

Matsumoto et al.

2(k2 + k3) [SiH3]0 k8

(10)

The value of the parameter β in eq 9 can be derived from the experimental time profile of SiH3 by using the method described in ref 6. Figure 2 shows a plot of β against the initial concentrations of SiH3. With the predetermined value of the wall loss rate k8, the rate constant for the SiH3 decay (k ) k2 + k3) is derived from the slope of this plot. The rate constant can also be obtained from the production rate of Si2H6. An example of the time profile of Si2H6 is shown in Figure 1b. With a steady state assumption for SiH2 in reactions 2-8, the following equation is obtained:

[

1 (1 + β)(1 - exp(-k8t)) ) ξ + [SiH3]0 2 1 + β(1 - exp(-k8t))

[Si2H6]

]

Figure 2. Plot of β ) 2k(SiH3)0/k8 as a function of initial concentration of SiH3. Open circles are derived from the decay curves of SiH3, and filled circles are obtained from the production rates of Si2H6. A line is a least squares fit to both of the circles.

1 1 (11) ln β 1 + β(1 - exp(-k8t)) where

ξ)

[

]

k4 1 k2 + k k2 + k3 k4 + k5 3

It is noted that the production rate of Si2H6 is always faster than the decay rate of SiH3, as can be seen in Figure 1a,b, and as expected from eq 11. The magnitude of β in eq 11 was evaluated by fitting calculated profiles to the measured time profile of Si2H6, and the results are also plotted in Figure 2. Both the estimated values of β derived from the decay rates of SiH3 and from the rise rate of Si2H6 agree well with each other, as in the case of the CCl4 precursor.6 The rate constant of k ) k2 + k3 ) (9.5 ( 3.5) × 10-11 cm3 molecule-1 s-1 was obtained from the slope of the plot in Figure 2. In the present work, C2Cl3 and C2Cl2 radicals might be produced by the photolysis of C2Cl4 at 193 nm. Possible effects of these chlorocarbon radicals on the kinetics of SiH3 have to be examined to validate the present results of the rate constant. Attempts have been made to detect C2Cl4, C2Cl3, and C2Cl2 produced by the 193 nm photolysis of the C2Cl4/SiH4 mixtures by means of low-energy ionization mass spectrometry. Because of the very large absorption cross section of C2Cl4 at 193 nm, the decrease of C2Cl4 concentration by the photolysis could be clearly observed, as shown in Figure 3a. The quantum yield for the C2Cl4 loss by photolysis was calculated to be close to unity on the basis of the absorption coefficient and the measured laser fluence. The absolute concentrations of HCl produced by the photolysis in C2Cl4/SiH4 mixtures were also measured (Figure 3b). It is found that the amount of HCl produced by the photolysis was 2.2 ( 0.3 times the amount of C2Cl4 photodecomposed. This indicates that the quantum yield of Cl atom for the 193 nm photolysis of C2Cl4 is close to 2. Figure 3c shows the very strong rise signal of C2Cl2 at m/z ) 94. On the other hand, the signal at m/z ) 129 (corresponding to C2Cl3 ion) shown in Figure 3d decreases after the photolysis, and the time profile of this signal is similar to that of C2Cl4, indicating that the signal at m/z ) 129 is the fragment ion signal of C2Cl4. Attempts to detect C2Cl3 by lowering the ionization energy of the mass spectrometer failed. These results are consistent with the quantum yield of 2 for the Cl atom production. Therefore, the photochemistry in the C2Cl4/SiH4 mixture at 193 nm is expected to be rather simple: the dominant channel for the photodissociation of C2Cl4 is likely to be C2Cl4 f C2Cl2 + 2Cl, and almost all the Cl atom is converted to HCl

Figure 3. Time profiles of C2Cln radicals after the photolysis of C2Cl4/SiH4/He mixtures: C2Cl4 ) 0.068 mTorr, SiH4 ) 5.6 mTorr, p ) 5.0 Torr with a laser fluence of 18 mJ/cm2. Signal intensities in (a) and (d) are normalized by the intensity before the laser shots. Signal intensities in (b) and (c) are normalized by the averaged intensity at t ) 10-20 ms.

via reaction 1. More importantly, C2Cl2 is unreactive in the present system as can be seen in Figure 3c. The effects of the chlorocarbon side reactions on the measurements of the rate constant are likely to be negligible. 3.2. Measurements of H2 Yield. Si2H6, HSiSiH3, and H2 are expected as the main products of the SiH3 + SiH3 reaction. Si2H6 is readily detected, as shown in Figure 1b. Since Si2H6 is expected to be produced from SiH2 through multiple step reactions 2, 4, 6, and 7, measurement of a stable direct product is desirable for the determination of the branching ratio of reactions 4 and 5. Detection of H2 has been tried in the present work. The signal at m/z ) 2 induced by the photolysis could be observed as shown in Figure 4. Because of the large background signal at m/z ) 2 caused by the high ionization energy (17.5 eV), the sensitivity of H2 detection is low, and the measurements were only performed at high initial concentrations of SiH3. As a result, the production rates of H2 were faster than the time resolution of the detection system. The signal at m/z ) 2 can contain contributions from fragment ions of some other products than H2. However, radicals such

Mechanism of the SiH3 + SiH3 Reaction

J. Phys. Chem., Vol. 100, No. 21, 1996 8799

Figure 4. Time profile of the signal at m/z ) 2 after the photolysis of C2Cl4/SiH4/He mixture: C2Cl4 ) 0.44 mTorr, SiH4 ) 2.5 mTorr, p ) 4.99 Torr. The data were obtained by averaging over 5000 laser shots.

Figure 5. Yields of Si2H6 and H2 produced by the SiH3 + SiH3 reaction. Data are obtained with SiH4 ) 2.2-7 mTorr and p ) 5 Torr.

as SiH2, SiH3, and HSiSiH3 are excluded as the origin of the observed signal at m/z ) 2, since the signal does not show any decay. The major stable product, Si2H6, can be a candidate of the parent molecule, but the energy for the formation of H2 ion from Si2H6 is much higher than the ionization potential of H2 itself (ionization energy for the production of H2 ion from H2 ) 15.5 eV and from Si2H6 ) 17.6 eV). In fact, no fragment signal from Si2H6 was detected at m/z ) 2 with the nominal ionization energy of 17.5 eV. Therefore, it is concluded that the signal at m/z ) 2 is dominantly originated from H2. This conclusion is further supported by the fact that the efficiency curve for the ion yield (i.e., a plot of ion signal intensity against the ionization energy) of H2 itself is similar to that of the signal at m/z ) 2 detected after the photolysis. The yield of H2, which is defined by 2[H2]/[SiH3]0, can be obtained in the present experiment with the assumption of [SiH3]0 ) [HCl]. Since SiH3 is consumed not only by reactions 2 and 3 but also by reaction 8, this yield does not directly correspond to the branching fraction for reaction 5. With the same procedure used to derive eq 11, the following equations are derived for the amount of H2 produced at t ) ∞:

[H2]∞ [SiH3]0

1 1 ) η 1 - ln(1 + β) 2 β

[

]

(12)

where

η)

k3 k5 k2 + k3 k4 + k5

(12′)

The parameter η represents the yield of H2 in the SiH3 + SiH3 reaction. The factor [1- (1/β)ln(1 + β)] represents the fraction of SiH3 consumed at the cell wall to the initial concentration of SiH3. Values of parameter η are plotted in Figure 5 against the initial concentrations of C2Cl4. As can be seen in the figure,

the yield of H2 is independent of the concentration of the precursor molecule, and an averaged value of 0.11 ( 0.04 was derived. Olbrich et al.11 obtained the product mole fractions of 0.93, 0.03 and 0.04 for Si2H6, Si3H8, and Si4H10, respectively, in the Hg-sensitized photolysis of H2/SiH4 mixtures. They argued that the Si3H8 and Si4H10 were produced from HSiSiH3 and H2SiSiH2, respectively. In this case, the yield of H2 was expected to be 0.07, which is rather close to the present value of 0.11. Loh and Jasinski5b also found that the yield of Si2H6 in the SiH3 + SiH3 reaction was more than 90% by measuring IR absorption. This result is also consistent with the present yield of H2. On the other hand, Koshi et al.6 reported 60% yield of Si2H6. In their experimental conditions, concentrations of CCl4 were comparable with that of SiH4. They speculated that the reaction of SiH2 with CCl4 was responsible for the decrease in Si2H6 yields with increasing CCl4 concentration. Therefore, their yield was estimated by extrapolating the observed yield to zero concentration of CCl4. Such extrapolation may result in a large uncertainty in the estimated yield. 3.3. Pathways of Si2H6 Formation. In the mechanism of the SiH3 + SiH3 reaction (reactions 2-7), Si2H6 is exclusively produced via the reaction of SiH2 with SiH4. According to this mechanism, Si2H6 is not produced if SiH2 is trapped completely. To confirm this, a large amount of H2 was added with constant partial pressures of C2Cl4 and SiH4, and the yield of Si2H6 was measured as a function of H2 partial pressure. Although the rate constant of Cl atom reaction with H2 is almost 1 order of magnitude smaller12 than that with SiH4,13 loss of Cl atom by the Cl + H2 reaction has to be taken into account for the Si2H6 yield measurements because of the high concentrations of H2 employed in these experiments. In addition, the sensitivity of our mass spectrometer depends on the average molecular weight of the sample gas mixtures. To cancel out these effects, the amount of Si2H6 produced by the photolysis was always normalized by the initial concentration of SiH3. The ratio R, defined by [the normalized Si2H6 yield with H2]/[the normalized Si2H6 yield without H2], is expressed by the following equations:

k15[H2] 1 )1+ R k14[SiH4]

(13)

where, the rate constants k14 and k15 correspond to the following reactions

SiH2 + SiH4 (+M) f Si2H6 (+M)

(14)

SiH2 + H2 (+M) f SiH4 (+M)

(15)

The reciprocal of the ratio R is plotted against the ratio of [H2]/ [SiH4] in Figure 6. The measurements have been performed at a constant total pressures of 2 and 5 Torr. The values of 1/R are linearly dependent on H2 concentration. This indicates that the concentration of Si2H6 goes to zero at the limit of H2f ∞. By using eq 13, the ratio of the rate constant can be derived from the plot in Figure 6. Resulting values of k15/k14 ) 2.2 × 10-3 at p ) 2 Torr and 2.6 × 10-3 at p ) 5 Torr are in reasonable agreement with the results of the direct measurements of k14 and k15. The rate constants for reactions14 and 15 have been measured by several groups,14-17 and it is well recognized that both of the reactions are pressure dependent. Jasinski and Chu15 showed that these reactions are in the falloff region at the pressure range 2-5 Torr. On the basis of their rate constants for reactions 14 and 15, values of k15/k14 ) 3 × 10-3 at 2 Torr and 3.5 × 10-3 at 5 Torr are obtained. Using the same experimental technique used by Jasinski and Chu, Baggott et

8800 J. Phys. Chem., Vol. 100, No. 21, 1996

Matsumoto et al.

Figure 6. Effect of H2 addition on the yield of Si2H6. The ratio R is defined by [Si2H6 yield with the addition of H2]/[Si2H6 yield without H2 addition]. Open circles are obtained at p ) 5 Torr and SiH4 ) 2.8 mTorr. Filled circles are obtained at p ) 2 Torr with 1.2 mTorr SiH4. Lines are the least squares fit to the data.

al.17 also measured absolute rate constant for reaction 14 and obtained values about 1.7 times higher over the same pressure range with He buffer gas. These values of k14 give ratios of 1.7 × 10-3 at 2 Torr and 2.1 × 10-3 at 5 Torr. Our values lie in between these ratios derived from direct measurements. Present results strongly indicates that Si2H6 observed in this experiment is exclusively produced via the SiH2 intermediate, and the production of Si2H6 via the collisional deactivation of Si2H6** is negligible. This is also consistent with the pressureindependent rate constant of the SiH3 + SiH3 reaction. With reactions 2-8, an expression similar to eq 12 is obtained for the yield of Si2H6:

[Si2H6]∞ [SiH3]0

1 1 ) ξ 1 - ln(1 + β) 2 β

[

]

(16)

Here, ξ is the yield of Si2H6 corrected for the wall loss of SiH3. Estimated values of ξ are also plotted in Figure 5. The yields seem to be still slightly dependent on the amount of C2Cl4 at the low-concentration region, and the large scatter of the data still prevents the precise determination of the yields. By the extrapolation of the data in Figure 5 to [C2Cl4] ) 0, the Si2H6 yield is expected to be larger than 80%. 3.4. The Branching Ratio for the Decomposition of Vibrationally Excited Si2H6. The yield of H2 obtained in the present work is a product of two branching fractions, as shown in eq 12′. There has been only one study on the branching ratio of the reactions 2 and 3. Reimann et al.9 obtained the value of k3/(k2 + k3) ) 0.59 in their isotope scrambling experiments. They found that the yields of the reaction products depended on the pressure at the range 70-640 Torr with H2 buffer gas. By using this value, combined with the present result of η ) [k3/(k2 + k3)][k5/(k4 + k5)] ) 0.11, the branching fraction for the decomposition of Si2H6** is evaluated as k5/(k4 + k5) ) 0.19. RRKM calculations of the microcanonical rateconstants for reactions 4 and 5 have been performed in order to understand the reason of the preferential dissociation of Si2H6** to SiH2 + SiH4 channel. Si2H6** produced via the silyl recombination reaction contains an excess energy of 76.5 kcal/mol (with the values of ∆Hf°(SiH3) ) 47.8 and ∆Hf°(Si2H6) ) 19.1 kcal/mol).18 This amount of energy is about 20 kcal/mol higher than the products of reactions 4 and 5. Since the difference in reaction enthalpies for these decomposition pathways is only 1-3 kcal/mol (depending on the values of heat of formation for SiH2 and HSiSiH3), it is expected that the rates of decomposition for these pathways are not so different. If there are activation barriers in the reverse reactions -4 and -5, the different decomposition

rate may be explained, but both reverse reactions are the insertion reactions of silylenes, and no or very low activation barriers are expected.10 One of the main factor for the preference of reaction 4 is the difference in the reaction path degeneracy, L. On the basis of the transition state geometries, L ) 18 for reaction 4 and L ) 6 for reaction 5 are used in the RRKM calculation11,19 for the thermal decomposition of Si2H6. However, the observed branching fraction for reaction 5 is smaller than that expected from the difference in the reaction path degeneracy only. Microcanonical decomposition rates for both pathways are calculated to compare with the observed branching ratio by using a standard formula:

W(E+) k(E**) ) L hN(E**)

(17)

Here, N(E**) is the density of state of Si2H6** (E** ) 76.5 kcal/mol in this case), and the W(E+) is the sum of states of the activated complex with an excess (nonfixed) energy of E+ ) E** - (Ea + ∆E). Ea is the reaction barrier for the reverse reaction and ∆E is the heat of reaction measured from the bottom of the Si2H6 potential. The density of states of Si2H6** and the sum of states for the activated complexes are calculated by using the Beyer-Swinehart algorithm for the direct counting.20 Several models for the activated complexes for reactions 4 and 5 have been proposed in the literature,8,11,19 and these models are used for the calculation of sum of states. However, the choice of the model (and, hence, the vibrational frequencies of the activated complex) is rather insensitive to the branching ratio, and it is concluded that the selection of the vibrational frequencies for the activated complex is unimportant. Results presented here are based on the transition state model proposed by Moffat et al.19 They used the BEBO method for the evaluation of the vibrational frequencies. The parameter in the BEBO method was determined by fitting the results of their RRKM calculations to the experimental data of the thermal decomposition of Si2H6. In their fitting calculations, the heats of formation for SiH2 and HSiSiH3 were also estimated as ∆Hf°(SiH2) ) 64.8 and ∆Hf°(HSiSiH3) ) 74.06 kcal/mol. These values are very sensitive to the rate constants for reactions 4 and 5. The heat of formation for SiH2 has become well established in recent years as 65.3 kcal/mol.3 However, there is no direct determination of the heat of formation for HSiSiH3. We employed the results by Moffat et al. for both SiH2 and HSiSiH3. These values result in ∆H ) 53.9 kcal/mol for reaction 4 and 54.96 kcal/mol for reaction 5. Another sensitive parameter for the branching fraction is the height of the activation barrier for the reverse reactions. Ho et al.10 predicted no activation barrier for reaction -4, and this was confirmed by the ab-initio calculation of Gordon et al.21 at the MP4-SDTQ computational level. Gordon et al. also found a small activation barrier of Ea ) 2.1 kcal/mol for reaction -5. The rate constant k4 ) 2.35 × 1010 s-1 is obtained with Ea(-4) ) 0. Assuming the gas kinetic rate for the deactivation of Si2H6**, the rate constant for reaction 4 is comparable with the rate of deactivation at the pressure of ca. 1200 Torr. This explains the present experimental findings that all Si2H6 detected at p ) 2-5 Torr is produced via the reaction of SiH2 with SiH4, that is, the formation of Si2H6 via the deactivation of Si2H6** is negligible in the present experimental condition. Since a small activation barrier for reaction -5 is expected by the ab-initio calculation, the rate of reaction 5 is calculated as a function of Ea(-5), and the resulting branching fractions are plotted in Figure 7. If the branching fraction is determined

Mechanism of the SiH3 + SiH3 Reaction

J. Phys. Chem., Vol. 100, No. 21, 1996 8801 Acknowledgment. The authors wish to thank Professor R. Walsh of University of Reading and Dr. J.M. Jasinski of IBM Watson Research Center for their helpful discussion on the rate constants of reactions 14 and 15. A part of this work is supported by a grant-in-aid from the Ministry of Education, Science and Culture of Japan. References and Notes

Figure 7. Branching fraction for reactions 4 and 5 as a function of the activation energy for reaction -5 calculated by a microcanonical RRKM formula.

only by the reaction path degeneracy, a value of 0.25 is expected. Because of the small difference of the heat of reaction between reactions 5 and 6, the branching fraction calculated at Ea(-5) ) 0 is close to this value. Since the branching fraction is sensitive to the barrier height, the value of Ea(-5) can be determined by using the experimental branching fraction, assuming heats of formation for SiH2 and HSiHiH3 used in this calculation are correct. The experimental branching fraction of 0.19 corresponds to the activation barrier of 1 kcal/mol. If the direct disproportionation reaction 2 is neglected, the branching fraction is 0.11 and the activation barrier for reaction -5 is 1.8 kcal/mol. This estimation of the barrier height for reaction -5 is consistent with the results of ab-initio calculations of Gordon et al.21 Present calculations show that the preference of the decomposition pathway 4 over channel 5 is primarily caused by the large path degeneracy of reaction 4. The small energy barrier for reaction -5 is also responsible for the slower rate of reaction 5. However, the estimation of the activation barrier is largely dependent on the magnitude of the heat of formation. Experimental information on the thermodynamic properties and the reactivity of the HSiSiH3 is required for further discussion of this reaction system.

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