Ab Initio Chemical Kinetics for the Unimolecular Decomposition of Si2H5 Radical and Related Reverse Bimolecular Reactions

Ab Initio Chemical Kinetics for the Unimolecular

Decomposition of Si

₂

H

₅

Radical and Related Reverse

Bimolecular Reactions

Shang-Ying Wu,

Yun-Min Lee,

Jong-Shinn Wu,

and Ming-Chang Lin*

For plasma enhanced and catalytic chemical vapor deposition (PECVD and Cat-CVD) processes using small silanes as precur-sors, disilanyl radical (Si2H5) is a potential reactive intermediate

involved in various chemical reactions. For modeling and opti-mization of homogeneous a-Si:H film growth on large-area substrates, we have investigated the kinetics and mechanisms for the thermal decomposition of Si2H5 producing smaller

sili-con hydrides including SiH, SiH2, SiH3, and Si2H4, and the

related reverse reactions involving these species by using ab initio molecular-orbital calculations. The results show that the lowest energy path is the production of SiH 1 SiH4 that

pro-ceeds via a transition state with a barrier of 33.4 kcal/mol rela-tive to Si2H5. Additionally, the dissociation energies for

breaking the SiASi and HASiH2 bonds were predicted to be

53.4 and 61.4 kcal/mol, respectively. To validate the predicted enthalpies of reaction, we have evaluated the enthalpies of formation for SiH, SiH2, HSiSiH2, and Si2H4(C2h) at 0 K by

using the isodesmic reactions, such as 2HSiSiH21 1

C2H6!1Si2H612HCCH2 and 1Si2H4(C2h) 11C2H6 ! 1

Si2H611C2H4. The results of SiH (87.2 kcal/mol), SiH2 (64.9

kcal/mol), HSiSiH2 (98.0 kcal/mol), and Si2H4 (68.9 kcal/mol)

agree reasonably well previous published data. Furthermore, the rate constants for the decomposition of Si2H5 and the

related bimolecular reverse reactions have been predicted and tabulated for different T, P-conditions with variational Rice–Ramsperger–Kassel–Marcus (RRKM) theory by solving the master equation. The result indicates that the formation of SiH 1 SiH4 product pair is most favored in the decomposition

as well as in the bimolecular reactions of SiH21SiH3,

HSiSiH21H2, and Si2H4(C2h) 1 H under T, P-conditions

typi-cally used in PECVD and Cat-CVD. VC _{2013 Wiley Periodicals,}

Inc.

DOI: 10.1002/qua.24557

Introduction

In the semiconductor industry, deposition of layers of silicon-based thin films is a widely adopted integral technol-ogy using either the plasma enhanced chemical vapor depo-sition (PECVD) or catalytic chemical vapor depodepo-sition (Cat-CVD) method.[1–3] Fundamental modeling of fluid dynamics and chemical reaction mechanisms is often required to understand the complex chemical processes occurring inside the CVD chamber for further optimization of the processes. The success of modeling requires detailed chemical kinetics with reliable rate constants for key reactions involved. Meas-urements of these rate constants may be possible, but it is often very expensive or difficult. The recent progress in ab initio calculations has made reliable predictions of rate con-stants possible and efficient. The objective of this article is to provide the kinetic data for the unimolecular decomposi-tion of Si2H5 and its related reverse bimolecular reactions

involving SiH, SiH2, SiH3, and Si2H3 radicals using ab initio

calculations. These radicals are known to coexist in CVD media for a-Si:H thin film growth with small silanes as pre-cursors.[1–3]

In a typical CVD process, the reactions may include the disso-ciation of source gases induced by electron collisions in a plasma environment, radicals reactions with silicon compounds, the thermal decomposition of compounds, and so on.[4–7]For

silicon-based film deposition, silane (SiH4) is often used as the

gas source; the disilanyl (Si2H5) radical may be generated by

H-atom abstraction by H or other radicals from the disilane (Si2H6)

formed by the recombination of SiH3radicals or the association

of SiH3with SiH2radical, among others.[8–10]The chemical

prop-erties of the transient silicon hydrides, Si2H5, Si2H4, Si2H3, and

Si2H2prepared from fluorine atom reactions with disilane were

first investigated and measured with the photoionization mass spectrometry method by Ruscic and Berkowitz.[11] In addition, they summarized the previous Si2Hn, (n 5 2–5) structures with

ab initio calculations and provided the enthalpies of formation derived by combining their ionization potentials with obtained appearance potentials and that of Si2H6 from previous works.

Jasinski et al.[4]_{reviewed the various gas-phase reactions}

regard-ing monosilicon hydride radicals. A rate constant of3 3 10212

[a] S.-Y. Wu, Y.-M. Lee, J. S. Wu

Department of Mechanical Engineering, National Chiao Tung University, Hsinchu 300, Taiwan

[b] M. C. Lin

Department of Applied Chemistry, Center for Interdisciplinary Molecular Science, National Chiao Tung University, Hsinchu 300, Taiwan E-mail: chemmcl@emory.edu

[c] M. C. Lin

Department of Chemistry, Emory University, Atlanta, Georgia 30322, USA VC_{2013 Wiley Periodicals, Inc.}

cm3molecule21s21at 500 K in the low pressure range for the reaction of silylidyne (SiH) with silane (SiH4) was estimated.

Recently, Sillars et al.[12]presented an experimental and theoreti-cal study on the Si2H5 radical. The molecular structures,

vibra-tional frequencies, and relative energy estimates of Si2H5,

H2SiHSiH2 (transition state, TS), and HSiHSiH3 (C1) were also

computed with electronic structure methods using the Gaus-sian 98 program. However, no related kinetic data were predicted.

In this study, we attempt to investigate the elementary reac-tions relevant to the thermal decomposition of the Si2H5

radi-cal and its related reverse bimolecular processes. The dissociation of Si2H5to elementary silicon hydride radicals are

considered as follows:

Si2H5! SiH1SiH4 (1)

! HSiSiH21H2 (2)

! SiH31SiH2 (3)

! Si2H4ðC2hÞ1H (4) and their reverse reactions are also considered, such as,

SiH1SiH4! Si2H5 ! products (5) SiH21SiH3! Si2H5 ! products (6) HSiSiH21H2! Si2H5 ! products (7) Si2H41H! Si2H5 ! products (8) In the above reactions, “Si2H5*” represents internally excited

disilanyl radical formed by bimolecular radical association reac-tions Eqs. (5–8) and the “products” represent all possibly prod-uct pairs which can be formed in each reverse reaction via the Si2H5* intermediate as depicted in the potential energy surface

(PES) to be discussed later. Additionally, the calculated enthal-pies of reaction including isodesmic reactions will be used to deduce the enthalpies of formation for silicon hydride species involved; these results will be validated by comparison with the published data wherever possible. Finally, temperature and pressure-dependent rate constants over a wide range of condi-tions, including those which are generally applied to deposi-tion by PECVD and Cat-CVD processes, will be predicted by statistical theory based on PES computed by high-level quan-tum chemical calculations discussed below.

Computational Methods

The geometries of the reactants, products, and TSs for the disi-lanyl (Si2H5) thermal decomposition reaction were optimized

by using density functional theory using Becke’s three parame-ter nonlocal exchange functions with the nonlocal correlation functions of Lee, Yang and Parr method (B3LYP)[13–15] with the 6–31111G(3df,2p) basis set. This calculation was further improved by the coupled-cluster method using single, double,

and perturbative triple excitations (CCSD(T))[16a] with the 6– 3111G(d,p)[16b]basis set. Vibrational frequencies of all species were also computed at the same level of theory to character-ize stationary points and zero-point energy (ZPE) corrections. The geometries of TSs were verified by their connectivity with the reactants and products using the intrinsic reaction coordi-nate calculations.[17,18] To obtain reliable energies, the single-point energy calculations of the stationary single-points were exe-cuted at the CCSD(T)/6–31111G(3df,2p) level of theory based on the optimized geometries using the CCSD/6–31111G(d,p) method. Complete basis set (CBS[19,20]) extrapolation technique was also used for further improving the energy accuracy. The basis set extrapolation was based on the calculations with the aug-cc-pVXZ (X 5 D, T, and Q) basis using the CCSD(T) opti-mized geometries. The CBS energies have been estimated using three-point extrapolation scheme, E(X) 5 ECBS1b

exp[2(X 2 1)] 1 c exp[2(X 2 1)2] where X is the cardinal num-ber of the basis sets associated with X 5 2 (DZ) (double Zeta), 3 (TZ) (triple Zeta), 4 (QZ) (quadruple Zeta), and ECBS is the

asymptotic value to approximate the CBS limit. The Gaussian 03 quantum chemical software was used throughout the study.[21]

Kinetics methods

For the barrierless reactions, the canonical variational TS theory (CVTST)[22–24] was used to minimize rate coefficients. The CVTST rate coefficient equation in the quasi-thermodynamic form could be expressed by

k T; sð Þ5a kð bT=hÞ exp 2DGð ðT; sÞ=kbTÞ (9) where s is the distance along the minimum energy path (MEP), with the saddle point at s 5 0, the reactants region cor-responding to s < 0 and the products region corcor-responding to s > 0. a is statistical factor and kbis the Boltzmann constant. T

is the temperature, h is Planck’s constant, and DG_{(T,s) is a} quasi-thermodynamic quantity (Gibbs standard free energy of activation). The condition for minimizing k(T,s) is equivalent to maximizing the free energy activation. The Gibbs standard free energy functions were determined using the thermodynamic functions of NIST-JANAF Thermochemical Tables.[25] Further-more, the pressure-dependent rate constants were calculated with the RRKM theory[22–24,26,27] by solving the master equa-tion with the VARIFLEX program suite.[28] The microcanonical rate coefficient of the standard RRKM form is expressed as a function of total energy E and angular momentum quantum number J by

k E; Jð Þ5N

1 1ðE; JÞ

hq E; Jð Þ (10)

where N11ðE; JÞ is the TS’s sum of states, q(E,J) is the density of

states of activated reactants, and again h is Planck’s constant. Then, one-dimensional master equations were solved to deter-mine the nonequilibrium distribution functions for each channel.

Figure 1. Optimized geometric parameters of various stationary points for Si2H5thermal decomposition reaction calculated at the CCSD(T)/6–3111G(d,p)

level. Bond lengths are in angstroms and angles are in degrees. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Figure 2. Potential energy diagram of the Si2H5 thermal decomposition reaction. Relative energies (kcal/mol) calculated at the CCSD(T)/6–

31111G(3df,2p)//CCSD(T)/6–3111G(d,p)1ZPE levels of theory at 0 K and the CBS energies with ZPE corrected are given in the parentheses. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Results and Discussions

Potential energy surfaces and reaction mechanisms

In this section, the Si2H5thermal decomposition is investigated

for formation of smaller silicon hydrides, specifically, SiH, SiH2,

SiH3, SiH4, HSiSiH2, and Si2H4. The geometric parameters of

reactants, intermediates, and TSs optimized at the CCSD(T)/6– 3111G(d,p) level are given in Figure 1. The potential energy diagram of Si2H5 of the fragmentation pathways using the

refined energies predicted with the CCSD(T)/6– 31111G(3df,2p)//CCSD(T)/6–3111G(d,p) method is presented in Figure 2. The relative energies of the stationary points obtained from different calculations are summarized in Table 1. In the following discussion, the extrapolated CBS energies are given in the accompanied parentheses for comparison; with the exception of a few cases, most values obtained by the two methods agree within 1 kcal/mol. The rotational con-stants and vibrational frequencies for all of the stationary points computed at the CCSD(T)/6–3111G(d,p) level are sum-marized in Table 2.

According to the CCSD(T)/6–31111G(3df,2p)//CCSD(T)/6– 3111G(d,p) calculations, the lowest energy pathway for Si2H5

fragmentation is the migration of one hydrogen atom from the SiH2-moiety of the H2Si-SiH3 structure to the SiH3 moiety

via the mono-hydrogen-bridged structure HSiHSiH3 at TS2

with a barrier height of 33.4 (33.5) kcal/mol. The production of the SiH 1 SiH4products occurs via the hydrogen-bridged

com-plex, SiHSiH4 (local minimal 1, LM1) locating at 21.6 (20.3)

kcal/mol relative to TS2. The decomposition reaction is endo-thermic by 38.8 (41.4) kcal/mol. Another pathway for the frag-mentation leading to the same products via LM1 is the simultaneous migration of two H-atoms from the SiH3 moiety

to the SiH2via TS5 with an energy barrier of 43.0 (43.2) kcal/

mol.

Aside from the production of the SiH 1 SiH4 product pair,

the disilanyl radical can also decompose by elimination of a hydrogen atom and a hydrogen molecule. The pathway of H2

elimination can take place from the SiH3 moiety, proceeding

over the saddle point at TS4 which has the characteristic HH bond length of 1.073 A˚ and a barrier height of 50.9 (50.7) kcal/mol. The elimination of the H-atom from Si2H5, however,

is a barrierless dissociation process producing Si2H4 (C2h) with

the largest endothermicity of 61.4 (63.3) kcal/mol relative to Si2H5. Si2H5 can also decompose by breaking the SiASi bond Table 1. Relative energies[a](kcal/mol) of various species at 0 K in the Si2H5thermal decomposition reaction calculated at the different levels.

Species B3LYP/6–31111G(3df,2p) CCSD(T)/6–3111G(d,p) CCSD(T)/6–31111G(3df,2p)// CCSD(T)/6–3111G(d,p) CBS//CCSD(T)/6–3111G(d,p) 2 Si2H5 0.0 0.0 0.0 0.0 2_{TS1 27.3 (28.2}[b]_{) 30.8 29.6 (29.0}[c]_{) 29.3} 2_{TS2 31.9 35.4 33.4 33.5} 2_{LM1(SiHSiH} 4) 30.7 (31.7[b]) 31.7 31.8 (31.2[c]) 33.2 2 SiH 11SiH4 37.6 (37.1[b]) 36.4 38.5 (39.0[c]) 41.4 2 TS3 35.3 39.1 37.3 36.9 2_{TS4 49.1 53.4 50.9 50.7} 2_{TS5 45.8 44.5 43.0 43.2} 2 H2SiSiH 11H2 37.6 41.1 38.8 41.4 2 SiH311SiH2 52.1 (51.8[b]) 51.6 53.4 (53.8[c]) 56.0 1_Si 2H4(C2h) 12H 64.7 61.4 61.4 63.3

[a] Energies are ZPE corrected. [b] Evaluated with B3LYP/6–311G(d,p) from Ref. [12]. [c] Evaluated with CCSD(T)/aug-cc-pVTZ from Ref. [12]

Table 2. Vibrational frequencies and rotational constants for the various stationary points of the Si2H5thermal decomposition reaction at the CCSD (T)/

6–3111G(d,p) level of theory. Species A (GHz) B (GHz) C (GHz) Frequencies (cm21₎ 2_{SiH 224.1 2064} 1_SiH 2 244.1 209.1 112.6 1042, 2094, 2098 2 SiH3 142.4 142.4 84.2 801, 957, 957, 2259, 2293, 2293 1_SiH 4 86.1 86.1 86.1 955, 955, 955, 991, 991, 2291, 2296, 2296, 2296 2_HSiSiH 2 96.0 6.1 5.8 189, 391, 419, 471, 689, 979, 2095, 2242, 2267 1_Si 2H4(C2h) 74.2 6.2 5.9 347, 414, 447, 516, 561, 634, 939, 966, 2268, 2273, 2287, 2297 2 Si2H5 53.5 5.3 5.2 144, 404, 432, 444, 623, 655, 905, 955, 968, 970, 2246, 2256, 2268, 2272, 2280 (127, 390, 405, 424, 596, 637, 875, 936, 949, 950, 2188, 2199, 2213, 2223, 2231)[12] 2_{LM1(SiHSiH} 4) 63.7 3.6 3.6 83, 138, 257, 454, 685, 804, 922, 957, 973, 1260, 1934, 2039, 2298, 2328, 2344 (31, 131, 234, 439, 648, 754, 887, 936, 957, 1209, 1829, 1988, 2242, 2275, 2291)[12] 2 TS1 58.3 5.5 5.3 i207, 112, 340, 424, 701, 713, 900, 921, 929, 1310, 1545, 2220, 2225, 2249, 2261 (i225, 128, 333, 400, 676, 705, 885, 904, 916, 1240, 1503, 2160, 2161, 2190, 2205)[12] 2_{TS2 54.3 5.1 5.0 i468, 212, 374, 442, 659, 760, 924, 950, 988, 1017, 1703, 2121, 2210, 2280, 2312} 2_{TS3 56.7 5.6 5.4 i903, 275, 417, 423, 549, 658, 667, 887, 938, 962, 1487, 2199, 2256, 2278, 2291} 2 TS4 49.4 5.5 5.3 i1160, 140, 303, 429, 455, 630, 691, 807, 927, 1013, 1668, 2074, 2224, 2234, 2249 2 TS5 63.38 4.69 4.57 i891, 289, 369, 449, 494, 718, 880, 929, 958, 1302, 1502, 1858, 2080, 2283, 2325

to produce SiH2and SiH3with an endothermicity of 53.4 (56.0)

kcal/mol; the reaction also occurs barrierlessly without an intrinsic TS. Additionally, there are two TSs of H-shift, TS1 and TS3, from the SiH3moiety both having a bridged H-atom with

C1symmetry giving rise to the same Si2H5structure after

rear-rangement with noticeably different barriers of 29.6 (29.3) and 37.3 (36.9) kcal/mol.

The above results for the SiHSiH4 complex (LM1),

SiH 1 SiH4, SiH21SiH3, and H2SiHSiH2 (TS1) obtained at the

higher levels of theory in the present work are in good agree-ment with previous estimates of 31.2, 39.0, 53.8, and 29.0 kcal/ mol relative to Si2H5, respectively, by Sillars et al. with the

CCSD(T)/aug-cc-pVTZ//B3LYP/6–311G(d,p) method.[12]It should be mentioned that aside from the TSs described above, we have also searched at length, but to no avail, for the existence of a roaming transition state in the bimolecular metathetical process SiH 1 SiH4 () SiH31SiH2at a long separation.

Enthalpies of the formation

For the purpose of validating the relative energies for predic-tion of rate coefficients, we compare the enthalpies of forma-tion DfH of some compounds with those of available

experimental results based on the calculated enthalpies of the reaction DrHat 0 K. Furthermore, isodesmic reactions are also

used to examine the calculated enthalpies of formation at 0 K, such as 1Si2H411C2H6!1Si2H611C2H4and2HSiSiH211C2H6

! 1

Si2H61 2

HCCH2. The predicted enthalpies of formation,

including2SiH, 1SiH2, HSiSiH2, and Si2H4(C2h) are presented in

Table 3, which are derived by the above calculated enthalpies of reaction at the CCSD(T)/6–31111G(3df,2p)//CCSD(T)/6– 3111G(d,p) level with published values of DfH(0 K) from the

NIST-JANAF Tables[25] and the relevant literature.[11,29–34] For instance, DfH (0 K) for Si2H4(C2h) could be obtained from the

equation as follows, DfHðSi2H4Þ5DfHðSi2H5Þ–DfHð Þ1DH rH; at 0 K: (11) These DfH (0 K) results of 2 SiH, 1SiH2, 2 HSiSiH2, and 1

Si2H4(C2h) using DrH (0 K) relevant to Si2H5 decomposition

reactions are 87.2, 64.9, 98.0, and 68.9 kcal/mol, respectively. In addition, DfH (0 K) results of

2

HSiSiH2 and 1

Si2H4(C2h) using

DrH (0 K) of isodesmic reactions are 97.3 and 69.4 kcal/mol,

respectively. These agree reasonably well with the reported findings of2SiH (89.6 6 2.0 kcal/mol, NIST[25]),1SiH2(65.5 6 0.7

kcal/mol, Berkowitz et al.[29]), 2HSiSiH2 (98.8 kcal/mol, Curtiss

et al.[30]), and1Si2H4(67.9 6 0.9, Ruscic and Berkowitz. [11]

).

Rate constant calculations

The present theoretical predictions of rate constants for the reactions were carried out with CVTST by searching for the position of the dividing surface with a maximum DGo_{(T,s 5 s}‡₎

for a barrierless process, specifically Si2H5 ! Si2H4(C2h) 1 H,

Si2H5! SiH31SiH2and the dissociation of LM1 to SiH 1 SiH4.

To reduce the computational expense, the MEPs are computed using the potential energies along the reaction coordinate (SiH) from about 1.5 to 5.5 A˚ with a step size 0.2 A˚ in Si2H5

!

Si2H4(C2h) 1 H and the reaction coordinate (SiSi) from

about 2.4 to 5.0 A˚ with a step size 0.2 A˚ in Si2H5! SiH31SiH2

at the UB3LYP/6–31111G(3df,2p) level combined with the cubic spline interpolation method[35]_{and the energy is scaled}

at the CCSD(T)/6–31111G(3df,2p)1ZPE level. The approxi-mate positions of the dividing surface for the barrierless reac-tions are estimated in Table 4. Furthermore, rate constants of RRKM calculations are based on CCSD(T)/6–31111G(3df,2p)// CCSD(T)/6–3111G(d,p) energies. The MEP for the dissociation of LM1(SiHSiH4) ! SiH 1 SiH4 followed by a similar search

can be represented by the Morse potential,

V rð Þ5Def12exp 2b½ eðr2reÞg2 according to the B3LYP/6– 31111G(3df,2p) calculations with the energy scaled at the CCSD(T)/6–31111G(3df,2p)1ZPE level, and obtained parame-ters of De56.76 kcal/mol, be52.311 A˚21, and re51.8 A˚ . The

effective sum of states for all of the TSs is estimated at the energy E and total angular momentum J resolved level using rigid-rotor harmonic oscillator assumptions for the energy

Table 3. Enthalpies of formation (DfH) of species at 0 K predicted at the

CCSD(T)/6–31111G(3df,2p)//CCSD(T)/6–3111G(d,p)1ZPE level of theory. The CBS energies with ZPE corrected are listed in the parentheses.

Species Reactions

Enthalpy of formation DfH0

(kcal/mol) Calculated Literatures

2

SiH 2Si2H5!1SiH412SiH 87.2 (90.0) 89.6 6 2.0[25] 1_SiH 2 2Si2H5!1SiH212SiH3 64.9 (67.5) 65.5 6 0.7[29] 2_HSiSiH 2 2Si2H5!2HSiSiH211H2 98.0 (100.6) 98.8[30] 2 HSiSiH211C2H6! 1_Si 2H6!2HCCH2 97.3 (99.6) 1_Si 2H4(C2h) 2Si2H5!2H 11Si2H4 68.9 (70.9) 67.9 6 0.9[11] 1_Si 2H411C2H6! 1 Si2H611C2H4 69.4 (71.1) 69.32; 68.84[31] 66.5[30] The experimental values are obtained based on the enthalpies of for-mation at 0 K for H 5 51.66 kcal/mol[25]_{; H}

250.0 kcal/mol[25];

HCCH2571.5 kcal/mol[32]; C2H4 514.6 kcal/mol[25]; C2H65 216.3 kcal/

mol[33]; SiH 5 89.6 kcal/mol[25]; SiH2565.5 kcal/mol[29]; SiH3547.7 6 1.2

kcal/mol[34]_{; SiH}

4510.5 kcal/mol[25]; Si2H4567.9 kcal/mol[11];

Si2H5559.2 kcal/mol[11]; and Si2H6522.9 kcal/mol[11].

Table 4. The estimated corresponding position of the dividing surface by CVTST method.

2_Si 2H5!1Si2H4(C2h) 12H T (K) 300–500 600–900 1000–1100 1200 1300–1500 1600–1700 1800–2000 SiH (A˚) 3.45 3.25 3.15 3.1 3.05 3.0 2.95 2_Si 2H5!1SiH212SiH3 T (K) 300–600 700–1000 1100–1400 1500–1800 1900–2000 SiSi (A˚ ) 4.15 4.05 3.9 3.75 3.65

levels. ThehDEdowni is assumed to be equal to 400 cm21. The parameters for the Lennard–Jones collision rate were approxi-mated by r 5 4.717 A˚ and e 5 213.2 cm21 _{for Si}

2H5[36] and

r 5 3.75 A˚ and e 5 98.3 cm21

for Ar[37].

Unimolecular Decomposition of Si2H5. The PES shown in

Fig-ure 2 indicates that the unimolecular decomposition of Si2H5

radical may produce SiH 1 SiH4, H2SiSiH 1 H2, SiH21SiH3, and

Si2H4(C2h) 1 H:

Si2H5 ! SiH1SiH4 ð Þ1 ! HSiSiH21H2 ð Þ2 ! SiH31SiH2 ð Þ3 ! Si2H4ðC2hÞ1H ð Þ4

Interestingly, the last product pair is most endothermic, con-trary to the decomposition of C2H5which produces exclusively

C2H41H because of the strong P-bond energy in ethylene. [38]

In the present case, the production of SiH 1 SiH4, reaction Eq.

(1), via TS2 (33.4 kcal/mol) and the product pair complex LM1 (31.8 kcal/mol), with 38.8 kcal/mol endothermicity, is most favor-able. The dehydrogenation process, reaction Eq. (2), giving H2SiSiH takes place via TS4 with a barrier of 50.9 kcal/mol and is

endothermic by 38.8 kcal/mol, the same as that of the SiH 1 SiH4

reaction. However, the much higher barrier for the dehydrogen-ation step makes the process less competitive as one would expect. Similarly reactions Eqs. (3) and (4) with higher endother-micities producing SiH21SiH3 (53.4 kcal/mol) and Si2H4

(C2h) 1 H (61.4 kcal/mol), both predicted to occur without

well-defined intrinsic barriers as aforementioned, are expected to be too slow to compete with the most favored process also. The high-pressure limits for the decomposition and the related reverse association reactions are shown in Figures 3 and 4, respectively, for comparison. Their relative importance in the decomposition reactions mainly reflects the enthalpy of

activa-tion controlled by the corresponding VTS’s for radical produc-tion and the TS for H2elimination. The formation of Si2H5from

the recombination processes under the high-pressure condition (Fig. 4) reflects the nature of the interaction between the reac-tion pair and the entropic changes at VTS’s along the MEP at large separations. It should be noted that the negative tempera-ture dependence of the rate constant for HSiSiH21H2reaction

at high temperatures can be attributed largely to the T23/2 -fac-tor deriving from the rotational and translational partition func-tion ratios of the TS and the reactants.

The least-squares-fitted three-parameter rate constants predicted for various pressures for the temperature range 300–1000 K are summarized in Tables 5 and 6 for kinetic modeling applications.

Related Bimolecular Reactions Involving Si2H5 as Intermediate.

Under PECVD conditions using SiH4 as the precursor, SiHx

(x 5 123) and the two isomers of Si2H4may coexist in the gas

phase. We have thus also evaluated the rate constants for the bimolecular processes involving these species in conjunction with Si2H5as the intermediate as fully characterized by the PES

shown in Figure 2. The mechanisms of these bimolecular reac-tions giving the most favorable products are described as follows:

i. 2SiH 11SiH4reactions: 2_SiH11_SiH

4$2Si2H5!2SiH311SiH2 #

2_Si 2H5

ii. 2HSiSiH211H2reactions: 2_HSiSiH

211H2$2Si2H5!2SiH11SiH4 #

2_Si 2H5 Figure 3. Comparisons of high-pressure limit rate constants between2_Si

2H5

!1_Si

2H4(C2h) 12H (green —),2Si2H5!2SiH311SiH2! (blue —),2Si2H5

!2

HSiSiH211H2(brown —), and2Si2H5!2SiH 11SiH4(black —) versus

the inverse of temperature. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Figure 4. Comparisons of high-pressure limit rate constants between1_Si 2H4

(C2h) 12H ! 2Si2H5 (green —), 2SiH311SiH2 ! 2Si2H5 (blue —), 2

HSiSiH211H2!2Si2H5(brown —), and 2SiH 11SiH4! 2Si2H5(black —)

versus the inverse of temperature. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

iii. 2SiH31 1

SiH2reactions: 2_SiH

311SiH2$2Si2H5!2SiH11SiH4 # 2_Si 2H5 iv. 1_Si 2H4(C2h) 12H reactions: 1_Si 2H4ðC2hÞ12H$2Si2H5!2SiH11SiH4 # 2_Si 2H5

For these bimolecular reactions, the predicted rate constants for energetically most favorable product channels as a function of pressure at T 5 500 K and the temperature dependence at different pressures are graphically presented as follows: Reac-tion I in Figures 5–7; reacReac-tion II in Figures 8–10; reacReac-tion III in Figures 11–13; and reaction IV in Figures 14–16. All the proc-esses involved in the decomposition and the reverse associa-tion reacassocia-tions are highly pressure dependent due to the small size of the system and the associated high energy changes. For the convenience of modeling application, the three

Figure 5. Predicted rate constants as a function of pressure at T 5 500 K for2_{SiH 1}1_SiH

4! 2Si2H5 and2SiH 11SiH4 !2SiH311SiH2. [Color figure

can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Figure 6. Arrhenius plots of rate constants for2_{SiH 1}1_SiH

4!2Si2H5at

dif-ferent pressures as labeled versus the inverse of temperature. Table 5. Arrhenius parameters[a]including high-pressure limit (k‘) and

low-pressure limit (k0) for the2Si2H5fi2SiH 11SiH4and2Si2H5fi 2_HSiSiH 211H2reactions. P (Torr) A n Ea/R (K) T range (K) 2_Si 2H5!2SiH 11SiH4 k1 1 4.98 3 1035 26.92 22146.7 300–2000 k0 – 2.52 3 1033 210.21 21795.7 300–2000 k 0.3 2.21 3 1043 210.35 22101.3 300–2000 k 0.4 3.32 3 1043 210.36 22135.3 300–2000 k 0.5 4.41 3 1043 _{210.37 22160.5 300–2000} k 0.6 5.65 3 1043 _{210.38 22184.0 300–2000} k 1 1.17 3 1044 210.40 22261.0 300–2000 k 10 1.78 3 1045 210.45 22721.0 300–2000 k 760 1.12 3 1042 _{29.02 22932.8 300–2000} 2_Si 2H5!2HSiSiH211H2 k1 1 3.38 3 1044 210.44 29284.9 300–2000 k0 – 6.04 3 1019 28.79 25005.2 300–2000 k 0.3 6.39 3 1030 _{29.19 25121.5 300–2000} k 0.4 1.63 3 1031 _{29.26 25150.3 300–2000} k 0.5 3.69 3 1031 29.33 25177.5 300–2000 k 0.6 7.90 3 1031 29.40 25208.3 300–2000 k 1 8.11 3 1032 _{29.60 25305.8 300–2000} k 10 2.67 3 1040 _{211.27 26419.5 300–2000} k 760 3.27 3 1051 213.04 29736.6 300–2000

[a] k(T) 5 ATnexp(2Ea/RT). Unit of the rate constants k(T) is (s21) and k0

is (cm3_molecule21_s21_).

Table 6. Arrhenius parameters[a]including high-pressure limit (k‘) and

low-pressure limit (k0) for the2Si2H5fi1Si2H4(C2h) 12H and2Si2H5fi 1_SiH 212SiH3reactions. P (Torr) A n Ea/R (K) T range (K) 2 Si2H5!1SiH212SiH3 k1 1 4.76 3 1026 24.26 26741.9 300–2000 k0 2 4.15 3 1026 0.15 23615.3 300–2000 k 0.3 1.12 3 105 20.09 23476.1 300–2000 k 0.4 2.27 3 105 20.14 23459.1 300–2000 k 0.5 4.21 3 105 _{20.18 23448.9 300–2000} k 0.6 6.86 3 105 _{20.22 23434.5 300–2000} k 1 3.71 3 106 20.35 23408.7 300–2000 k 10 6.44 3 1012 21.71 23686.6 300–2000 k 760 8.85 3 1029 _{25.60 26818.0 300–2000} 2_Si 2H5!1Si2H4(C2h) 12H k1 1 6.58 3 1039 28.68 33992.1 300–2000 k0 2 3.23 3 1014 26.36 32558.9 300–2000 k 0.3 7.99 3 1023 _{26.36 32504.3 300–2000} k 0.4 1.12 3 1024 _{26.36 32478.9 300–2000} k 0.5 1.52 3 1024 26.37 32459.7 300–2000 k 0.6 1.89 3 1024 26.37 32440.4 300–2000 k 1 4.10 3 1024 _{26.40 32389.8 300–2000} k 10 8.63 3 1026 _{26.73 32112.8 300–2000} k 760 4.52 3 1038 29.08 33070.4 300–2000

[a] k(T) 5 ATnexp(2Ea/RT). Unit of the rate constants k(T) is (s21) and k0

parameter equations for the modified Arrhenius expressions in the temperature range of 30022000 K at various pressures are presented in Table 7 (for reaction I), Table 8 (for reaction II), Table 9 (for reaction III), and Table 10 (for reaction IV).

The predicted results show that in reactions (II)–(IV), prod-ucts such as SiH 1 SiH4 are dominant at low pressure, while

the stabilized adduct Si2H5becomes gradually prevalent as the

pressure increases. The other product pairs (SiH31SiH2, Si2H4

(C2h) 1 H, and HSiSiH21H2) are energetically inaccessible from

SiH 1 SiH4. At room temperature and low pressure of silicon

CVD environments, the reaction of SiH 1 SiH4to produce Si2H5

is predominant, followed in order by SiH31SiH2, Si2H4

(C2h) 1 H, and HSiSiH21H2. The predicted rate constant for

SiH 1 SiH4 at 500 K in the low pressure (mTorr) range is in

close agreement with the estimate of Jasinski et al.,[4]_{on the}

order of 10212_cm3_molecule21_s21_{. For these bimolecular and}

the unimolecular dissociation of Si2H5, their high-pressure limit

rate constants as presented before in Figures 3 and 4, respec-tively, clearly depict their relative importance.

Concluding Remarks

In the present work, we have investigated the fundamental reactions relevant to the thermal decomposition of Si2H5

radi-cal and its related reverse bimolecular reactions with ab initio MO calculations based on the B3LYP/6–31111G(3df,2p), CCSD(T)/6–31111G(3df,2p)//CCSD(T)/6–3111G(d,p), and CC SD(T)/6–3111G(d,p)//CBS methods. Based on the predicted values at the CCSD(T)/6–31111G(3df,2p)//CCSD(T)/6–3111 G(d,p) level, the lowest energy path leads to the production of SiH and SiH4via a transition state (TS2) with a barrier height

of 33.4 kcal/mol relative to Si2H5. Additionally, to break the

HASiH2 and SiASi bonds require 61.4 and 53.4 kcal/mol,

respectively. Furthermore, the enthalpies of the formation DfH

for the major products at 0 K have been predicted using the

Figure 7. Arrhenius plots of rate constants for2_{SiH 1}1_SiH

4!2SiH311SiH2

at different pressures as labeled versus the inverse of temperature.

Figure 8. Predicted rate constants as a function of pressure at T 5 500 K for2_HSiSiH

211H2!2Si2H5and2HSiSiH211H2!2SiH 11SiH4. [Color

fig-ure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Figure 9. Arrhenius plots of rate constants for2_HSiSiH

211H2! 2Si2H5at

different pressures as labeled versus the inverse of temperature.

Figure 10. Arrhenius plots of rate constants for 2_HSiSiH

211H2 ! 2_{SiH 1}1_SiH

4 at different pressures as labeled versus the inverse of

Figure 11. Predicted rate constants as a function of pressure at T 5 500 K for

2_SiH

311SiH2!2Si2H5and2SiH311SiH2!2SiH 11SiH4. [Color figure can be

viewed in the online issue, which is available at wileyonlinelibrary.com.]

Figure 12. Arrhenius plots of rate constants for2_SiH

311SiH2 !2Si2H5at

different pressures as labeled versus the inverse of temperature.

Figure 13. Arrhenius plots of rate constants for2_SiH

311SiH2!2SiH 11SiH4

at different pressures as labeled versus the inverse of temperature.

Figure 14. Predicted rate constants as a function of pressure at T 5 500 K for

1_Si

2H4(C2h) 12H!2Si2H5and1Si2H4(C2h) 12H!2SiH 11SiH4. [Color figure

can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Figure 15. Arrhenius plots of rate constants for1Si2H4(C2h) 12H!2Si2H5

at different pressures as labeled versus the inverse of temperature.

Figure 16. Arrhenius plots of rate constants for1_Si

2H4(C2h) 12H!2SiH 11SiH4

computed enthalpies of the reaction DrHat 0 K, including the

isodesmic reactions at this level. The results are in reasonable agreement with previous experimental values, for example, SiH (87.2 kcal/mol), SiH2 (64.9 kcal/mol), HSiSiH2 (98.0 kcal/mol),

and Si2H4 (68.9 kcal/mol). Finally, the rate constants for Si2H5

decomposition into these smaller silicon hydrides and their corresponding reverse reactions via the disilanyl intermediate have been calculated using the variational RRKM theory by solving the master equation. The results indicate that the for-mation of the energetically most favored products SiH 1 SiH4

is predominant under varying P, T conditions. The rate con-stants predicted under different practically accessible condi-tions have been evaluated and tabulated for future modeling and optimization of homogenous a-Si:H film growth on large-area substrates.

Acknowledgments

The authors deeply appreciate a partial support of this work by the Ministry of Economics under contract no. 98-EC-17-A-07-S2-0043. M.C.L. wants to thank the National Science Council of Taiwan for the support of this work and for the distinguished visiting professor-ship at the National Chiao Tung University in Hsinchu, Taiwan. Keywords: Si2H5







kinet-ics



How to cite this article: S.-Y. Wu, Y.-M. Lee, J. S. Wu, M. C. Lin. Int. J. Quantum Chem. 2014, 114, 278–288. DOI: 10.1002/qua.24557

[1] J. K. Rath, Sol. Energy Mater.Sol. Cells 2003, 76, 431. [2] A. Matsuda, Jpn. J. Appl. Phys. 2004, 43, 7909.

Table 10. Arrhenius parameters[a]including high-pressure limit (k‘) and

low-pressure limit (k0) for the1Si2H4(C2h) 12Hfi2Si2H5and1Si2H4

(C2h) 12Hfi2SiH 11SiH4reactions.

P (Torr) A n Ea/R (K) T range (K) 1_Si 2H4(C2h) 12H!2Si2H5 k1 1 5.41 3 1014 28.31 2438.8 300–2000 k0 2 2.26 3 1027 27.88 1477.1 300–2000 k 0.3 7.27 3 102 27.89 1423.8 300–2000 k 0.4 1.01 3 103 _{27.89 1415.4 300–2000} k 0.5 1.27 3 103 _{27.89 1405.1 300–2000} k 0.6 1.55 3 103 _{27.89 1396.6 300–2000} k 1 2.67 3 103 27.90 1362.2 300–2000 k 10 8.10 3 104 _{28.01 1005.7 300–2000} k 760 3.54 3 1020 _{211.42 1944.2 300–2000} 1_Si 2H4(C2h) 12H!2SiH 11SiH4 k 106 8.25 3 104 25.63 1981.6 300–2000 k low P760 5.41 3 1014 _{28.31 2438.8 300–2000} [a] k(T) 5 ATn_exp(2E

a/RT). Unit of the rate constants k(T) is (cm3

mole-cule21_s21_{) and k}

0is (cm6molecule22s21).

Table 8. Arrhenius parameters[a]_{including high-pressure limit (k} ‘) and

low-pressure limit (k0) for the1SiH212SiH3fi2Si2H5and1SiH212SiH3fi 2

SiH 11SiH4reactions.

P (Torr) A n Ea/R (K) T range (K) 1_SiH 212SiH3!2Si2H5 k1 1 2.17 3 1027 21.80 21330.4 300–2000 k0 2 5.78 3 10225 22.04 22367.0 300–2000 k 0.3 1.63 3 10214 _{22.28 22481.3 300–2000} k 0.4 3.45 3 10214 _{22.33 22490.4 300–2000} k 0.5 6.00 3 10214 22.37 22505.2 300–2000 k 0.6 1.01 3 10213 22.40 22514.9 300–2000 k 1 5.32 3 10213 _{22.53 22536.1 300–2000} k 10 7.29 3 1027 _{23.84 22224.6 300–2000} k 760 1.88 3 108 26.80 624.4 300–2000 1

SiH212SiH3!2SiH 11SiH4

k 106 _{1.61 3 10}223 _{2.53 22737.9 300–2000}

k low P10 1.17 3 1026 _{22.02 21205.6 300–2000}

k 760 1.30 3 1026 22.01 2805.2 300–2000

[a] k(T) 5 ATnexp(2Ea/RT). Unit of the rate constants k(T) is (cm3

mole-cule21_s21_{) and k}

0is (cm6molecule22s21).

Table 7. Arrhenius parameters[a]including high-pressure limit (k‘) and

low-pressure limit (k0) for the2SiH 11SiH4fi2Si2H5and2SiH 11SiH4fi 1_SiH 212SiH3reactions. P (Torr) A n Ea/R (K) T range (K) 2_{SiH 1}1_SiH 4!2Si2H5 k1 1 1.89 3 101 23.70 1184.0 300–2000 k0 2 4.02 3 1015 212.35 3270.2 300–2000 k 0.3 5.72 3 1025 212.53 3644.3 300–2000 k 0.4 8.54 3 1025 212.55 3680.4 300–2000 k 0.5 1.20 3 1026 _{212.56 3714.0 300–2000} k 0.6 1.56 3 1026 _{212.57 3740.7 300–2000} k 1 3.55 3 1026 212.60 3833.4 300–2000 k 10 1.05 3 1026 212.11 4006.7 300–2000 k 760 5.35 3 106 _{25.55 1785.0 300–2000} 2_{SiH 1}1_SiH 4!1SiH212SiH3 k 106 2.62 3 10217 1.24 5890.2 300–2000 k low P1 6.75 3 1023 _{22.61 7071.6 300–2000} k 10 9.57 3 1022 _{22.95 7270.9 300–2000} k 760 6.47 3 1021 _{23.17 7681.8 300–2000} [a] k(T) 5 ATn_exp(2E

a/RT). Unit of the rate constants k(T) is (cm3

mole-cule21s21) and k0is (cm6molecule22s21).

Table 9. Arrhenius parameters[a]including high-pressure limit (k‘) and

low-pressure limit (k0) for the2HSiSiH211H2fi2Si2H5and2HSiSiH211H2

fi2_{SiH 1}1_SiH 4reactions. P (Torr) A n Ea/R (K) T range (K) 2_HSiSiH 211H2!2Si2H5 k1 1 2.22 3 1015 29.23 8436.0 300–2000 k0 2 1.27 3 108 213.09 6960.2 300–2000 k 0.3 9.72 3 1018 213.44 7061.2 300–2000 k 0.4 2.40 3 1019 213.51 7089.4 300–2000 k 0.5 5.27 3 1019 _{213.58 7116.0 300–2000} k 0.6 1.02 3 1020 _{213.63 7138.9 300–2000} k 1 9.86 3 1020 213.83 7234.8 300–2000 k 10 1.26 3 1028 215.35 8301.2 300–2000 k 760 1.79 3 1036 _{216.18 11205.7 300–2000} 2_HSiSiH 211H2!2SiH 11SiH4 k 106 2.17 3 1025 23.66 6501.6 300–2000 k low P10 2.22 3 1015 _{29.23 8436.0 300–2000} k 760 1.14 3 1017 _{29.70 9249.9 300–2000} [a] k(T) 5 ATn_exp(2E

a/RT). Unit of the rate constants k(T) is (cm3

mole-cule21_s21_{) and k}

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Received: 14 June 2013 Revised: 1 August 2013 Accepted: 10 September 2013 Published online 7 October 2013