J. Phys. Chem. A 2010, 114, 633–639
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Ab Initio Chemical Kinetic Study for Reactions of H Atoms with SiH4 and Si2H6: Comparison of Theory and Experiment S. Y. Wu,a P. Raghunath,b J. S. Wu,a and M. C. Lin*,b a
Department of Mechanical Engineering, National Chiao Tung UniVersity, Hsinchu 300, Taiwan, and b Center for Interdisciplinary Molecular Science, Institute of Molecular Science, National Chiao Tung UniVersity, Hsinchu 300, Taiwan ReceiVed: August 25, 2009; ReVised Manuscript ReceiVed: October 30, 2009
The reactions of hydrogen atom with silane and disilane are relevant to the understanding of catalytic chemical vapor deposition (Cat-CVD) and plasma enhanced chemical vapor deposition (PECVD) processes. In the present study, these reactions have been investigated by means of ab initio molecular-orbital and transitionstate theory calculations. In both reactions, the most favorable pathway was found to be the H abstraction leading to the formation of SiH3 and Si2H5 products, with 5.1 and 4.0 kca/mol barriers, respectively. For H + Si2H6, another possible reaction pathway giving SiH3 + SiH4 may take place with two different mechanisms with 4.3 and 6.7 kcal/mol barriers for H-atom attacking side-way and end-on, respectively. To validate the calculated energies of the reactions, two isodesmic reactions, SiH3+CH4fSiH4+CH3 and Si2H5+C2H6fSi2H6+C2H5 were employed; the predicted heats of the formation for SiH3 (49.0 kcal/mol) and Si2H5 (58.6 kcal/mol) were found to agree well with the experimental data. Finally, rate constants for both H-abstraction reactions predicted in the range of 290-2500 K agree well with experimental data. The result also shows that H+Si2H6 producing H2+Si2H5 is more favorable than SiH3+SiH4. 1. 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), is one of the most important technologies required in the semiconductor industry. These films have been widely used as the basic material for solar cells, thin film transistors (TFTs) for liquid crystals, and light emitting diodes, among others. These films are prepared either by plasma enhanced chemical vapor deposition (PECVD) or, increasingly, by catalytic chemical vapor deposition (Cat-CVD).1-10 Both methods employ silane and hydrogen as the source gases. In PECVD, source gases are decomposed by collisions with energetic electrons, which are generated in a gas discharge. In contrast, in Cat-CVD, source gases are decomposed by the catalytic cracking reaction with a heated hightemperature catalyst (such as tungsten). These silane-hydrogenbased physical-chemical processes are very complex. Both PECVD and Cat-CVD involve gas-phase reactions in a chamber; surface reactions occur at the substrate with species transporting in the chamber. Understanding these phenomena is vital to the successful development and better application of the technology, which may eventually lead to optimization for production of silicon thin films and lower material cost. Although the experiments proved useful in understanding the physics to some extent, detailed modeling can definitely play a key role in advancing these technologies in the future. Modeling of these complicated physicochemical phenomena requires accurate rate constants for the chemical processes involved. Some information on the kinetics and mechanisms for silane-hydrogen-based chemistry can be found.11-16 However, in these studies, the rate constants of silane destruction related reactions are questionable because they were either estimated based on incomplete/simple theory or obtained under very * Corresponding author; email address:
[email protected].
limited experimental conditions. Reliable modeling of these processes is hampered by the inaccurate data of the rate constants of silane-related reactions. Thus, how to obtain these rate coefficients accurately is among one of the top priorities in advancing related modeling of silane-hydrogen-based PECVD or Cat-CVD processes. Unfortunately, obtaining these rate constants accurately through experiments can be very expensive or even impossible. Recent progress in the first-principles quantum chemistry calculation has provided a viable route to obtain these rate constants accurately. It is well-known that SiH3 is easily generated in the silane-hydrogen-based chemical process: H + SiH4 f H2 + SiH3 (reaction A). Abundant SiH3 in the gas phase can easily form Si2H6, which further reacts with H through the following likely channels: H + Si2H6 f H2 + Si2H5 (reaction B1) or H + Si2H6 f SiH3 + SiH4 (reaction B2). There were several previous studies which predicted the rate constant of reaction A using quantum chemistry calculations; the results were found to agree well with the available experimental data [for forward reaction17-19 and for forward and reverse reactions20]. However, there was no study in predicting the rate constants of reactions B1 and B2 using first-principles calculations, except that of Kerwin and Doren,21 who only calculated the potential energy surface of reaction B2. In the present study, the objectives are to elucidate the mechanisms and to predict quantitatively the rate constants of the reactions (A, B1, and B2) by a full quantum chemical calculation. Predicted rate constants are then compared with experiments and previous predictions wherever are available. Reaction (A) was studied essentially for validation of the computational methods employed. The present work is organized as follows: The Computational Methods are briefly described in Section 2 followed by presentation of the Results and Discussion based on the prediction of potential energy surfaces and reaction mechanisms, validation by calculating
10.1021/jp908222g 2010 American Chemical Society Published on Web 11/25/2009
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heats of formation with isodesmic reactions, and the prediction of reaction rate constants. Finally, the Conclusions of the current studies are summarized with possible future studies.
∆′ ) E[UMP2/6-311 + G(3df,2p)] E[UMP2/6-311G(2df,p)] - E[UMP2/6-311 + G(d,p)] + E[UMP2/6-311G(d,p)] ∆E(HLC,CC2) ) -5.78nβ-0.19nR
2. Computational Methods
where nR and nβ are the numbers of R (spin up) and β (spin down) valence electrons with nR g nβ. Moreover, the heats of formation are calculated by the energies obtained at the CCSD(T)/6-311++G(3df,2p)//CCSD(T)/6-311+G(d,p) level. In our calculations, equilibrium geometrical parameters of SiH4 and Si2H6 molecules are in good agreement with the experiment data. All of the calculations have been carried out with the GAUSSIAN 03 program.26 The rate constants for all reactions were calculated by the transition state theory (TST) with Eckart quantum tunneling corrections in TheRate program at the CSEOnline Internet site.27
The geometries of the reactants, products and transition states for the H + SiH4 and H + Si2H6 reactions have been optimized with Becke’s three-parameter nonlocal exchange functionals with the nonlocal correction functionals of Lee, Yang and Parr method (B3LYP)22 using the 6-311++G(3df,2p) basis set and further improved with Coupled-Cluster method using Single, Double, and Perturbative Triple excitations (CCSD(T))23 using the 6-311+G(d,p) basis set. The vibrational frequencies of all species, also calculated at both levels of theory, have been used to characterize stationary points, zero-point energy (ZPE) corrections, and rate constant calculations. The number of imaginary frequencies is 1 for transition states and 0 for local minima. The geometries of transition states are used as an input for IRC (Intrinsic Reaction Coordinate) calculations to verify the connectivity of the reactants and products.24 To obtain more reliable energies of all species, we have used the single-point energy (SPE) calculation with CCSD(T)/6311+G(d,p) optimized geometries at the CCSD(T)/6311++G(3df,2p) level as well as the G2M(CC2) method,25 which employed the series of calculations with the B3LYP/6311++G(3df,2p) optimized geometries and zero point energies (ZPE). The total G2M(CC2) energy with ZPE corrections is calculated as follows:
E[G2M(CC2)] ) E[PMP4/6-311G(d,p)] + ∆E(+) + ∆E(2df) + ∆E(CC) + ∆′ + ∆E(HLC,CC2) + ZPE ∆E(+) ) E[PMP4/6-311 + G(d,p)] E[PMP4/6-311G(d,p)] ∆E(2df) ) E[PMP4/6-311G(2df,p)] E[PMP4/6-311G(d,p)] ∆E(CC) ) E[CCSD(T)/6-311G(d,p)] E[PMP4/6-311G(d,p)]
3. Results and Discussions 3.1. Potential Energy Surfaces and Reaction Mechanisms. 3.1.1. Reactions of Hydrogen with Silane (SiH4). In order to validate the accuracy of the theoretical methods chosen in this study, we first consider the formation of SiH3 when silane reacts with hydrogen. We have conducted the calculations for all of the reaction steps by using the two different methodologies, namely B3LYP and CCSD(T). The resulting relative energies of the reactants, products, and transition states at 0 K for this reaction by all of the employed methods are summarized in Table 1. Corresponding vibrational frequencies and moments of inertia of all species used in the rate constant calculations at the CCSD(T)/6-311+G(d,p) level are summarized in Table 2. The optimized geometries of the reactants, transition states and products at the same level of theory are shown in Figure 1. For SiH4, its Si-H bond length, 1.477 Å, is in close agreement with the experimental value 1.481 Å.28 The potential energy diagram obtained at the CCSD(T)/6-311++G(3df,2p)//CCSD(T)/6311+G(d,p) level of theory is presented in Figure 2. The relative energies are calculated with respect to the reactants, H + SiH4. The likely mechanism is the hydrogen atom attacks on one of the hydrogen atoms in SiH4 through TS1 to yield the doublet
TABLE 1: Relative Energiesa (kcal/mol) of Various Species at 0 K in the H + SiH4 Reaction Calculated at the Different Levels species
B3LYP/ 6-311++G(3df,2p)
G2M(CC2)
CCSD(T)/ 6-311+G(d,p)
CCSD(T)/6-311++G(3df,2p)// CCSD(T)/6-311+G(d,p)
H + 1SiH4 TS1 1 H2 + 2SiH3
0.0 1.0 -15.0
0.0 4.9 -13.0
0.0 6.1 -12.8
0.0 5.1 -13.4
2 2
a
Energies are ZPE-corrected.
TABLE 2: Vibrational Frequencies and Moments of Inertia for Reactants, Intermediates, Transition States, And Products of the H+ SiH4 and H+ Si2H6 Reactions at CCSD (T) /6-311+G(d,p) Level of Theory species
Ia,Ib,Ic(a.u.)
frequencies (cm-1)
H2 SiH3 SiH4 Si2H5 Si2H6
0.0, 1.0, 1.0 12.7, 12.7, 21.4 21.0, 21.0, 21.0 33.8, 337.7, 346 41.7, 356.4, 356.4
TS1 TS2
21.2, 48.1, 48.1 64.8, 374.9, 397.8
TS3
49.1, 372.3, 377.8
TS4
44.1, 398.9, 399
4421 801, 957, 957, 2259, 2293, 2293 955, 955, 955, 991, 991, 2291, 2296, 2296, 2296 144, 404, 432, 444, 623, 655, 905, 955, 968, 970, 2246, 2256, 2268, 2272, 2280 147, 389, 389, 442, 653, 653, 884, 958, 959, 963, 975, 975, 2260, 2268, 2269, 2270, 2276, 2277 i1355, 309, 310, 902, 963, 963, 999, 1000, 1156, 2277, 2295, 2295 i1242, 112, 165, 291, 409, 437, 453, 657, 677, 895, 948, 962, 968, 971, 986, 1223, 2256, 2267, 2268, 2274, 2279 i192, 172, 308, 392, 541, 677, 715, 769, 824, 873, 930, 988, 989, 997, 1043, 2122, 2142, 2281, 2284, 2295, 2302 i752, 156, 216, 219, 373, 459, 460, 752, 752, 872, 873, 894, 960, 960, 1000, 2179, 2228, 2229, 2254, 2269, 2269
Reactions of H Atoms with SiH4 and Si2H6
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Figure 1. All optimized geometries of intermediates and transition states are calculated using CCSD(T)/6-311+G(d,p) level for H + SiH4 and H + Si2H6 reaction. Bond lengths are in angstroms and angles in degree.
SiH3 radical and H2. The barrier at TS1 is predicted to be 5.1 kcal/mol, which may be compared with the values of 1.0 and 4.9 kcal/mol calculated by B3LYP and G2M(CC2) methods, respectively. Our results obtained at higher levels of theory are in close agreement with those reported earlier: 5.3 kcal/mol by Crosby et al. with CCSD/aug-cc-pVDZ,20 5.5 kcal/mol by Yu et al. with the G2//QCISD/6-311+G(d,p) method,18 and 5.1 kcal/ mol from an analytical PES constructed by Espinosa-Garcı´a et al.,19 which was employed in the Quantum Instanton (QI) calculation by Wang et al.17 At TS1, the length of the forming H · · · H bond was computed to be 1.134 Å, the breaking Si-H bond length to be 1.598 Å, and the H-H-Si bond angle to be collinear at 180.0° as shown in Figure 1. The exothermicity of the process is predicted to be 13.4 kcal/mol. This value is in good agreement with the experimental heat of reaction, -14.5 ( 1.2 kcal/mol. 3.1.2. Reactions of Hydrogen with Disilane (Si2H6). In this section, we study the mechanism for the H + Si2H6 reaction based on the PES computed at the CCSD(T)/6-311++G(3df,2p)//
CCSD(T)/6-311+G(d,p) level of theory presented in Figure 3. The calculated relative energies of the reactants, products, and transition states of different methods at 0 K are listed in Table 3 and their optimized geometries are shown in Figure 1. For the Si2H6 structure, the bond lengths of Si-H, Si-Si, and the bond angle of ∠HSiSi are 1.481 Å (1.486 Å), 2.343 Å (2.327 Å), and 110.3° (111.0°), respectively, with the experimental values given in parentheses.28 There are two possible reaction mechanisms for the interaction of Si2H6 with H, as alluded to in the introduction. They are respectively described in the following. The first mechanism is the direct hydrogen abstraction reaction, occurring by the attack of H at one of the hydrogen atoms of Si2H6 to produce the doublet Si2H5 radical and H2 via TS2. The forming H · · · H bond length is predicted to be 1.192 Å, while the breaking H-Si bond length is 1.579 Å. Furthermore, the barrier and exothermicity of this channel are computed to be 4.0 and 16.1 kcal/mol, respectively, at the CCSD(T)/6311++G(3df,2p)//CCSD(T)/6-311+G(d,p) level. Due to the
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H + SiH4 98 H2 + SiH3 B1
H + Si2H6 98 H2 + Si2H5 B2
98 SiH3 + SiH4 Figure 2. Potential energy surface of the H + SiH4 reaction. Relative energies (kcal/mol) calculated by the CCSD(T)/6-311++G(3df,2p)// CCSD(T)/6-311+G(d,p) + ZPVE levels of theory at 0 K.
3.2. Heats of the Formation. For the purpose of confirming the computed results and calculating the rate constants of the reactions, we compare the heats of formation ∆fH0° (0 K) of the radical products with experimental values based on the heats of the reaction ∆rH0° (0K) computed at the CCSD(T)/6311++G(3df,2p)//CCSD(T)/6-311+G(d,p) level. In addition, isodesmic reactions are also considered to verify the calculated heats of formation, specifically by employing SiH3 + CH4 f SiH4 + CH3 and Si2H5 + C2H6 f Si2H6 + C2H5. The predicted heats of formation including SiH3 and Si2H5 are presented in Table 4. The heat of formation of SiH3 is determined by combining the computed heat of reaction from reaction (A) with experimental ∆fH0° (0 K) values for SiH4 (10.5 kcal/mol), H (51.66 kcal/mol) and H2 (0.0 kcal/mol) which are taken from NISTJANAF Tables.29 The heats of formation are calculated by using the general formula given below:
∆fH0o(SiH3) ) ∆fH0o(SiH4) + ∆fH0o(H) - ∆fH0o(H2) + Figure 3. Potential energy surface of the H + Si2H6 reaction. Relative energies (kcal/mol) calculated by the CCSD(T)/6-311++G(3df,2p)// CCSD(T)/6-311+G(d,p) + ZPVE levels of theory at 0 K.
importance of this transition state barrier for prediction of the metathetical reaction rate constant, the barrier is also calculated at the B3LYP/6-311++G(3df,2p), G2M(CC2), and CCSD(T)/ 6-311+G(d,p) levels, giving rise to 0.6, 3.7, and 5.0 kcal/mol, respectively. The value of the G2M(CC2) method, which is a multistep SPE computation, agrees closely with that obtained by the direct CCSD(T) calculation mentioned above. In the second mechanism, the reaction takes place by the attack of the H atom at one of the silicon atoms of Si2H6 to form the doublet radical SiH3 and SiH4. In principle, there are two possible transition states. One of the possibilities is that the incoming hydrogen atom inserted into Si-Si bond of Si2H6 from the side, namely TS3 whose geometry is shown in Figure 1. TS3 is of a three-membered ring structure, in which the forming Si-H and H-Si bond lengths are 1.857 Å and 1.855 Å, respectively, and the Si-Si breaking bond length is elongated to 2.399 Å, which is 0.056 Å longer than that of Si2H6. The second possibility is that the incoming hydrogen atom attacks a silicon atom of Si2H6 end-on from the backside via TS4 (see Figure 1). The transition state of this reaction channel involves the new forming Si-H bond, the separating Si-Si bond and the elongated Si-H bond attached to the interacting Si atom with their lengths at 1.783, 2.411, and 1.486 Å, respectively. The energy of the TS3 barrier is 4.3 kcal/mol, which is
∆rH0o The heats of reaction ∆rH0° of the products H2 + SiH3 (from reaction A), H2 + Si2H5 and SiH3 + SiH4 (from reaction B) are predicted to be -13.4, -16.1, and -15.4 kcal/mol, respectively; they are in good agreement with experimental values (see Table 4). It is worth noting that predicted heats of formation of SiH3 and Si2H5 at 0 K listed in Table 4, 48.8 and 58.5 kcal/mol, also agree very well with the values derived from isodesmic reactions, 49.0 and 58.6 kcal/mol, as well as with the experimental data, 47.7 ( 1.2 and 59.2 (
