Ab Initio Chemical Kinetics for SiH3 Reactions with SixH2x+2 (x = 1−4

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J. Phys. Chem. A 2010, 114, 13353–13361

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Ab Initio Chemical Kinetics for SiH3 Reactions with SixH2x+2 (x ) 1-4) P. Raghunath and M. C. Lin* Center for Interdisciplinary Molecular Science, Department of Applied Chemistry, National Chiao Tung UniVersity, Hsinchu 300, Taiwan ReceiVed: August 30, 2010; ReVised Manuscript ReceiVed: NoVember 8, 2010

Gas-phase kinetics and mechanisms of SiH3 reactions with SiH4, Si2H6, Si3H8, and Si4H10, processes of relevance to a-Si thin-film deposition, have been investigated by ab initio molecular orbital and transition-state theory (TST) calculations. Geometric parameters of all the species involved in the title reactions were optimized by density functional theory at the B3LYP and BH&HLYP levels with the 6-311++G(3df,2p) basis set. The potential energy surface of each reaction was refined at the CCSD(T)/6-311++G(3df,2p) level of theory. The results show that the most favorable low energy pathways in the SiH3 reactions with these silanes occur by H abstraction, leading to the formation of SiH4 + SixH2x+1 (silanyl) radicals. For both Si3H8 and n-Si4H10 reactions, the lowest energy barrier channels take place by secondary Si-H abstraction, yielding SiH4 + s-Si3H7 and SiH4 + s-Si4H9, respectively. In the i-Si4H10 reaction, tertiary Si-H abstraction has the lowest barrier producing SiH4 + t-Si4H9. In addition, direct SiH3-for-X substitution reactions forming Si2H6 + X (X ) H or silanyls) can also occur, but with significantly higher reaction barriers. A comparison of the SiH3 reactions with the analogous CH3 reactions with alkanes has been made. The rate constants for low-energy product channels have been calculated for the temperature range 300-2500 K by TST with Eckart tunneling corrections. These results, together with predicted heats of formation of various silanyl radicals and Si4H10 isomers, have been tabulated for modeling of a-Si:H film growth by chemical vapor deposition. Introduction Low-temperature growth of silicon-based thin films, which include hydrogenated amorphous silicon (a-Si:H), polycrystalline silicon (p-Si), and silicon nitride (SiNx),1-5 is one of the important technologies in the semiconductor industry for the application to solar cells, 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 In both processes, silanes and hydrogen are used as the source gases in a chamber. In the CatCVD method, deposition species are generated by the catalytic cracking reaction of source gases on a heated catalyst, instead of the collisions between energetic electrons and molecules as in the PECVD method, leading to the generation of radicals, atoms, and ions. These species diffuse onto the substrate after the secondary reactions in the gas phase, depositing an a-Si:H film through surface reactions. The SiH3 radical plays a central role in the SiH4 PECVD process11 because its lifetime12 is much longer than those of SiH and SiH2. It is well-known that SiH3 is easily generated in the electron dissociation reaction of silane and hydrogen. The mechanisms and rate constants for some silyl radical reactions have been studied experimentally and theoretically.13,14 In 1973, Pollock et al. first studied the possibility of SiH3 + Si2H6 f SiH4 + Si2H5 reaction in a mercury photosensitization of disilane experiment.13e Loh and Jasinski15 investigated the gas-phase reaction of the SiH3 radical (generated by SiH3I photolysis at 248 nm) with SiH4 and Si2H6 at room temperature using infrared diode laser spectroscopy. It was found that contributions of SiH3 + SiD4 f SiH3D + SiD3 and SiH3 + Si2H6 f SiH4 + Si2H5 reactions are kinetically slow. They estimated the upper limits of the rate constants

at 300 K for these reactions as 4 × 10-14 and 7 × 10-15 cm3 molecule-1 s-1, respectively.15 Sax et al. theoretically interpreted the decomposition of silanes up to Si5H12 by reactions with hydrogen atom to form various products and also calculated their heats of formation.16 The generated radicals and ions in the reaction chamber undergo a variety of reactions with silanes before they reach the substrate. To the best of our knowledge, there has been no temperaturedependent study, experimentally or theoretically, on the rate constants for the SiH3 and SixH2x+2 (x ) 1-4) reactions, which are critical to our ability in realistic simulations of a-Si thin film growth by PECVD and Cat-CVD. In the present work, we studied the detailed mechanisms for the title reactions by fully characterizing the potential energy surfaces of these systems, employing ab initio molecular orbital methods. These silyl radical reactions may take place in principle by H-abstraction and substitution processes giving different products as presented below:

SiH3 + SiH4 f SiH4 + SiH3

(R1)

fSi2H6 + H

(R2)

SiH3 + Si2H6 f SiH4 + Si2H5

(R3)

fSi2H6 + SiH3

(R4)

fSi3H8 + H

(R5)

* Corresponding author. E-mail: [email protected].

10.1021/jp1082196  2010 American Chemical Society Published on Web 12/03/2010

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SiH3 + Si3H8 f SiH4 + s-Si3H7

(R6)

fSiH4 + p-Si3H7

(R7)

fSi2H6 + Si2H5

(R8)

SiH3 + n-Si4H10 f SiH4 + s-Si4H9

(R9)

fSiH4 + p-Si4H9

(R10)

fSi2H6 + p-Si3H7

(R11)

SiH3 + i-Si4H10 f SiH4 + t-Si4H9

(R12)

fSiH4 + i-Si4H9

(R13)

fSi2H6 + s-Si3H7

(R14)

The calculated geometries, vibrational frequencies, and heats of formation for new radical products at 0 K are given in the Results and Discussion. We also provide the rate constants for all individual product channels mentioned above predicted by means of transition state theory (TST) along with Eckart tunneling corrections. Computational Methods The geometries of the reactants, transition states, and products have been optimized by Becke’s nonlocal exchange functionals17 with the nonlocal correlation functional of Lee et al.,18 using the B3LYP17 and BH&HLYP19 methods using the standard 6-311++G(3df,2p) basis set. 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.20 For more accurate evaluation of energies for all the species, we have used higher level singlepoint energy calculation with the B3LYP and BH&HLYP optimized geometries at the CCSD(T)21a/6-311++G(3df,2p) level. The single-determinant nature of the wave function of all calculated structures was confirmed by performing T1 diagnostics using CCSD(T) method. These values are given in Table S1. The T1 diagnostics for all the structures are calculated to be within 0.011-0.017, suggesting that our single-reference results are reasonable. The relative energies presented in the PES’s have been corrected for zero-point vibrational energies (ZPVE, unscaled). All the calculations were carried out using the Gaussian 03 program package.22 Rate constants for the given reactions were calculated using the transition state theory (TST)23 with Eckart tunneling corrections24 using the ChemRate program.25 Results and Discussion Potential Energy Surface and Reaction Mechanism. The potential energy surfaces (PES’s) of SiH3 reactions with SiH4, Si2H6, Si3H8, and Si4H10 (n-Si4H10 and i-Si4H10) systems were predicted at the CCSD(T)/6-311++G(3df,2p)//B3LYP/6311++G(3df,2p)+ZPVE and CCSD(T)/6-311++G(3df,2p)// BH&HLYP/6-311++G(3df,2p)+ZPVE levels of theory. All

PESs are presented in Figure 1; the relative energies computed by both methods as shown in the figure agree very closely. The optimized geometries of the reactants, transition states, and products involved in different reaction channels at the BH&HLYP/6-311++G(3df,2p) levels of theory are shown in Figure 2, along with the available experimental values.26 The theoretical geometric parameters of SiH3, SiH4, Si2H6, and Si3H8 are in good agreement with the corresponding experimental values.26 The moments of inertia and the vibrational frequencies of all the species involved in these reactions are listed in Table S1 for the kinetic calculations. The calculated heats of reaction and formation are given in Table 1. The following discussion will be based on the results computed at the CCSD(T)/6311++G(3df,2p)//BH&HLYP/6-311++G(3df,2p) level of theory. Reactions of SiH3 + SiH4. A schematic potential energy diagram for the SiH3 + SiH4 reaction is shown in Figure 1A. In principle, there are two possible reaction paths: H abstraction and SiH3-for-H substitution. In the first process, H-abstraction occurs by SiH3 attacking on one of the hydrogen atoms in SiH4 through TS1 to yield the SiH4 + SiH3 with a barrier of 9.5 kcal/mol, resulting in no net change in the reactant concentration. The transition state (TS1) was found to have D3d symmetry. Its geometrical parameters are given in Figure 2. To validate the accuracy of the theoretical method chosen in this study, we have compared the result for the same reaction using the CCSD(T)/ 6-311++G(3df,2p)//CCSD(T)/6-311+G(d,p) method, 9.3 kcal/ mol, which is very close to the value obtained by the two methods presented above. The barrier is higher than that for H-abstraction in H + SiH4, 5.1 kcal/mol,14a as one would expect. The substitution reaction takes place via TS2 yielding Si2H6 + H with 15.4 kcal/mol endothermicity. The predicted heat of reaction is in good agreement with available experimental and computed values14a as shown in Table 1. The potential barrier of TS2, 19.8 kcal/mol, is 10.3 kcal/mol higher than TS1. Reactions of SiH3 + Si2H6. There are obviously three possibilities: The first mechanism is the direct hydrogen abstraction reaction, occurring by the attack of SiH3 at one of the hydrogen atoms of Si2H6 to produce SiH4 + Si2H5 via TS3 with 6.9 kcal/mol barrier energy shown in Figure 1B. The forming H3Si · · · H bond length is predicted to be 1.819 Å, slightly longer than breaking H-Si bond length, 1.711 Å (see Figure 2). Furthermore, the exothermicity of this channel is computed to be 2.8 kcal/mol, which is close to the upper limit of the experimental value of 0.9 ( 1.2 kcal/mol (Table 1).27 Significantly, the H-abstraction barrier decreases by 2.6 kcal/ mol from SiH4 to Si2H6. In the second mechanism, the reaction takes place by the attack of the SiH3 at one of the silicon atoms of Si2H6 end-on via TS4 (see Figure 2) to give Si2H6 + SiH3, resulting in no change in the reactants. The reaction barrier is 11.3 kcal/mol at the CCSD(T)//BH&HLYP level, which is 4.4 kcal/mol higher than TS3. Finally, the third reaction channel producing Si3H8 + H via TS5 has the highest barrier, 16.7 kcal/ mol, with 13.5 kcal/mol endothermicity. Reactions of SiH3 + Si3H8. The three potential reaction channels considered for this reaction system are shown in Figure 1C. The lowest energy barrier channel is hydrogen abstraction reaction, which occurs by the SiH3 attack on one of the two secondary Si-H bonds in the Si3H8, forming s-Si3H7 (SiH3SiHSiH3) radical and SiH4 via TS6. The barrier height of this reaction predicted by both methods is 4.8 kcal/mol. The exothermicity of the process is predicted to be 5.3 kcal/mol, which is in reasonable agreement with the experimental value, 2.9 ( 2.2 kcal/mol.14b,27 At TS6, the length of the breaking Si · · · H was predicted to be 1.682 Å and the forming H · · · SiH3

Kinetics for SiH3 Reactions with SixH2x+2 (x ) 1-4)

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Figure 1. Potential energy profiles of the SiH3 reactions with SixH2x+2 (x ) 1-4) are in units of kcal/mol. Relative energies with ZPVE are calculated using CCSD(T)/6-311++G(3df,2p)//B3LYP/6-311++G(3df,2p). The values at the CCSD(T)/6-311++G(3df,2p)//BH&HLYP/6311++G(3df,2p) level are given in parentheses.

bond to be 1.865 Å calculated by the BH&HLYP method (Figure 2). The second channel is the SiH3 reaction with one of the terminal Si-H bonds in the Si3H8 forming SiH4 + p-Si3H7 (SiH3SiH2SiH2) via TS7 with a 6.1 kcal/mol barrier. The third channel is the SiH3 radical reacting with one of the terminal Si atoms at the silyl group via TS8 (10.4 kcal/mol) producing Si2H6 + Si2H5. In TS8, the newly formed H3Si · · SiH3 bond length is 2.516 Å, while the SiH2 · · SiH3 bond is stretched by 0.171 Å. The heats of reaction for the SiH4 + p-Si3H7 and Si2H6 + Si2H5 product channels calculated on the basis of experimental data, -1.4 ( 2.2 and 0.9 ( 2.2 kcal/mol, are close to the predicted values, -3.2 and -0.8 kcal/mol, respectively, shown in Table 1. From the PES, we observe that the reaction of the SiH3 radical attacking the terminal Si atom of Si3H8 (via TS8) requires a higher energy as compared to those of the H abstraction reactions. To summarize the results, the H-abstraction barrier from the first p-Si-H bond of Si3H8 decreases slightly to 6.1 kcal/mol from that of the Si2H6 reaction, 6.9 kcal/mol, and that for the s-Si-H bond abstraction is lower by 1.3 kcal/mol. The

TS for SiH3-for-H substitution in Si3H8 has not examined because of its expected high barrier and kinetic insignificance. Reactions of SiH3 + Si4H10. Tetrasilane (Si4H10) has two structural isomers, that is, n-Si4H10 with C2h symmetry and i-Si4H10 with C3V symmetry, as shown in Figure 2. The structure of n-Si4H10 is 1.3 kcal/mol less stable than i-Si4H10 predicted by both methods. Their optimized structures are given in Figure 2. The computed potential energy surfaces of SiH3 reactions with n-Si4H10 and i-Si4H10 are shown in Figure 1D and 1E, respectively. In the SiH3 reaction with n-Si4H10, similar to the SiH3 + Si3H8 reaction, three possible channels were studied as shown in Figure 1D. First is the direct H-abstraction channel occurring by the SiH3 reaction with one of the secondary Si-H bonds to produce SiH4 + s-Si4H9 (SiH3SiHSiH2SiH3) through TS9 (see Figure 2). The barrier height of this reaction was predicted to be 4.6 kcal/mol, which is close to the value 4.8 kcal/mol calculated for the SiH3 + Si3H8 reaction. In the second channel, SiH3 abstracts one of the primary Si-H bonds through TS10 with a 6.1 kcal/mol barrier producing SiH4 + p-Si4H9

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Figure 2. The optimized geometries of the reactants, transition states, and products at the BH&HLYP/6-311++G(3df,2p) level for SiH3 reactions with SixH2x+2 (x ) 1-4). The values in parentheses are the experimental values (ref 26) (length in Å and angle in deg).

(SiH3SiH2SiH2SiH2) exothermically 3.4 kcal/mol. In the third reaction channel, the SiH3 attacks one of the terminal Si atoms of the silyl groups, and requires an activation energy of 10.1 kcal/mol via TS11 to yield Si2H6 + p-Si3H7 with an exothermicity of 0.8 kcal/mol. The potential energy diagram for the SiH3 radical reaction with i-Si4H10 involving three channels is plotted in Figure 1E. Initially, we consider the reaction channels proceeding by direct H-abstraction, which takes place by attacking the H atom at either the tertiary hydrogen atom or the SiH3 group. The first reaction produces t-Si4H9 (Si(SiH3)3 or 1,1-disilyl-disilanyl)

radical and SiH4 with 7.2 kcal/mol exothermicity via TS12 (see Figure 2). The barrier height of this reaction predicted by both methods is 3.1 kcal/mol. At TS12, the length of the breaking Si · · · H was predicted to be 1.664 Å and the forming H · · · SiH3 bond to be 1.905 Å calculated by the BH&HLYP method (Figure 2). The second H-abstraction reaction occurs by the SiH3 attack on one of the primary Si-H bonds, forming SiH4 and i-Si4H9 [(SiH3)2SiHSiH2 or 2-silyl-trisilanyl] radical via TS13. The predicted enthalpy of this reaction is 3.2 kcal/mol, and the required barrier energy is 6.0 kcal/mol, which is essentially the same as those for p-Si-H bond abstraction in Si3H8 and n-Si4H10

Kinetics for SiH3 Reactions with SixH2x+2 (x ) 1-4)

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TABLE 1: Heats of Reaction (∆rH0o) and Heats of Formation (∆fH0o) of Species at 0 K Predicted at the CCSD(T)/ 6-311++G(3df,2p)//BH&HLYP/6-311++G(3df,2p) Level of Theory Given in kcal/mol heat of reaction ∆rH0o species SiH3 SiH3 Si2H5 SiH3 Si3H8 s-Si3H7 p-Si3H7 Si2H5 s-Si4H9 p-Si4H9 n-Si4H10 t-Si4H9 i-Si4H9 i-Si4H10

reactions

SiH3 + SiH4 f SiH4 + SiH3 (R1) SiH3 + SiH4 f Si2H6 + H (R2) SiH3 + Si2H6 f SiH4 + Si2H5 (R3) SiH3 + Si2H6 f Si2H6 + SiH3 (R4) SiH3 + Si2H6 f Si3H8 + H (R5) SiH3 + Si3H8 f SiH4 + s-Si3H7 (R6) SiH3 + Si3H8 f SiH4 + p-Si3H7 (R7) SiH3 + Si3H8 f Si2H6 + Si2H5 (R8) SiH3 + n-Si4H10 f SiH4 + s-Si4H9 (R9) SiH3 + n-Si4H10 f SiH4 + p-Si4H9 (R10) SiH3 + n-Si4H10 f Si2H6 + p-Si3H7 (R11) SiH3 + i-Si4H10 f SiH4 + t-Si4H9 (R12) SiH3 + i-Si4H10 f SiH4 + i-Si4H9 (R13) SiH3 + i-Si4H10 f Si2H6 + s-Si3H7 (R14)

calculated

literaturea

heat of formation ∆fH0o calculated

literaturea 47.7 ( 1.2

0

0

47.7 ( 1.2(48.8)

15.4 (15.4)b

16.4 ( 1.2

48.8 (48.8)b

47.7 ( 1.2

-2.8

-0.9 ( 1.2

57.3 ( 1.2 (58.5)b

59.2, secondary (4.8 kcal/mol) > tertiary (3.1 kcal/mol). These findings are consistent with the known Si-H bond strengths and the bond lengths involved (p-Si-H

) 1.471 Å, s-Si-H ) 1.477 Å, and t-Si-H ) 1.480 Å). Recently, we observed a similar trend in the barriers for p-Habstractions by H atoms from SixH2x+2 (x ) 1-3) reactions, 5.1, 4.0, and 3.8 kcal/mol for x ) 1, 2, and 3, respectively, while that for the s-Si-H abstraction decreases by 0.6 to 3.2 kcal/mol.14 It is worthwhile to compare the above results for the SiH3 + SixH2x+2 reactions with those for the analogous CH3 + alkanes reactions, which have been studied in some detail recently by Dybala-Defratyka et al. and Kungwan et al.29,30 For clarity, we have summarized the computed barriers for p-H-abstraction reactions in Figure 3A and those for H-abstraction from different sites in Figure 3B. Significantly, the trends in the predicted barriers from x ) 1 to x ) 4 and from the p- to the t-site in both series of reactions are seen to be nearly parallel with the barriers for the CH3 + alkanes reactions being higher by 8-9 kcal/mol, reflecting the much stronger corresponding C-H bonds. Another interesting aspect of the finding lies in the X-for-H substitution reactions (where X ) SiH3 or CH3). For the SiH3-

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∆fHo0(SiH3) ) ∆fHo0(Si2H6) + ∆fHo0(H) ∆fHo0(SiH4) - ∆rHo0

Figure 3. (A) Reaction barriers of primary H-abstraction reactions for CH3 + alkanes and SiH3 + silanes. (B) Reaction barriers of primary (p), secondary (s), and tertiary (t) H-abstraction reactions for CH3 + alkanes and SiH3 + silanes (Cx, CxH2x+2 (x ) 1-4); Six, SixH2x+2 (x ) 1-4); i-C4, i-C4H10; and i-Si4, i-Si4H10). Symbols represent both reaction results as indicated in the following: O, CH3 + CxH2x+2; 0, SiH3 + SixH2x+2 (x ) 1-4).

for-H exchange process in the SiH3 + SiH4 reaction presented above, the barrier at TS2 is predicted to be 19.8 kcal/mol. At the transition state, the dissociating H atom forms a bridge between the Si-Si bond of Si2H6 with a C2V symmetry. This bridging conformation stabilizes the structure of Si2H7 and decreases the barrier energy. The bridged two Si-H bonds have the same distance of 1.842 Å, and the forming Si-Si bond length is 2.401 Å, which is 0.06 Å longer than that of Si2H6 (see Figure 2). The bond angle of ∠HSiSi is 49.3°. Significantly, for the analogous CH3 + CH4 f C2H6 + H reaction, we found that it requires a very high barrier of 53.4 kcal/mol (TS-S2). In addition, its transition state has a linear C-C-H structure with C3V symmetry, the breaking C-H bond lengthens from 1.081 to 1.422 Å, and the forming C-C bond becomes 1.869 A, which is longer by 0.351 Å than a regular C-C bond length (see Figure S2). The transition state structures in the two analogous substitution reactions are, therefore, seen to be very different, resulting in part in the very different energy barriers. Heats of Formation. The predicted heats of formation of all the species related to SiH3 reactions with SixH2x+2 (x ) 1-4) are presented in Table 1 on the basis of the energies computed at the CCSD(T)//BH&HLYP level. The heats of formation of all the species were determined by combining the computed heats of reaction (∆rH0o) and experimental heats of formation (∆fH0o) at 0 K. The heat of formation is calculated using the general formula given below for R2 reaction as an example:

Theoretically, the heats of formation of n-Si4H10 and i-Si4H10 are available as 38.3 and 37.5 kcal/mol at 298 K.27b The corresponding values at 0 K, ∆fH0o ) 43.8 and 42.9 kcal/mol, are calculated using the [H°(0) - H°(298.15 K)] values of n-Si4H10 -7.71 kcal/mol and i-Si4H10 -7.85 kcal/mol and standard reference states of Si(Cr) and H2, -0.77 and -2.02 kcal/ mol, respectively.27c Thus, by using these values and experimental heats of formation, we obtained the values at 0 K of n-Si4H10, i-Si4H10, s-Si4H9, p-Si4H9, t-Si4H9, and i-Si4H9 ((SiH3)2SiHSiH2) to be 45.3, 44.4, 75.7, 77.7, 72.9, and 76.9 kcal/mol, respectively, with an estimated error of (1.2 kcal/ mol based on the experimental heat of formation of SiH3 (47.7 ( 1.2 kcal/mol). Our predicted heats of formation of the species listed in Table 1 are in good agreement with the values derived from available experimental and theoretical data.14b,27 In our previous study,14a we reported the heats of formation of SiH3 (49.0 kcal/mol) and Si2H5 (58.6 kcal/mol) radicals through the isodesmic reactions, which agree well with experimental data also. To assess the quality of our theoretical predictions, we derived accurate enthalpies of formation for Si3H7 and Si4H9 through the different isodesmic reactions given in Table 2. The predicted heats of formation of these species agree well with the values derived from SiH3 reactions given in Table 1 as well as with other available theoretical and experimental results. Rate Constant Calculations. Rate constants for all the product channels of SiH3 reactions with SixH2x+2 (x ) 1-4) have been calculated by the transition state theory (TST) with Eckart tunneling corrections (denoted as TST/Eckart), employed in the ChemRate program.23-25 For the calculations, we used the CCSD(T)//BH&HLYP barrier heights and the BH&HLYP/ 6-311++G(3df,2p) molecular parameters of the reactants and transition states presented in Table S1. We have also carried out SiH3 + SiH4 reaction using the CCSD(T)/6-311++G(3df,2p)// CCSD(T)/6-311+g(d,p) level, the predicted rate constant agreeing well with the BH&HLYP method. However, as compared to the same reactions, the CCSD(T)//B3LYP method slightly overpredicted the rate constants due to smaller frequencies obtained by B3LYP. These results are given in Supporting Information Figure S3a. In our calculation, the lowest vibrational modes, 20 cm-1 in TS1, 27 cm-1 in TS3, 9 cm-1 in TS6, 34 cm-1 in TS7, 25 cm-1 in TS9, 12 cm-1 in TS10, 14 cm-1 in TS12, and 26 cm-1 in TS13 corresponding to the SiH3 torsional motions, were treated as a one-dimensional free rotor. The SiH3 groups in Si3H8 and Si4H10 have small internal rotation barriers. However, in our previous study,14a we found that the contribution of hindered rotations does not have any effect on the predicted rate constant; accordingly, they are treated as free rotors. The calculated rate constant expressions for all the reaction channels (H-abstraction and substitution) R1-R14 obtained by three-parameter fitting for the 300-2500 K temperature range are given in Table 3, along with the rate constants at 300 K. For the SiH3 + SiH4 reaction, two reaction channels take place with widely different rates because the barrier at TS1 is less than that at TS2 by 10.3 kcal/mol as shown in Figure S3b. In the case of SiH3 + Si2H6 reaction, the formation of products SiH4 + Si2H5 (kR3) is predominant when compared to other two reactions as shown in Figure S3c. The experimentally estimated upper limit of the rate constant for the SiH3 + Si2H6 f SiH4 + Si2H5 reaction is 7 × 10-15 cm3 molecule-1 s-1 at 300 K, which is consistent with our predicted value (1.2 × 10-16 cm3

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TABLE 2: Heats of Reaction (∆rH0o) and Heats of Formation (∆fH0o) of All the Radicals Related to Si3H7 and Si4H9 Calculated by Using the Isodesmic Reactions at 0 K Are Given in kcal/mol heat of reaction ∆rH0o species

reactions

heat of formation ∆fH0o

calculateda

calculated

literatureb

p-Si3H7

p-Si3H7 + C3H8 f Si3H8 + p-C3H7

13.3

68.2 ( 1

69.3d

s-Si3H7

s-Si3H7 + C3H8 f Si3H8 + s-C3H7

12.1

(68.6)c 67.7 ( 1

67.8d

p-Si4H9 + n-C4H10 f n-Si4H10 + p-C4H9 s-Si4H9 + i-C4H10 f i-Si4H10 + s-C4H9 t-Si4H9 + i-C4H10 f i-Si4H10 + t-C4H9 i-Si4H9 + i-C4H10 f i-Si4H10 + i-C4H9

p-Si4H9 s-Si4H9 t-Si4H9 i-Si4H9

13.3

(66.6) 75.3

12.3

74.4

12.6

74.1

13.5

77.7

c

a All reaction enthalpies include ZPE corrections calculated at the CCSD(T)/6-311++G(3df,2p)//BH&HLYP/6-311++G(3df,2p) level of theory. b The experimental heats of formation at 0 K values are given in kcal/mol C3H8 ) -19.7; p-C3H7 ) 28.3; s-C3H7 ) 26.6; n-C4H10 (n-butane) ) -23.5; i-C4H10 (isobutane) ) -25.4; p-C4H9 (CH3CH2CH2CH2) ) 21.3; s-C4H9 (CH3CH2CHCH3) ) 19.4; t-C4H9 (C(CH3)3) ) 18.4; i-C4H9 ((CH3)2CHCH2) ) 22.9; Si3H8 ) 33.5 ( 1; n-Si4H10 ) 43.8; i-Si4H10 ) 42.9 (refs 14b, 27, and 28). c Our calculated values are taken from ref 14b. d Theoretical values of s-Si3H7 ) 67.8 (64.1); p-Si3H7 ) 69.3 (65.7) (calculated from 298 K values given in parentheses (taken from ref 27b) using vibrational frequencies; see ref 14b).

TABLE 3: Calculated Rate Constants (cm3 molecule-1 s-1) for the SiH3 Reactions with SixH2x+2 (x ) 1-4) Using the CCSD(T)/ 6-311++G(3df,2p)//BH&HLYP/6-311++G(3df,2p) Level of Theory reactions

SiH3 + SiH4 f SiH4 + SiH3 SiH3 + SiD4 f SiH3D + SiD3 SiH3 + SiH4 f Si2H6 + H SiH3 + Si2H6 f SiH4 + Si2H5 SiH3 SiH3 SiH3 SiH3 SiH3 SiH3 SiH3 SiH3 SiH3 SiH3 SiH3 a

+ + + + + + + + + + +

Si2H6 f Si2H6 + SiH3 Si2H6 f Si3H8 + H Si3H8 f SiH4 + s-Si3H7 Si3H8 f SiH4 + p-Si3H7 Si3H8 f Si2H6 + Si2H5 n-Si4H10 f SiH4 + s-Si4H9 n-Si4H10 f SiH4 + p-Si4H9 n-Si4H10 f Si2H6 + p-Si3H7 i-Si4H10 f SiH4 + t-Si4H9 i-Si4H10 f SiH4 + i-Si4H9 i-Si4H10 f Si2H6 + s-Si3H7

3-param (300-2500 K) 3.47 × 10

-22

T

-22

3.6

300 K 3.66 × 10-18

exp[-3380/T]

2.43 × 10 T exp[-3206/T] 2.09 × 10-21 T3.4 exp[-3781/T]b 1.46 × 10-20 T3.1 exp[-4402/T]

7.92 × 10-18a 1.60 × 10-18b 3.06 × 10-19

8.67 × 10-24 T3.0 exp[-8799/T]

2.34 × 10-28

a

exp[-2305/T]

1.19 × 10-16

5.83 × 10-23 T3.2 exp[-4949/T]

e7.0 × 10-15c 3.77 × 10-22

5.69 × 10-24 T3.6 exp[-7649/T]

4.08 × 10-26

8.88 × 10

-22

3.7

2.80 × 10

-21

3.19 × 10

-21

9.17 × 10

-23

4.62 × 10

-21

T

3.4

T

3.3

exp[-1504/T]

2.38 × 10-15

T

3.4

exp[-2020/T]

8.57 × 10-16

T

3.2

exp[-4536/T]

2.14 × 10-21

T

3.3

exp[-1396/T]

5.51 × 10-15

2.15 × 10-21 T3.3 exp[-2017/T]

5.23 × 10-16

7.61 × 10

-23

T

3.2

4.58 × 10

-21

exp[-4373/T]

2.95 × 10-21

T

3.1

3.86 × 10

-21

exp[-864/T]

1.59 × 10-14

T

3.4

exp[-1959/T]

1.24 × 10-15

1.28 × 10-22 T3.2 exp[-4176/T]

9.0 × 10-21

Calculated from CCSD(T)//CCSD(T). b Calculated from CCSD(T)//B3LYP. c Experimental value is taken from ref 16.

molecule-1 s-1) at the same temperature.16 All the H-abstraction channels appear to have bigger tunneling effects at low temperatures because of the larger imaginary frequencies at the transition states. For the substitution reactions, R4 and R5, the tunneling effect is negligible as expected due to their small imaginary frequencies (see Table S1) as shown in Figure S3c. In the case of SiH3 reactions with Si3H8 and n-Si4H10, Habstraction (R6 and R9) from one of the secondary Si-H bonds yielding s-Si3H7 and s-Si4H9, respectively, is more dominant (see Figure S3d and S3e). For H-abstraction reactions from primary Si-H bonds (R7 and R10), the rates are smaller at low temperatures, reflecting their higher barriers; however, as the temperature increases, they become more competitive. Finally, in the SiH3 + i-Si4H10 reactions, H-abstraction from the tertiary Si-H bond is dominant, resulting from the weaker Si-H bond, as shown in Figure 1f. From Table 3, we can conclude that the contributions to the overall rate constants from the substitution reactions, R2, R4, R5, R8, R11, and R14, are minor due to their

relatively higher reaction barriers and tighter transition states (see Figure S3 and Table S1). We compared all the H-abstraction reactions of SiH3 with SixH2x+2 (x ) 1-4) in Figure 4. Graphically, we can see that R12 for SiH3 attack at the tertiary Si-H bond is the major reaction over the whole temperature range because of its low energy barrier, 3.1 kcal/mol, as compared to the reactions with secondary Si-H bonds, R9 (4.6 kcal/mol) and R6 (4.8 kcal/ mol), and with H-abstraction reactions with primary Si-H bonds, R13 (6.0 kcal/mol), R10 (6.1 kcal/mol), R7 (6.1 kcal/ mol), and R3 (6.9 kcal/mol). These processes are relatively minor at low temperatures, but they become more competitive at higher temperatures (see Figure 4). No temperature-dependent experimental data are available for quantitative comparison. Conclusion Kinetics and mechanisms of SiH3 reactions with SixH2x+2 (x ) 1-4) have been investigated at the CCSD(T)/6-311++G-

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J. Phys. Chem. A, Vol. 114, No. 51, 2010

Raghunath and Lin 17-A-07-S2-0043. M.C.L. acknowledges the support from the Taiwan Semiconductor Manufacturing Co. for the TSMC Distinguished Professorship and from the National Science Council of Taiwan for the Distinguished Visiting Professorship at National Chiao Tung University in Hsinchu, Taiwan. P.R. would also like to acknowledge partial support from the ATU Plan of MOE, Taiwan, and thank Dr. Z. F. Xu for useful discussions.

Figure 4. The predicted rate constants for all the H-abstraction reaction products related to SiH3 reactions with SixH2x+2 (x ) 1-4) using TST with Eckart tunneling corrections calculated at the CCSD(T)/6311++G(3df,2p)//BH&HLYP/6-311++G(3df,2p) level. Experimental rate constant value as an upper limit of SiH3 + Si2H6 f SiH4 + Si2H5 (R3) at 300 K is taken from ref 16.

(3df,2p)//B3LYP/6-311++G(3df,2p) and CCSD(T)/6-311+ +G(3df,2p)//BH&HLYP/6-311++G(3df,2p) levels of theory. All these reactions can proceed via two distinct mechanisms, H-abstraction and SiH3-for-X (X ) H or silanyls) substitution, and between them the H-abstraction mechanism is energetically more favorable. In the hydrogen abstraction reactions, the energy barriers decrease according to the order primary (6.0-9.6 kcal/ mol) > secondary (4.6-4.8 kcal/mol) > tertiary (3.1 kcal/mol), consistent with the strengths of the corresponding Si-H bonds. For the primary Si-H abstraction by SiH3, the predicted energy barriers decrease according to the order SiH4 (9.6 kcal/mol) > Si2H6 (6.9 kcal/mol) > Si3H8 (6.1 kcal/mol) ≈ n-/i-Si4H8 (6.0 kcal/mol). The above trends are essentially similar to those predicted for the analogous CH3 + alkanes reactions, albeit with much greater energy barriers, consistent with the much stronger corresponding C-H bonds. For the X-for-H substitution reactions, using SiH4 and CH4 as examples (where X ) SiH3 or CH3), their corresponding transition state structures were found to be very different, with the departing H atom in the silane reaction forming a bridged ring structure with the two Si atoms, whereas the departing H atom in the methane reaction forms a colinear C-C-H structure, which has an exchange barrier 2.7 times higher than that in the former reaction. The computed heats of formation ∆fH0o at 0 K for n-Si4H10, i-Si4H10, s-Si4H9, p-Si4H9, t-Si4H9, and i-Si4H9 are 45.3, 44.4, 75.7, 77.7, 72.9, and 76.9 kcal/mol, respectively, with an estimated error of (1.2 kcal/mol. These and the values for the smaller silanyl radicals (SiH3, Si2H5, p-Si3H7, and s-Si3H7) agree very well with available theoretical and experimental results within the error. The rate constants for all the channels of the SiH3 + SixH2x+2 (x ) 1-4) reactions have been calculated over the temperature range 300-2500 K using transition state theory (TST) along with Eckart tunneling corrections. These results allow us to better understand the overall reactions as well as to provide for the first time reliable kinetics for a more realistic simulation of silane-hydrogen-based Si-thin film growth by PECVD and Cat-CVD. Acknowledgment. We deeply appreciate the support of this work by the Ministry of Economics under contract no. 98-EC-

Supporting Information Available: Calculated T1diag, moments of inertia, and vibrational frequencies of the species involved in the SiH3 reactions with SixH2x+2 (x ) 1-4) computed at the BHandHLYP/6-311++G(3df,2p) level are given in Table S1. Potential energy profiles and optimized geometries of the CH3 reactions with CH4 and C2H6 are given in Figures S1 and S2. Rate constants for all the H-abstraction and substitution channels of the SiH3 + SixH2x+2 (x ) 1-4) reactions have been calculated over the temperature range 300-2500 K using transition state theory and transition state theory (TST) along with Eckart tunneling corrections and are given in Figure S3. This material is available free of charge via the Internet at http://pubs.acs.org. 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. Electron. 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) (a) Jasinski, J. M.; Gates, S. M. Acc. Chem. Res. 1991, 24, 136. (b) Jasinski, J. M.; Meyerson, S. B.; Scott, B. A. Annu. ReV. Phys. Chem. 1987, 38, 109. (12) Itabashi, N.; Kato, K.; Nishiwaki, N.; Goto, T.; Yamada, C.; Hirota, E. Jpn. J. Appl. Phys. 1989, 28, L325. (13) (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. (d) Meeks, E.; Larson, R. S.; Ho, P.; Apblett, C.; Han, S. M.; Edelberg, E.; Aydil, E. S. J. Vac. Sci. Technol., A 1998, 16, 544. (e) Pollock, T. L.; Sandhu, H. S.; Jodhan, A.; Strausz, O. P. J. Am. Chem. Soc 1973, 95, 1017. (14) (a) Wu, S. Y.; Raghunath, P.; Wu, J. S.; Lin, M. C. J. Phys. Chem. A 2010, 114, 633. (b) Varma, D. H.; Raghunath, P.; Lin, M. C. J. Phys. Chem. A 2010, 114, 3642. (15) Loh, S. K.; Jasinski, J. M. J. Chem. Phys. 1991, 95, 4914. (16) Sax, A. F.; Kalcher, J. J. Phys. Chem. 1991, 95, 1768. (17) (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. (18) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B 1988, B37, 785. (19) Becke, A. D. J. Chem. Phys. 1993, 98, 1372–1377. (20) (a) Gonzalez, C.; Schlegel, H. B. J. Chem. Phys. 1989, 90, 2154. (b) Gonzalez, C.; Schlegel, H. B. J. Phys. Chem. 1990, 94, 5523. (21) (a) Pople, J. A.; Head-Gordon, M.; Raghavachari, K. J. Chem. Phys. 1987, 87, 5968. (b) Lee, T. J.; Taylor, P. R. Int. J. Quantum Chem. Symp. 1989, 23, 199. (22) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; 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.;

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