Ab Initio Chemical Kinetics for the Reaction of an H Atom with Si3H8

Feb 23, 2010 - The kinetics and mechanism for the reaction of H with Si3H8 have been ... by H Atom. Han-Bing Rao , Xian-Yin Zeng , Hua He , and Ze-Ron...
0 downloads 0 Views 2MB Size
Download PDF
3642

J. Phys. Chem. A 2010, 114, 3642–3648

Ab Initio Chemical Kinetics for the Reaction of an H Atom with Si3H8 D. H. Varma, P. Raghunath, and M. C. Lin* Center for Interdisciplinary Molecular Science, Institute of Molecular Science, National Chiao Tung UniVersity, Hsinchu 300, Taiwan ReceiVed: December 6, 2009; ReVised Manuscript ReceiVed: February 2, 2010

The kinetics and mechanism for the reaction of H with Si3H8 have been investigated using various theoretical methods including CCSD(T)/6-311++G(3df,2p)//B3LYP/6-311++G(3df,2p), G2M(RCC2), and CCSD(T)/ 6-311++G(3df,2p)//CCSD/6-311+G(d,p). The results obtained by the latter method show that H abstraction from a primary Si-H bond and a secondary Si-H bond leads to the formation of n-Si3H7 and i-Si3H7 products, with 3.8 (TS1) and 3.2 (TS2) kcal/mol barriers, respectively. Significantly, the hydrogen substitution of SiH3 and Si2H5 groups by attacking at the central Si atom via TS3 (3.3 kcal/mol) and a terminal Si atom of Si3H8 from side and end on (via TS4, 4.2 kcal/mol and TS5, 6.3 kcal/mol), were found to give SiH3 + Si2H6 and SiH4 + Si2H5 products, respectively. The heats of formation of Si3H8, n-Si3H7, and i-Si3H7 at 0 K are predicted to be 32.3 ( 1.2, 68.6, and 66.6 kcal/mol, respectively. These values are in good agreement with the experimental and other theoretical values. The rate constants and branching ratios for the four product channels of the title reaction have been calculated by the transition state theory with Eckart tunneling corrections over a wide temperature region of 250-2500 K. These results may be employed for simulations of catalytic and plasma-enhanced chemical vapor deposition processes of a-Si:H films. Introduction Much attention has been paid to higher silanes in silane plasma processing of hydrogenated amorphous silicon (a-Si: H), polycrystalline silicon (p-Si), and silicon nitride (SiNx) thin films,1–5 for application to solar cells and thin film transistors and so on.6,7 These films are prepared either by plasma enhanced chemical vapor deposition (PECVD) or, increasingly, by catalytic chemical vapor deposition (Cat-CVD).1–10 Both processes involve gas-phase reactions in a chamber. Higher silanes represent the molecules that are composed of more than two silicon atoms. PECVD starts as the dissociation of a silane source gas by collisions with electrons in a plasma, leading to generation of radicals, atoms, and ions. These species diffuse onto substrate after the secondary reactions in the gas phase of the plasma, depositing a-Si:H film through surface reactions on the substrate. Experimentally, using the PECVD technique, Du et al.11 prepared hydrogenated amorphous silicon films using gases such as Si2H6 and Si3H8 at a similar hydrogen dilution. It was found that when using Si3H8 as a source gas, the deposition rate was increased by a factor of ∼1.5, compared to Si2H6.11 During this dissociation process, H atoms and SiH3 radicals were generated, which led to the deposition of a high quality a-Si:H thin film. Various works have been done with Si2H6 and Si3H8 as source gases for preparation of a-Si:H thin film by low temperature CVD.12 The same source gas is used to obtain a higher deposition rate from photochemical vapor deposition.13 Sax et al. theoretically explains the decomposition of silanes up to Si5H12 by reactions with hydrogen atoms to form various products and also calculated their heats of formation.14 The rate constants for the reaction of hydrogen with Si2H6 and others silanes are experimentally and theoretically available,15,16 but those for Si3H8 are not. To the best of our knowledge there is * To whom correspondence should be addressed. E-mail: chemmcl@ emory.edu.

still no experimental and theoretical study on the rate constant for the reaction of H with Si3H8, which is important in the simulations of CVD of silicon thin films from silanes. The objective of the present study is to elucidate the detailed mechanism of the title reaction by fully characterizing the potential energy surface of the system, employing high level ab initio molecular orbital methods. The hydrogen atom is one of the key reactive species in the decomposition of trisilane to form the primary products exothermically via the processes.

H + Si3H8 f n-Si3H7 + H2

(R1)

f i-Si3H7 + H2

(R2)

f Si2H6 + SiH3

(R3)

f Si2H5 + SiH4

(R4)

The calculated geometries, vibrational frequencies, and heats of formation for new radical products at 0 K are given in the Results and Discussion section. We also provide the rate constants and the branching ratios for all individual product channels mentioned above predicted by means of transition state theory (TST) along with Eckart tunneling corrections. Computational Methods All the calculations were carried out using Gaussian 03 program package.17 We employed a hybrid density functional B3LYP18,19 (Becke 3-parameter hybrid exchange functional combined with the LYP exchange-correlation functional) with the standard 6-311++G(3df,2p) basis set for the full geometry optimization of the reactants, products, and transition states. On the basis of these optimized geometries, we did higher level single-point energy calculations by the CCSD(T)/6311++G(3df,2p) and G2M(RCC2) method.20 The G2M method calculates the base energy at the MP4/6-311G(d,p) level of

10.1021/jp911574k  2010 American Chemical Society Published on Web 02/23/2010

Kinetics of the Reaction of an H Atom with Si3H8 theory and improves it with expanded basis set and coupled cluster corrections as well as a “higher level correction”. In addition, the geometries of all species in the H + Si3H8 reaction were also optimized with the coupled cluster technique incorporating single and double substitutions (CCSD)21 with the 6-311+G(d,p) basis set. We improved the energy of the predicted structures by performing single-point CCSD(T)/6311++G(3df,2p) calculations. All the stationary points have been identified for local minima and transition states by vibrational analyses. Intrinsic reaction coordinate analysis was performed to confirm the connection between transition states and designated reactants and products.22 All the relative energies presented in the tables have been corrected for zero-point vibrational energies (ZPVE, unscaled). Heats of formation are predicted for several species for comparison with experimental values, using the energies obtained at the G2M(RCC2) and CCSD(T)/6-311++G(3df,2p)// CCSD/6-311+G(d,p) levels. Rate constants for all reactions were calculated using the transition state theory (TST)23 with Eckart tunneling corrections24 using “TheRate” program from the online resource (http://cse-online.net/kinetics.html).25 Results and Discussions Potential Energy Surface and Reaction Mechanism. We carried out geometry optimization for all the molecules and radicals involved in different reaction channels using B3LYP/ 6-311++G(3df,2p), and CCSD/6-311+G(d,p) methods. The optimized geometries of all the species for the H + Si3H8 reaction are shown in Figure 1. The moments of inertia and the vibrational frequencies computed at the CCSD/6-311+G(d,p) level of theory are listed in Table 1 and the results of B3LYP method are given in Supporting Information Table S1. The relative energies obtained at various levels of theory are given collectively in Table 2. The potential energy diagram drawn with the energies predicted at the CCSD(T)/6-311++G(3df,2p)// CCSD/6-311+G(d,p) level is shown in Figure 2. The relative energies are calculated with respect to the reactants. The following discussion will be based on the results of the calculations at the CCSD(T)/6-311++G(3df,2p)//CCSD/6311+G(d,p) level of theory. To validate the accuracy of the theoretical method chosen in this study, we had compared the predicted heats of reaction for H + Si2H6 yielding the products Si2H5 + H2 and SiH4 + SiH3 using the G2M, CCSD(T)/6311++G(3df,2p)//B3LYP/6-311++G(3df,2p) and the CCSD(T)/ 6-311++G(3df,2p)//CCSD/6-311+G(d,p) methods with available experimental data. The values predicted by all 3 methods, as will be shown later, agree closely. The results for the heats of reaction are also in good agreement with experimental values.15,16 Trisilane has a C2V structure with the primary and secondary Si-H bond lengths of 1.479 Å (expt, 1.483 Å) and 1.483 Å (expt, 1.486 Å), respectively. The calculated Si-Si bond length is 2.344 Å, which is in good agreement with the 2.322 Å value obtained experimentally.26 In Figure 2, we have plotted schematically the potential energy surface of the five possible reaction channels for H + Si3H8 via hydrogen abstraction and substitution channels forming four products. Hydrogen Abstraction. There are obviously two possibilities: The first mechanism involves H-atom attack on one of the terminal Si-H bonds to form H2 + n-Si3H7 (SiH3SiH2SiH2) via TS1 with a 3.8 kcal/mol barrier. The values obtained by other methods CCSD, G2M, and CCSD(T)//B3LYP are 5.2, 3.3, 3.1 kcal/mol respectively. However, at the B3LYP/6311++G(3df,2p) level, the energy of TS1 becomes about 0.5

J. Phys. Chem. A, Vol. 114, No. 10, 2010 3643 kcal/mol higher than that of initial reactants. Regarding the structure of TS1, the breaking bond length of the Si · · · Ha bond is 1.577 Å, while that for forming the H · · · H bond is 1.191 Å. The ∠Si-H-H bond angle was found to be collinear at 180.0°. The exothermicity of the process is predicted to be 16.6 kcal/ mol, which is in good agreement with the experimental heat of reaction, 16.0 kcal/mol, as alluded to above. The second hydrogen abstraction reaction occurs by the H-atom attack on one of the two secondary Si-H bonds to form the i-Si3H7 (SiH3SiHSiH3) radical and H2 via TS2. The barrier height of this reaction was predicted to be 3.2 kcal/mol, which may be compared with the values of 4.6, 2.5, and 2.8 kcal/mol calculated using CCSD, CCSD(T)//B3LYP, and G2M(RCC2) methods, respectively. At TS2, the length of the breaking Si · · · Hb was predicted to be 1.569 Å and that of the forming Hb · · · H bond to be 1.228 Å calculated by the CCSD method (Figure 1). In the case of B3LYP, the Hb · · · H bond distance is 0.354 Å longer. The exothermicity of this process is predicted to be 18.6 kcal/mol, which is 2.0 kcal/mol higher than that in the primary Si-H reaction, suggesting that the secondary Si-H bond is 2.0 kcal/mol weaker. Thus, from the PES (Figure 2) we can conclude that the primary hydrogen abstraction reaction requires a higher activation energy compared to the secondary hydrogen abstraction reaction similar to the H + C3H8 reaction.27 The activation energy for the abstraction of primary hydrogen from Si2H6 by atomic hydrogen was found to be (4.0 kcal/mol for CCSD(T)// CCSD) approximately 0.2 kcal/mol higher than that for the analogous reaction with Si3H8.16 Substitution Reactions. There are three possible transition states in the substitution reactions with the H atom attacking on an Si-Si bond and on a terminal silicon atom of Si3H8 from the side and end-on, respectively, to form products presented by R3 and R4 reactions. When the hydrogen atom attacks an Si-Si bond directly from the side, the Si-Si bond was found to be broken readily, giving either SiH3 + Si2H6 or SiH4 + Si2H5 product pairs, requiring a minimum energy of 3.3 or 4.2 kcal/mol, via TS3 or TS4, respectively. As seen in Figure 1, for the optimized geometry of TS3, the bond lengths of the forming two Si-H bonds are 2.124 and 2.261 Å. The bond angle of ∠Si-Si-Si decreases from 112.2 to 105.1°. The endon reaction of Si3H8, that is, H atom attacking one of the terminal Si atoms at the silyl group, requires an energy of 6.3 kcal/mol via TS5. In TS5, the newly formed Si · · · H bond length is 1.786 Å, while the Si · · · Si bond is stretched by 0.074 Å. From the PES we observe that the reaction of the H atom attacking the terminal silicon atom of Si3H8 (via TS5) requires a higher energy comparing with the H atom attacking the central one. The exothermicity of this channel is 16.2 kcal/mol predicted by the CCSD(T)//CCSD method and is close to the experimental value of 15.4 kcal/mol. Heats of Formation. The predicted heats of reaction for all the reaction channels are given in Table 2. The calculated results at the CCSD(T)/6-311++G(3df,2p)//CCSD/6-311+G(d,p) and G2M levels, as forementioned, are in close agreement with experimental values similar to the H + SiH4 and Si2H6 cases.16 On the basis of these results, we calculated heats of formation ∆fH0° (0 K) of the n-Si3H7, i-Si3H7, and Si3H8 using available experimental data given in Table 3, by using general formula, for example, for n-Si3H7:

∆fH°(n-Si + ∆fH°(Si 0 3H7) ) ∆fH°(H) 0 0 3H8) - ∆fH°(H 0 2) + ∆γH°0

3644

J. Phys. Chem. A, Vol. 114, No. 10, 2010

Varma et al.

Figure 1. The optimized geometries of the reactants, transition states, and products at the CCSD/6-311+G(d,p) level and B3LYP 6-311++G(3df,2p) level. The values at the B3LYP 6-311++G(3df,2p) level are given in parentheses. (Length in Å and angle in degrees).

Experimentally, the heat of formation of Si3H8 is available as 28.9 ( 1 kcal/mol at 298 K.28 Katzer et al.29 employed a multireference averaged coupled-pair functional method with

the TZdp basis set and applied a correction scheme to determine the heats of formation at 298 K for n-Si3H7 and i-Si3H7 as 65.7 and 64.1 kcal/mol, respectively. The conversion from 298 to 0

Kinetics of the Reaction of an H Atom with Si3H8

J. Phys. Chem. A, Vol. 114, No. 10, 2010 3645

TABLE 1: Calculated Moments of Inertia and Vibrational Frequencies of the Species Involved in the H + Si3H8 Reaction Computed at CCSD/6-311+G(d,p) Level species

frequencies (cm-1)

Ia, Ib, Ic (a.u.)

Si3H8

92.1, 916.5, 1046.4

n-Si3H7

187.6, 889.3, 1014.3

i-Si3H7

158.3, 957.2, 1067.9

Si2H6 Si2H5 SiH4 SiH3 H2 TS1

41.6, 356.3, 356.3 33.6, 337.4, 345.7 20.9, 20.9, 20.9 12.7, 12.7, 21.4 0.0, 0.9, 0.9 196.2, 983.5, 1117.3

TS2

229.1, 945.7, 1081.4

TS3

230.8, 872.9, 1040.5

TS4

198.1, 957.8, 1082.7

TS5

206.7, 966.5, 1108.5

79, 100, 101, 334, 396, 440, 458, 478, 593, 621, 731, 760, 923, 927, 963, 972, 972, 976, 982, 2252, 2259, 2270, 2275, 2277, 2280, 2281, 2281 91, 103, 109, 330, 398, 449, 469, 485, 584, 619, 738, 767, 920, 947, 958, 973, 974, 2252, 2258, 2264, 2272, 2275, 2279, 2283 68, 82, 99, 341, 386, 466, 487, 517, 579, 606, 753, 917, 947, 965, 970, 976, 979, 2250, 2261, 2265, 2277, 2280, 2284, 2286 144, 394, 394, 444, 658, 658, 891, 965, 965, 970, 982, 982, 2270, 2278, 2278, 2281, 2286, 2286 140, 407, 436, 446, 627, 659, 911, 962, 974, 976, 2258, 2268, 2278, 2283, 2290 961, 961, 961, 996, 996, 2300, 2303, 2303, 2303 806, 962, 962, 2269, 2302, 2302 4419 i1273, 57, 93, 178, 291, 339, 400, 453, 470, 501, 625, 626, 731, 770, 923, 939, 958, 969, 973, 979, 992, 1227, 2256, 2263, 2265, 2274, 2276, 2282, 2282 i1191, 76, 94, 100, 157, 166, 390, 420, 452, 466, 498, 590, 629, 741, 838, 924, 931, 963, 970, 972, 974, 982, 1267, 2252, 2270, 2275, 2278, 2281, 2283, 2285 i555, 98, 104, 121, 290, 296, 355, 396, 434, 503, 508, 616, 616, 761, 789, 906, 918, 942, 967, 968, 975, 987, 2227, 2260, 2270, 2272, 2278, 2281, 2289, 2300 i218, 56, 89, 152, 345, 364, 417, 459, 528, 605, 647, 732, 756, 774, 835, 908, 935, 968, 971, 989, 1010, 1038, 2121, 2141, 2274, 2279, 2284, 2286, 2292, 2302 i796, 79, 89, 101, 233, 250, 355, 362, 451, 487, 508, 674, 698, 769, 772, 881, 884, 919, 953, 972, 974, 998, 2194, 2242, 2242, 2249, 2260, 2271, 2278, 2279

TABLE 2: Relative Energiesa (kcal/mol) of Reactants, Transition States, and Products of the Reaction H + Si3H8 species

B3LYP/ 6-311++G(3df,2p)

CCSD(T)/Ib// B3LYP/Ib

G2 M (RCC2)

CCSD/ 6-311+G (d,p)

CCSD(T)/Ib// CCSD/6-311+G (d,p)

H + Si3H8 n-Si3H7 + H2 i-Si3H7 + H2 Si2H6 + SiH3 Si2H5 + SiH4 TS1 TS2 TS3 TS4 TS5

0.0 -18.6 -20.5 -18.4 -21.4 0.5 0.4 1.7 2.3 2.2

0.0 -16.5 -18.5 -13.5 -16.4 3.1 2.5 2.2 3.2 5.1

0.0 -16.3 -18.4 -13.4 -16.1 3.3 2.8 2.4 3.5 5.5

0.0 -16.0 -17.9 -16.5 -19.1 5.2 4.6 6.8 8.2 10.3

0.0 -16.6 -18.6 -13.4 -16.2 3.8 3.2 3.3 4.2 6.3

exptlc -16.0 -17.7 -14.5 ( 1.2 -15.4

a

Energies are ZPVE-corrected. b I: 6-311++G(3df,2p). c The experimental enthalpies of formations at 0 K are as follows (in kcal/mol): Si3H8, 33.5 ( 1.; i-Si3H8, 67.8.; n-Si3H7, 69.3.; H, 51.7.; Si2H6, 22.9.; Si2H5, 59.2.; SiH4, 10.5.; SiH3, 47.7 ( 1.2 kcal/mol (see refs 28–30)

Figure 2. Schematic pathways for the H + Si3H8 reaction. Relative energies with ZPVE are in kcal/mol calculated using the CCSD(T)/6311++G(3df,2p)//CCSD/6-311+G(d,p) level.

K for all three molecules was made by using the sum of elements in the standard reference states of Si(Cr) (-0.769 kcal/mol) and H2 (-2.024 kcal/mol).30 The [H°(0) - H°(298.15 K)] values of Si3H8, -5.83 kcal/mol; n-Si3H7, -5.74 kcal/mol; and i-Si3H7,

-5.70 kcal/mol are obtained by using vibrational frequencies of CCSD/6-311+G(d,p) method. Thus, by using these values, we obtained the values at 0 K of Si3H8, n-Si3H7, and i-Si3H7 to be as 33.5, 69.3, and 67.8 kcal/mol, respectively. Our predicted heats of formation ∆fH°(0 K) are 32.3-34.2 (Si3H8), 68.6 (n0 Si3H7), and 66.6 (i-Si3H7), by both CCSD(T)//CCSD and G2 M methods. The agreement between experiment and theory is thus excellent. These results are summarized in Table 3. The value of Si3H8 was predicted based on the known values of Si2H6 and Si2H5 as referenced in the footnote of Table 3. Rate Constant Calculations. The molecular parameters and predicted energies presented in Tables 1 and 2 were utilized to calculate the bimolecular rate constant for the H + Si3H8 reaction using the transition state theory (TST) with Eckart tunneling corrections (denoted as TST/Eckart) employed in the TheRate program.23–25 The moments of inertia and unscaled harmonic vibrational frequencies obtained at the CCSD/6311+G(d,p) level of theory were employed for the calculation. The energy at each stationary point of the minimum energy path (MEP) is refined by single-point energy calculations at the CCSD(T)/6-311++ G(3df,2p) level. Due to the lack of experimental data for the H + Si3H8 reaction, we have also done the H + Si2H6 reaction using the CCSD(T)//CCSD method and predicted the rate constants with TST/Eckart for all product channels forming H2 + Si2H5 and SiH3 + SiH4, agreeing well with the experimental and our reported theoretical data.15,16 For

3646

J. Phys. Chem. A, Vol. 114, No. 10, 2010

Varma et al.

TABLE 3: Calculated Heats of Formation (∆fH°) 0 of Species at 0 K Predicted at the Different Levels of Theory heat of formation, ∆fH0° (kcal/mol) species n-Si3H7 i-Si3H7 Si3H8 Si3H8

reactions H H H H

+ + + +

Si3H8 Si3H8 Si3H8 Si3H8

f f f f

n-Si3H7 + H2 i-Si3H7 + H2 Si2H6 + SiH3 Si2H5 + SiH4

G2M(RCC2)

CCSD(T)//CCSDa

exptlb

68.6 66.8 32.3 34.1

68.6 66.6 32.3 ( 1.2 34.2

69.3 67.8 33.5 ( 1 33.5 ( 1

a CCSD(T)/6-311++G(3df,2p)/CCSD/6-311+G(d,p). b The experimental values are obtained based on heats of formation at 0 K as follows (in kcal/mol): Si3H8, 33.5 ( 1 (28.9 ( 1); i-Si3H8, 67.8 (64.1); n-Si3H7, 69.3 (65.7); (calculated from 298 K values given in parentheses (from refs 26 and 27) using vibrational frequencies in this work); H, 51.7; Si2H6, 22.9; Si2H5, 59.2; SiH4, 10.5; SiH3, 47.7 ( 1.2 kcal/mol; (see refs 28–30)

the same reaction, the CCSD(T)//B3LYP method overpredicted the rate constants by a factor of 2-3. This was also shown to be the case for the present H + Si3H8 system as indicated by the results summarized in Table S2 of the Supporting Information. For practical applications, the predicted rate constants for these reaction channels R1, R2, R3, and R4 have been represented by the following three parameter expressions given in units of cm3 molecule-1 sec-1 for the temperature range 250-2500 K.

kR1(TS1) ) 3.06 × 10-17T2.11exp[-807/T] kR2(TS2) ) 8.82 × 10-17T2.0exp[-694/T] kR3(TS3) ) 9.10 × 10-16T1.47exp[-1083/T] kR4(TS4) ) 3.62 × 10-15T1.14exp[-1502/T]

Figure 3. The predicted rate constants for the H + Si3H8 reaction forming n-Si3H7 + H2 (kR1(TS1)), i-Si3H7 + H2 (kR2(TS2)), Si2H6 + SiH3 (kR3(TS3)), Si2H5 + SiH4 (kR4(TS4 and TS5), and ktot using TST with Eckart tunneling corrections. Inset shows the comparison between kR1 and kR3 with and without Eckart tunneling corrections.

kR4(TS5) ) 6.31 × 10-16T1.63exp[-2502/T] ktot ) kR1 + kR2 + kR3 + kR4 ) 1.22 × 10-16T2.06exp[-752/T] The 2-parameter Arrhenius expressions, also given in units of cm3 molecule-1sec-1, fitted in the temperature range 300-500 K can be given by

kR1(TS1) ) 6.33 × 10-11exp[-1579/T] kR2(TS2) ) 8.70 × 10-11exp[-1432/T] kR3(TS3) ) 2.46 × 10-11exp[-1645/T] kR4(TS4) ) 1.83 × 10-10exp[-1513/T] kR4(TS5) ) 1.15 × 10-11exp[-1971/T] ktot ) kR1 + kR2 + kR3 + kR4 ) 5.09 × 10-11exp[-3119/T] Comparing the rate constants for the hydrogen abstraction and the substitution reactions given in Figure 3, one can see

that the contribution to the overall rate constant by the hydrogen substitution reactions, producing SiH3 + Si2H6 and SiH4 + Si2H5 by R3 and R4, respectively, is minor due to its relatively tighter transition states and lower imaginary frequencies (see Table 1 and 2). The inset of Figure 3 shows that without the Eckart tunneling correction at lower temperature, kR3 is faster than kR1 but as the temperature increases kR1 becomes more competitive, whereas with the Eckart tunneling correction kR1 is much faster than kR3 over the entire temperature range of 250-2500 K even though EaR1 is 0.5 kcal/mol lower than EaR3. The SiH3 groups in Si3H8 have small internal rotation barriers. However, in our previous study16 we found that the contribution of hindered rotations does not have any effect on the predicted rate constant. Table 4 gives a comparison of the rate constants for all channels of hydrogen reactions with SiH4, Si2H6, and Si3H8 at 300 and 1000 K. Significantly, for the abstraction channels giving H2 + SiH3, H2 + Si2H5, and H2 + Si3H7, the values of rate constants are not proportional to the number of hydrogen atoms in silanes. The branching ratios of these four product channels are shown in Figure 4. The product channels for both hydrogen abstraction reactions are predominant up to about 2500 K, with that for channel R2 producing i-Si3H7 + H2 being predominant. It is evident from this figure that channel R3 producing Si2H6 and SiH3 R4 giving SiH4 + Si2H5 are noncompetitive throughout the entire temperature range. Similarly, the rate constant calculations are also done with the B3LYP molecular parameters (moments of inertia and vibrational frequencies) and the energies from CCSD(T)//

Kinetics of the Reaction of an H Atom with Si3H8 TABLE 4: Comparison of the Rate Constants for All Channels of H + SiH4, H + Si2H6, and H + Si3H8 at 300 and 1000 K

reaction H + SiH4 f SiH3 + H2a H + Si2H6 f Si2H5 + H2a H + Si2H6 f SiH3 + SiH4a H + Si3H8 f n-Si3H7 + H2 (R1) H + Si3H8 f i-Si3H7 + H2 (R2) H + Si3H8 f Si2H6 + SiH3 (R3) H + Si3H8 f Si2H5 + SiH4 (R4(TS4)) H + Si3H8 f Si2H5 + SiH4 (R4(TS5))

k (300 K) k (1000 K) cm3 molecule-1 cm3 molecule-1 sec-1 sec-1 2.58 × 10-13 1.47 × 10-12 7.47 × 10-14 3.50 × 10-13 7.9 × 10-13 1.08 × 10-13 1.62 × 10-14

6.07 × 10-11 1.65 × 10-10 1.73 × 10-11 2.92 × 10-11 4.41 × 10-11 7.92 × 10-12 2.12 × 10-12

1.64 × 10-15

4.0 × 10-12

a All values are taken from ref 16 using TST with Eckart quantum tunneling correction.

J. Phys. Chem. A, Vol. 114, No. 10, 2010 3647 The computed heats of formation ∆fH°0 at 0 K for Si3H8 and n-Si3H7, i-Si3H7 radicals are 32.3 ( 1.2, 68.6, and 66.6 kcal/ mol, respectively. These values agree excellently with experimental and theoretical results within (1.2 kcal/mol. The rate constants and branching ratios for the four channels have been calculated over the temperature range 250-2500 K using transition state theory along with the Eckart tunneling corrections. It was found that both hydrogen abstraction reactions are more significant than the substitution reactions in the overall reaction rate. The results presented in this study afford an understanding of the overall reaction of H + Si3H8, which is useful for simulation of silane-hydrogen-based Si-thin film growth by PECVD and Cat-CVD. Supporting Information Available: The moments of inertia and the vibrational frequencies computed at the B3LYP/6311++G(3df,2p) level of theory are listed in Table S1, and the comparison of rate constants by both CCSD(T)//CCSD and CCSD(T)//B3LYP methods is done at three temperatures, 298, 500, and 1000 K, given in Table S2. All the product channels of H + Si3H8 reaction rate constants calculated at the CCSD(T)/ 6-311++G(3df,2p)//B3LYP/ 6-311++G(3df,2p) level are given in Figure S1. This material is available free of charge via the Internet at http://pubs.acs.org. Acknowledgment. The authors deeply appreciate the support of this work by the Ministry of Economics under contract No 98-EC-17-A-07-S2-0043 and for the use of TheRate program at the CSE-Online Internet site. M.C.L. acknowledges the support from the Taiwan Semiconductor Manufacturing Company for the TSMC Distinguished Professorship and for the National Science Council of Taiwan for the Distinguished Visiting Professorship at National Chiao Tung University in Hsinchu, Taiwan. R.P. would also like to acknowledge a partial support from the ATU Plan of MOE, Taiwan.

Figure 4. Branching ratios of the products n-Si3H7 + H2 (R1), i-Si3H7 + H2 (R2), Si2H6 + SiH3 (R3), and Si2H5 + SiH4 (R4) channels.

B3LYP method for comparison. These results are given in Supporting Information Figure S1. The comparison of rate constants by both methods is done at three temperatures 298, 500, and 1000 K as given in Supporting Information Table S2. The results predicted with the CCSD(T)//B3LYP method are higher than those with CCSD(T)//CCSD by a factor of 3-4, due primarily to the lower reaction barriers and, to some extents, smaller frequencies by the former technique. On the basis of these calculations, we concluded that, for H-atom reactions with Si2H6 and Si3H8, the latter method appears to be more suitable. Conclusion The mechanism for the Si3H8 + H reaction has been investigated at the CCSD(T)/6-311++G(3df,2p)//B3LYP/6311++G(3df,2p),G2M(RCC2),andCCSD(T)/6-311++G(3df,2p)// CCSD/6-311+G(d,p) levels of theory. This reaction involves two distinct pathways, hydrogen abstraction and substitution. One is the direct H abstraction from a primary and secondary Si-H bond in the Si3H8 forming n-Si3H7 + H2 and i-Si3H7 + H2 products via TS1 and TS2, respectively, among which the secondary Si-H reaction is energetically the most favorable one. The second path is a hydrogen substitution process by the H atom attacking on an Si-Si bond and on a terminal silicon atom of Si3H8 from the side and end-on, respectively, to yield two product channels Si2H6 + SiH3 (via TS3) and SiH4 + Si2H5 (via TS4 and TS5).

References and Notes (1) Icabarrocas, P. R. J. Non-Cryst. Solids. 1993, 37, 164. (2) Das, D.; Sharma, S. N.; Banerjee, R. J. Non-Cryst. Solids. 1997, 229, 211. (3) Wyrch, N.; Torres, P.; Goetz, M.; Dubail, S.; feitknecht, L.; Cuperus, J.; Shah, A.; Rech, B.; Kluth, O.; Wieder, S.; Vetterl, O.; Stiebig, H.; Beneking, C.; Wagner, H., Proceedings 2nd World Conference on PhotoVoltaic Energy ConVersion, Vienna, 1998; Vol I, p 467. (4) Saito, K.; Sano, M.; Matsuda, K.; Kondo, T.; Nishimoto, T.; Ogawa, K. Kajita, I. Proceedings 2nd World Conference on PhotoVoltaic Energy ConVersion, Vienna, 1998; Vol I, p 351. (5) (a) Spear, W. E.; Lecomber, P. G. Solid State Commun. 1975, 17, 1193. (b) Suzuki, A. Jpn. J. Appl. Phys. 1999, 38, L1315. (6) Lecomber, P. G.; Spear, W. E.; Ghaith, A. Electro. Lett. 1979, 15, 179. (7) Carlson, D. E.; Wronski, C. R. Appl. Phys. Lett. 1976, 28, 671. (8) Matsuda, A. Jpn. J. Appl. Phys. 2004, 43, 7909. (9) Matsumura, H. Jpn. J. Appl. Phys. 1998, 37, 3175. (10) Matsumura, H.; Umemoto, H.; Masuda, A. J. Non-Cryst. Solids 2004, 19, 338. (11) Du, W.; Yang, X.; Povolny, H.; Liao, X.; Deng, X. J. Phys. D: Appl. Phys. 2005, 38, 838. (12) (a) Breddels, P. A.; Kanoh, H.; Sugiura, O.; Matsumura, M. Electronic lett. 1989, 25, 1637. (b) Kanoh, H.; Sugiura, O.; Matsumura, M. Jpn. J. Appl. Phys. 1993, 32, 2613. (c) Gau, S. C.; Weinberger, B. R.; Akhtar, M.; Kiss, Z.; MacDiarmid, A. G. Appl. Phys. Lett. 1981, 39, 436. (d) Ellis, F. B., Jr.; Gordon, R. G. J. Appl. Phys. 1983, 54, 5381. (13) Kumata, K.; Itah, U.; Toyoshima, Y.; Tanaka, N.; Anzai, H.; Matsuda, A. Appl. Phys. Lett. 1986, 48, 1380. (14) Sax, A. F.; Kalcher, J. J. Phys. Chem. 1991, 95, 1768. (15) (a) Perrin, J.; Leroy, O.; Bordage, M. C. Contrib. Plasma Phys. 1996, 36, 3. (b) Arthur, N. L.; Potzinger, P.; Reimann, B.; Steenbergen, H. P. J. Chem. Soc. Faraday Trans. 2 1989, 85, 1447. (c) Fabry, L.; Potzinger, P.; Reimann, B.; Ritter, A.; Steenbergen, H. P. Organometallics 1986, 5, 1231.

3648

J. Phys. Chem. A, Vol. 114, No. 10, 2010

(16) Wu, S. Y.; Raghunath, P.; Wu, S. Y.; Lin, M. C. J. Phys. Chem. A 2010, 114, 633. (17) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, Jr. J. A.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, ReVision C.02; Gaussian, Inc.: Wallingford CT 2004. (18) (a) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (b) Becke, A. D. J. Chem. Phys. 1992, 96, 2155. (c) Becke, A. D. J. Chem. Phys. 1992, 97, 9173. (19) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B 1988, B37, 785. (20) Mebel, A. M.; Morokuma, K.; Lin, M. C. J. Chem. Phys. 1995, 103, 7414.

Varma et al. (21) (a) Cizek, J. AdV. Chem. Phys. 1969, 14, 35. (b) Purvis, G. D.; Bartlett, R. J. J. Chem. Phys. 1982, 76, 1910. (c) Scuseria, G. E.; Janssen, C. L.; Schaefer III, H. F. J. Chem. Phys. 1988, 89, 7382. (d) Scuseria, G. E.; Schaefer III, H. F. J. Chem. Phys. 1989, 90, 3700. (22) (a) Gonzalez, C.; Schlegel, H. B. J. Chem. Phys. 1989, 90, 2154. (b) Gonzalez, C.; Schlegel, H. B. J. Phys. Chem. 1990, 94, 5523. (23) Glasstone, S.; Laidler, K. J.; Eyring, H. The Theory of Rate Processes; McGraw-Hill: New York, 1941. (24) Miller, W. H. J. Am. Chem. Soc. 1979, 101, 6810. (25) Truong, T. N.; Nayak, M.; Huynh, H. H.; Cook, T.; Mahajan, P.; Tran, L.-T. T.; Bharath, J.; Jain, S.; Pham, H. B.; Boonyasiriwat, C.; Nguyen, N.; Andersen, E.; Kim, Y.; Choe, S.; Choi, J.; Cheatham, T. E. III.; ]?>; Facelli, J. C. J. Chem. Inf. Model. 2006, 46, 971. (26) Haaland, A.; Rypdal, K.; Stuger, H.; Volden, H. V. Acta Chem. Scand. 1994, 48, 46. (27) Campbell, J. M.; Strausz, O. P.; Gunning, H. E. Can. J. Chem. 1969, 47, 3759. (28) Pedley, J. P.; Iseard, B. S. CATCH Tables; University of Sussex: 1972, 1976. (29) Katzer, G.; Ernst, M. C.; Sax, A. F.; Kalcher, J. J. Phys. Chem. A 1997, 101, 3942. (30) Chase, M. W., Jr., NIST-JANAF Thermochemical. Tables, 4th ed., J. Phys. Chem. Ref. Data 1998 Monograph No. 9 (Parts I and II).

JP911574K