Ab Initio Chemical Kinetics for Reactions of H Atoms with
SiH
x
(x 5 1–3) Radicals and Related Unimolecular
Decomposition Processes
Putikam Raghunath,
[a]Yun-Min Lee,
[b]Shang-Ying Wu,
[b]Jong-Shinn Wu,
[b]and Ming-Chang Lin*
[a] Hydrogen atoms and SiHx (x ¼ 1–3) radicals coexist during thechemical vapor deposition (CVD) of hydrogenated amorphous silicon (a-Si:H) thin films for Si-solar cell fabrication, a technology necessitated recently by the need for energy and material conservation. The kinetics and mechanisms for H-atom reactions with SiHx radicals and the thermal decomposition of their
intermediates have been investigated by using a high high-level ab initio molecular-orbital CCSD (Coupled Cluster with Single and Double)(T)/CBS (complete basis set extrapolation) method. These reactions occurring primarily by association producing excited intermediates, 1SiH2, 3SiH2, SiH3, and SiH4, with no
intrinsic barriers were computed to have 75.6, 55.0, 68.5, and 90.2 kcal/mol association energies for x ¼ 1–3, respectively, based on the computed heats of formation of these radicals. The excited intermediates can further fragment by H2
elimination with 62.5, 44.3, 47.5, and 56.7 kcal/mol barriers
giving 1Si, 3Si, SiH, and 1SiH2 from the above respective
intermediates. The predicted heats of reaction and enthalpies of formation of the radicals at 0 K, including the latter evaluated by the isodesmic reactions, SiHx þ CH4 ¼ SiH4 þ CHx, are in
good agreement with available experimental data within reported errors. Furthermore, the rate constants for the forward and unimolecular reactions have been predicted with tunneling corrections using transition state theory (for direct abstraction) and variational Rice–Ramsperger–Kassel–Marcus theory (for association/decomposition) by solving the master equation covering the P,T-conditions commonly employed used in industrial CVD processes. The predicted results compare well experimental and/or computational data available in the literature.VC 2013 Wiley Periodicals, Inc.
DOI: 10.1002/qua.24396
Introduction
Chemical vapor deposition (CVD) is one of the most exten-sively performed processes for thin-film growth of hydrogen-ated amorphous silicon (a-Si:H),[1] polycrystalline silicon (p-Si),[2] and silicon nitride (SiNx).[3] These materials have been
widely applied in devices such as solar cells, thin-film transis-tors for liquid crystals, and light emitting diodes, and protec-tion films of semiconductor devices.[4,5] In the Si-solar cell manufacturing industry, the employment of a-Si:H thin films for cell fabrication has recently gained considerable interest due to the need for energy and material conservation. The a-Si:H thin films can be manufactured by CVD at a lower cost with hydrogen passivation that effectively reduces the dan-gling bond density by several orders of magnitude affording a sufficiently low amount of defects for device fabrications.
CVD processes such as plasma-enhanced CVD (PECVD) or catalytically enhanced CVD (Cat-CVD) for deposition of a-Si:H films are very complicated; they involve intertwining gas-phase and surface reactions. Characteristics of deposited films are largely affected by the plasma density (in PECVD) or the hot wire configuration and temperature (in Cat-CVD), as well as the fluxes and varieties of the precursor molecules transported by gas flow, following electrical discharge or catalytic decom-position over a hot wire, onto substrates. In the case of the PECVD of a-Si:H using SiH4and H2as precursor gases, H atoms
and SiHx(x¼ 1–3) radicals may coexist in high concentrations
by collisions between energetic electrons and molecules; the reactions between these reactive species may play a pivotal
role in film growth at the substrate. To further refine the tech-nology to ensure uniform growth of an a-Si:H film over a large substrate area, chamber-scale modeling is inevitable; it can help delineate and control the intricate coupling plasma and thermal field with the complex Si-chemistry. Therefore, it is im-portant to understand the reactions involved quantitatively for successful development and better applications of the technology.
The kinetics and mechanisms for the reactions of H atoms with the SiHx radicals present in the SiH4 PECVD process
remain largely unknown; these radicals have been experimen-tally detected under various conditions,[6–11] and qualitatively the life time of SiH3 was found to be much longer than those
of SiH and SiH2 in plasma media.[12,13] The mechanism and
rate constant for SiH4decomposition reaction have been
stud-ied theoretically by various groups.[14–23] Chemical properties and some kinetic information regarding SiH (silylidyne), SiH2
(silylene), and SiH3 (silyl) have been discussed previously by [a] P. Raghunath, M. C. Lin
Center for Interdisciplinary Molecular Science, Department of Applied Chemistry, National Chiao Tung University, Hsinchu 300, Taiwan [b] Y. M. Lee, S. Y. Wu, J. S. Wu
Department of Mechanical Engineering, National Chiao Tung University, Hsinchu 300, Taiwan
E-mail: [email protected]
Contract grant sponsor: Taiwan’s National Science Council (NSC); Contract grant number: NSC100-2113-M-009-013 (to M.C.L. and P.R.).
Contract grant sponsor: Ministry of Economics; Contract grant number: 98-EC-17-A-07-S2-0043 (to S.Y.W. and J.S.W.).
Jasinski et al.[24] They also summarized several experimental methods for the detection and monitoring of these radicals and provided the enthalpies of formation of these radicals. Gordon et al.[25] have applied ab initio quantum mechanical methods to study the SiH insertion into the H2 molecule.
Walch and Dateo[21]have studied various reactions relevant to the thermal decomposition of SiH4, SiH3, SiClH3, SiCl2H2, and
SiCl3H. Recently, we have theoretically interpreted the
decom-position of silane up to Si3H8 by the reactions with hydrogen
atoms and SiH3 giving various products and also calculated
their heats of formation of larger silalyl radicals for comparison with available experimental data.[26]
The generated radicals and ions in a PECVD chamber may undergo various kinds of reactions with silane, before they reach the substrate. For H and SiHx (x ¼ 1–3) radical species,
they may interact with one another by the following chemical reactions in the forward and reverse directions:
Hþ SiH3! SiH4! SiH4 (1a)
! SiH2þ H2 (1b)
Hþ SiH2! SiH3! SiH3 (2a)
! SiH þ H2 (2b)
Hþ SiH ! SiH2! SiH2 (3a)
!3Siþ H2 (3b)
!1Siþ H
2 (3c)
In the above reaction schemes, ‘‘*’’ denotes an internally acti-vated intermediate that can fragment into smaller radicals by dehydrogenation or be collisionally deactivated to give SiHx.
The kinetics of these reactions, albeit simple mechanistically, have not been experimentally or computationally studied sys-tematically; for example, what are the effects of temperature and pressure on the competing processes that are critical to a faithful and realistic simulation of a-Si:H thin-film growth by PECVD or Cat-CVD process.
In this work, the potential energy surfaces (PESs) of the title reactions have been predicted by high-level ab initio molecu-lar-orbital (MO) calculations. Furthermore, the enthalpies of for-mation of the SiHx species have been reliably predicted and
compared with available experimental data to validate our cal-culated heats of reaction. The temperature and pressure dependences of the rate constants for the forward and its related unimolecular processes have been derived using varia-tional Rice–Ramsperger–Kassel–Marcus (RRKM) theory by solv-ing the master equation coversolv-ing the conditions commonly used in industrial deposition of a-Si:H films.
Computational Methods
Ab Initio MO calculationsThe various stationary points (minima or saddle points) on the PES for H-atom reactions with the three SiHx radicals were
optimized using CCSD(T)/6-311þG(d,p) basis set and for improved energies, single-point calculations at the
CCSD(T)/6-311þþG(3df,3pd) level of theory[27]were used. The vibrational frequencies were determined at the same levels of theories to obtain zero-point energy (ZPE) corrections and to characterize the stationary points. Based on the CCSD(T) optimized geome-tries, the PES was calculated and mapped using the CCSD(T)/ CBS method,[28] in which the basis set extrapolation was based on the calculations with the aug-cc-pVXZ (X¼ D, T, and Q) basis sets of Dunning.[29]The Gaussian 03 quantum chemical software was used in each of these evaluations.[30]The CBS energies have been estimated using three-point extrapolation scheme,
EðXÞ ¼ ECBSþ b exp½ðX 1Þ þ c exp½ðX 1Þ2 (1) where X is the cardinal number of the basis sets associated with X¼ 2 (DZ) (double Zeta), 3 (TZ) (triple Zeta) 4 (QZ) (quadruple Zeta) and ECBSis the asymptotic value, which is taken to
approx-imate the CBS limit.
Rate constant calculations
The rate constants were calculated using the microcanonical transition-state theory (TST) and the RRKM theory by solving the one-dimensional master equation to derive the nonequili-brium distribution function for each channel with the VARI-FLEX program suite.[31]For a barrierless association/decomposi-tion process, the variaassociation/decomposi-tional TST (VTST)[32] was approximated with the Morse function, V(R)¼ De{1 exp[ b (R Re)]}
2
, in conjunction with a potential anisotropy function to repre-sent the minimum potential energy path (MEP), which will be discussed later. Here, Deis the binding energy excluding
zero-point vibrational energy for an association reaction, R is the reaction coordinate (i.e., the distance between the two bond-ing atoms), and Reis the equilibrium value of R at the stable
intermediate structure. For a loose transition-state process, the potential for the transitional degrees of freedom orthogonal to the reaction coordinate is described in terms of internal angle with sinusoidal functions.[33] The coefficient in the potential expression can be determined by the appropriate force con-stant matrix [Fij(R)] at the potential minimum, assuming that
Fij(R) decays exponentially with the bond distance:
FijðRÞ ¼ Fi jðR0Þ exp½gðR R0Þ
Here, R is the bond distance along with the reaction coordi-nate; R0 is the bond distance at the equilibrium structure; and
g is a decay parameter with R increasing. For a spin forbidden crossing reaction, we apply the nonadiabatic TST[34,35] to
esti-mate its crossing probability. The procedure is given in the Supporting Information.
Results and Discussion
PESs and reaction mechanismsFigure 1 presents the PESs of the three SiHx reactions with H
atoms based on the energies obtained with the CCSD(T)/6-311þG(d,p)/CBS method. The optimized geometric parameters of reactants, intermediates, and transition states computed at
the CCSD(T)/6-311þG(d,p) level and their structures are pre-sented in Figure 2. The corresponding energies estimated at dif-ferent levels of the theory are summarized in Table 1. The rota-tional constants and vibrarota-tional frequencies of the various stationary points predicted at the CCSD(T)/6-311þG(d,p) level are given in Table 2. The calculated heats of reaction and formation values compared with experimental data at 0 K are given in Table 2. The following discussion will be based on the results computed at the CCSD(T)/CBS level, and all the energies of TSs and inter-mediates are relative to the reactants. In Table 2, the values of T1 diagnostics for all the structures are calculated at the CCSD(T)/6-311þG(d,p) level, and the results are within 0.006–0.025 range, suggesting that our single-reference results are reasonable.
H þ SiH3 reaction. The initial association mechanism of the H
atom with SiH3leading to SiH4as shown in Figure 1a was
pre-dicted to be exothermic by 90.2 kcal/mol, which is close to the experimental SiAH bond energy 88.9 1.2 kcal/mol as listed in Table 3. For SiH4, its SiAH bond length, 1.477 A˚, is
also in close agreement with the experimental value, 1.481 A˚ . This association process does not have a well-defined transi-tion state; its associated potential functransi-tion was computed var-iationally to cover the range of SiAH bond separations in the forming SiH4from 1.477 to 5.677 A˚ with the second-order
mul-tireference perturbation theory (CASPT2) based on the CASSCF (Complete Active Space Self-Consistent Field) optimized geo-metries with eight active electrons and eight active orbitals
using the 6-311þG(3df,2p) basis set. Other geometric parame-ters were fully optimized. These calculations were performed with the MOLPRO code.[36] The calculated potential energy curve can be fitted to the Morse function with the parameter of b ¼ 1.872 A˚1, and the estimated decay parameters of in-ternal angles corresponding to the vicinity of variational
Figure 1. Potential energy profiles of H reactions with SiHx (x¼ 1–3) in
units of kcal/mol. Relative energies with ZPVE are calculated at the CCSD(T)/6-311þG(d,p)/CBS level.
Figure 2. The optimized geometries of the reactants, transition states, and products calculated at the CCSD(T)/6-311þG(d,p) level.
Table 1. Calculated relative energies (kcal/mol, ZPE corrections are included) for the H atom reactions with SiHx(x 5 1–3) at various levels
of theory. Reactions CCSD(T)/ 6–311þG(d,p) CCSD(T)/ 6–311þþG(3df,3pd)// CCSD(T)/6–311þG(d,p) CCSD(T)/ CBS 2 Hþ2 SiH3 0.0 0.0 0.0 1SiH 4 86.8 89.0 90.2 TS1 27.8 32.1 33.5 1SiH 2þ1H2 33.2 34.9 34.7 3 TS2 5.7 4.4 4.2 3SiH 2þ1H2 14.8 14.7 14.2 2Hþ1SiH 2 0.0 0.0 0.0 2SiH 3 66.4 67.3 68.5 TS3 16.6 19.8 21.0 2LM 27.6 29.7 30.1 2SiHþ1H 2 28.0 28.1 27.6 TS4 2.5 1.5 1.3 2 Hþ2 SiH 0.0 0.0 0.0 1SiH 2 71.5 74.1 75.6 3SiH 2 53.1 53.9 55.0 1Siþ1H 2 9.0 12.5 13.1 3 Siþ1 H2 33.8 33.1 32.4 3TS5 6.9 10.9 10.7 3TS6 1.9 1.1 1.0 CP 25.3 29.1 30.0
transition state are g(H3Si2H1)¼ 1.029 A˚1 and g(H4H3Si2H1) ¼ 1.005 A˚1, which will be used later for rate constant calcula-tions. The excited SiH4 product can decompose to form SiH2
þ H2 with 56.7 kcal/mol barrier via TS1. Previous results show
that the barrier energy is 6.7 kcal/mol lower using a semiempi-rial method,[15]and other two calculations are in good agree-ment with the 59.9 kcal/mol barrier predicted with CCSD(T)/ aug-cc-pvtz basis set extrapolation to the basis set limit at the MP2 level[21] and 57.0 kcal/mol barrier calculated at the CCSD(T)/CBS level.[23] The endothermicity of this process is 55.5 kcal/mol, and the overall enthalpy change for H þ SiH3
! SiH2 þ H2 is predicted to be 34.7 kcal/mol, which is in
close agreement with the experimental value,33.9 1.2 kcal mol. The calculation shows that the direct hydrogen abstrac-tion reacabstrac-tion occurs by the attack of the H atom at one of the SiAH bonds of SiH3to produce
3
SiH2þ H2via triplet transition
state TS2 with a 4.3 kcal/mol barrier energy. It is worth noting that we have also performed an extensive search for a roam-ing transition state of the Hþ SiH3reaction directly leading to
the formation of1SiH2þ H2, but our attempts failed to locate
the existence of such a loose RTS (Roaming transition state), which may compete with the very fast association/decomposi-tion process via SiH4and TS1.
H þ SiH2 reaction. A schematic potential energy diagram for
the Hþ1SiH2reaction is shown in Figure 1b; the reaction can
occur in two possible pathways. The first mechanism occurred through association of H and 1SiH2 to form SiH3 barrierlessly
with 67.3 and 68.5 kcal/mol exothermicities predicted at the CCSD(T)/6-311þþG(3df,3pd)//CCSD(T)/6-311þG(d,p) and CCSD(T)/CBS levels, respectively. The latter agrees better with the experimental value of 69.5 1.2 (see Table 3). We opti-mized SiH3 geometry with C3v symmetry. The SiH3 radical can
further dissociate with 47.5 kcal/mol barrier energy (TS3), which lies 9.1 and 6.6 kcal/mol above the product complex (LM, SiH…H2) and SiH þ H2 products, respectively. The
transi-tion state barrier for SiHþ H2! SiH3, 6.6 kcal/mol, is in good
agreement with the estimation of Gordon et al.,[25] 5.6 1 kcal/mol (with ZPE correction). Walch and Dateo[21] also have studied the same reaction and estimated a barrier height of 6 kcal/mol at the CCSD(T)/a-cc-pVTZ level of theory with
extrap-olation to the complete basis set (CBS) limit by the MP2 method. The second reaction is direct hydrogen abstraction from one of hydrogen atoms of1SiH2 to produce
2
SiHþ H2
through TS1 with 1.3 kcal/mol barrier. The formation of SiH3
from Hþ 1SiH2 is a barrierless association process, as shown
in Figure 1b. Its associated potential function was computed variationally to cover the range of SiAH separation from 1.5 to 5.5 A˚ at the CASPT2(7,9)/6-311þG(3df )//CASSCF(7,9)/6-311þG(3df ) level. The computed potential energies could be fitted to the Morse function with the parameter b ¼ 2.902 A˚1. Estimated decay parameters of internal angles corre-sponding to vicinity of variational transition state are g(H3Si2H1)¼ 1.089 A˚1and g(H4H3Si2H1)¼ 0.73 A˚1.
Hþ SiH reaction. The PES of the Hþ SiH system shown in Fig-ure 1c has been computed at the CCSD(T)/CBS level also. On the PES, there are two possible mechanisms for H atom reac-tions with the SiH radical; one occurs by direct abstraction, involving a colinear SiHH structure, and the other occurs bar-rierlessly forming the excited SiH2radical followed by
dehydro-genation to give Si þ H2. The barrier to the linear
H-abstrac-tion TS6 via the triplet path is predicted to be 1.0 kcal/mol relative to SiHþ H, or 33.3 kcal/mol relative to3Siþ H2. The
association reactions producing singlet and triplet states of SiH2 take place without intrinsic barriers and are predicted to
be exothermic by 75.6 and 55.0 kcal/mol, respectively, which agree excellently with experimental heats of reaction 75.7 0.5 and 54.7 0.5 kcal/mol at 0 K (see Table 3). For barrierless association reactions of H with SiH producing the singlet SiH2,
we computed variationally the SiAH separation from 1.5 to 5.5 A˚ at an interval of 0.1 A˚ using the CASPT2(6,7)/6-311þG(3df)// CASSCF(6,7)/6-311þG(3df ) method; the predicted MEP was fit-ted to the Morse function with b ¼ 1.76 and 3.38 A˚1. The Morse potential for the dissociation reaction1SiH2!
1
Siþ H2
was determined to be b¼ 4.44 A˚1.
The predicted energy difference between singlet and triplet splitting energy of SiH2 at the CCSD(T)/CBS level is 20.6 kcal/
mol, which is also in close agreement with the experimental value, 21.0 0.7 kcal/mol.[37a]The1Siþ H2products may be
produced by the direct dissociation of the1SiH2 radical with
predicted dissociation energy 62.5 kcal/mol without an intrinsic
Table 2. Calculated vibrational frequencies of the species involved in the H atom reactions with SiHx(x 5 1–3) computed at CCSD(T)/6–3111G(d,p)
level.
Species Frequencies (cm1) Rotational constants (cm1) T1 diag. Symm. No.
1 SiH4 955, 955, 955, 991, 991, 2292, 2297, 2297, 2297 2.872, 2.872, 2.872 0.009 12 2SiH 3 799, 956, 956, 2263, 2297, 2297 4.752, 4.752, 2.811 0.010 3 2LM 126, 280, 743, 881, 2087, 3992 6.841, 2.106, 1.707 0.019 1 1 SiH2 1042, 2095, 2099 8.149, 6.964, 3.755 0.014 2 3SiH 2 900, 2236, 2297 15.628, 5.186, 3.894 0.013 2 2SiH 2063 7.468 0.015 1 1H 2 4421 60.475 0.006 2 1 TS1 i1225, 751, 767, 987, 1050,1606, 2164, 2258, 2280 3.439, 2.692, 2.309 0.014 1 3TS2 i1305, 288, 421, 781, 936, 990, 1261, 2265, 2300 4.650, 1.532, 1.242 0.016 1 2TS3 i1371, 717, 968, 1611, 1953, 2150 5.626, 3.705, 2.584 0.043 1 2TS4 i792, 134, 283, 1006, 1469, 2098 7.474, 1.576, 1.302 0.020 1 3 TS5 i644, 1630, 1876 13.389, 4.757, 3.51 0.025 2 3TS6 i572, 210, 398, 1620 1.468 0.019 1 CP i221, 1649, 1774 33.80, 3.49,3.16 0.016 2
barrier. The singlet1Si atom may be deactivated to its ground triplet state3Si by collisional quenching during the reaction. As shown in the PES, the dissociation of the3SiH2intermediate to 3
Si þ H2 can occur by overcoming a 44.3 kcal/mol barrier at
TS5 with 32.7 kcal/mol exothermicity. Our predicted barrier energy is in good agreement with a previous theoretical value 44.7 kcal/mol computed by PMP4/6-31þþG(3d,3p)//HF/6-31G* þ ZPVE.[38] Furthermore, the exothermicity of the product channel 3Si þ H2, 32.4 kcal/mol, is close to the experimental
value, 34.8 kcal/mol. The energy difference between singlet and triplet states of Si atom at the CCSD(T)/CBS level is 19.3 kcal/mol, which is also in reasonable agreement with the ex-perimental value, 18.01 kcal/mol.[37b] As shown in Figure 1c, there exists a crossing point (CP) between the triplet and sin-glet SiH2 dissociation curves. To search for the CP, the
mini-mum energy path for 1SiH2! 1
Siþ H2 was calculated along
the reaction coordinate offfHASiAH angle reduced from 92.5 to 14 with a step size of 2.0 at the CCSD(t)/6-311þG(d,p) level. Similarly, for triplet SiH2case, minimum energy path was
calculated along the reaction coordinate of ffHASiAH angle decreases from 118.4 to 14with a step size of 2.0separated to3Siþ H2. The reaction coordinate for the CP was obtained at
ffHASiAH ¼ 32.9. The CP geometry was reoptimized at the CASSCF(6,6,Slaterdet)/ 6-311þG(3df,2p) level. Finally, the single-point energy for the CP with a 45.6 kcal/mol barrier from1SiH2
was obtained at the CCSD(T)/CBS level based on the optimized geometry using the CASSCF method.
Enthalpies of the formation
To validate the energetics for reliable prediction of rate con-stants, the predicted values of heats of formation (DfH) of all
the species related to Hþ SiHxreactions have been calculated
based on enthalpies of reaction at the CCSD(T)/6-311þG(d,p)/ CBS level with experimental values of DfH (0 K) from the
NIST-JANAF tables[39] and the relevant literature.[24,40,41] Fur-thermore, isodesmic (bond and spin conserving) reactions, such as2SiHþ 1CH4! 1 SiH4 þ 2 CH,1,3SiH2 þ 1 CH4 ! 1 SiH4 þ1,3CH2, and 2 SiH3þ 1 CH4! 1 SiH4þ 2
CH3allowing the
can-cellation of computed errors are also used to confirm the cal-culated heats of formation at 0 K. The predicted heats of for-mation of all the species are presented in Table 3. The two sets of DfH(0 K) values presented in Table 3 for
2
SiH, 88.6 1.2 and 90.2 kcal/mol,1SiH2, 66.0 and 66.9 kcal/mol, SiH3, 49.0
and 49.6 kcal/mol, were obtained by the corresponding unim-olecular dissociation processes and isodesmic reactions, respectively. The results obtained by the CBS method agree closely with existing experimental data listed in the Table 3. The 20.6 kcal/mol triplet–singlet energy difference of SiH2 also
agrees well with the experimental value, 21.0 0.7 kcal/ mol.[37a]It is interesting to note that comparing with the anal-ogous CH2 radical, not only the spins of the two lowest
elec-tronic states are reversed but also the energy difference appears to be very large (8.8 kcal/mol for the singlet–triplet splitting in CH2 versus 20.6 kcal/mol for the triplet–singlet
splitting in SiH2).
Rate Constant Calculations
The rate constants for the bimolecular reactions of H and SiHx
radicals and related unimolecular decomposition processes can be computed with the predicted PES using energies obtained by CCSD(T)/CBS extrapolation. For the HASiHx bond breaking
process without an intrinsic barrier, we apply the VTST method
Table 3. Heats of reaction (DrH
0) and heats of formation (DfH
0) of species at 0 K predicted at the CCSD(T)/6–3111G(d,p)/CBS level of theory given in
kcal/mol.
Species Reactions[a]
Heat of reaction DrH
0 Heat of formation DfH
0
Calculated Experimental Calculated Experimental
2SiH
3 1SiH4!2Hþ2SiH3 90.2 88.9 6 1.2 49.0 47.7 6 1.2
1SiH
2 1SiH4!1SiH2þ1H2 55.5 55 66.0 65.6 6 0.7
1
SiH2 2Hþ2SiH3!1SiH2þ1H2 34.7 33.9 6 1.2 64.7 6 1.2 65.6 6 0.7
2SiH 3 2SiH3!2Hþ1SiH2 68.5 69.5 6 1.2 48.8 6 0.7 47.7 6 1.2 2SiH 2SiH 3!2SiHþ1H2 40.9 41.9 6 1.2 88.6 6 1.2 89.6 6 1.2 1SiH 2 2Hþ1SiH2!2SiHþ1H2 27.6 27.6 65.5 6 1.2 65.6 6 0.7 1
SiH2 1SiH2!2Hþ2SiH 75.6 75.7 65.7 6 1.2 65.6 6 0.7
3SiH 2 3SiH2!2Hþ2SiH 55.0 54.7 86.3 6 1.2 86.6 6 0.7 3Si 3SiH 2!3Siþ1H2 22.6 20 6 1.2 109.2 6 0.7 106.6 6 1.9 1Si 1SiH 2!1Siþ1H2 62.5 – 128.1 6 0.7 124.6 6 1.9 3 Si 2Hþ2SiH!3 Siþ1 H2 32.4 34.8 108.9 6 1.2 106.6 6 1.9 1 Si 2Hþ2SiH!1 Siþ1 H2 13.1 – 128.2 6 1.2 124.6 6 1.9 2SiH 2SiHþ1CH 4!1SiH4þ2CH 76.8 78.1 90.2 89.6 6 1.2 1SiH 2 1SiH2þ1CH4!1SiH4þ1CH2 62.0 63.4 66.9 65.6 6 0.7 3
SiH2 3SiH2þ1CH4!1SiH4þ3CH2 32.6 – 86.2 86.6 6 0.7
2SiH
3 2SiH3þ1CH4!1SiH4þ2CH3 12.5 14.4 49.6 47.7 6 1.2
49.0[b]
[a] The experimental values used in the calculations are obtained based on the enthalpies of formation at 0 K for H¼ 51.7 kcal/mol; H2¼ 0.0 kcal/mol
; SiH4¼ 10.5 kcal/mol[39]; SiH3¼ 47.7 1.2 kcal/mol[40];1SiH2¼ 65.6 0.7 kcal/mol[37a]; SiH2and Si singlet–triplet splitting energy is 21.0 0.7 and
18.01 kcal/mol,[37] respectively; SiH ¼ 89.6 1.2 kcal/mol[37a];3Si¼ 106.6 1.9 kcal/mol[39]; CH¼ 141.2 kcal/mol[39]; CH
2(3B1)¼ 92.3 kcal/mol[39];
CH2(1A1)¼ 102.4 kcal/mol[41]; CH3¼ 35.6 kcal/mol[39]; (CH4¼ 16.0 kcal/mol.[39][b] Ref.[26a](calculated at the CCSD(T)/6–311þþG(3df,2p)//CCSD(T)/6–
to search for the MEP computed using the potential energies along the reaction coordinate (SiH) from about 1.5 to 5.5 A˚ with a step size 0.1 A˚ at the CASPT2//CASSCF level as described earlier. The rate constants for the bimolecular reac-tions 1–3 and the unimolecular dissociation reacreac-tions of their corresponding excited intermediates have been derived as functions of temperature and pressure by RRKM calculations:
SiH4! SiH3þ H (1c) ! SiH2þ H2 (1d) SiH3! SiH2þ H (2c) ! SiH þ H2 (2d) SiH2! SiH þ H (3d) 3SiH 2!3Siþ H2 (3e) 1SiH 2!1Siþ H2 (3f)
In the calculation of the specific rate constant, k(E,J) the num-ber of available states at the transition state is obtained at the
energy E and with the total angular momentum J resolved level based on the rigid-rotor harmonic oscillator assumption for the energy levels. For the evaluation of the electronic parti-tion funcparti-tion of SiH, the spin–orbit coupling energy of 142.83 cm1for X2P (1/2, 3/2) is used.[42] The average energy trans-ferred by downward collisionshDEdowni is assumed to be 400
cm1for SiHxand Ar collisions. Additionally, the Lennard-Jones
parameters for collision rate estimates are obtained by using r ¼ 4.08 A˚ and e ¼ 144 cm1for SiH
4[43]; r ¼ 3.943 A˚ and e ¼
118.3 cm1 for SiH3[43]; r ¼ 3.80 A˚ and e ¼ 92.5 cm1 for
SiH2[43]; and r¼ 3.75 A˚ and e ¼ 98.3 cm1for Ar.[23]
Bimolecular association of H with SiH3and
decomposition of SiH4
The bimolecular reaction of H and SiH3 occurs exclusively by
the association process forming the excited SiH4 intermediate
carrying as much as 90.2 kcal/mol of internal energy with 33.5 kcal/mol of excess energy above the transition state for H2
elimination at TS1; giving the SiH2radical as shown by the PES Table 4. Arrhenius parameters[a]for bimolecular reaction of H with SiHx(x 5 1–3) at various pressures including high-pressure limit (k‘) and
low-pressure limit (k0). P (Torr) A n Ea/R (K) kP(500 K) SiH3þ H ! SiH4(k1a) k1 3.32 1010 0.03 74 2.3 1010 k0 8.90 1019 5.32 1676 1.21 1034 0.3 2.44 6.31 1672 6.99 1019 1 8.43 6.32 1675 2.33 1018 10 8.82 101 6.32 1677 2.36 1017 760 8.87 103 6.34 1628 2.26 1015 SiH3þ H ! SiH2þ H2(k1b) 103–104b 3.55 1010 0.05 77 2.3 1010 103–104c 1.86 108 0.54 593 SiH3þ H !3SiH2þ H2(kTS2) 9.43 1018 2.28 765 2.83 1012 1 SiH2þ H2! SiH4 k1 1.66 1017 1.65 832 2.73 1012 k0 7.04 1018 4.44 1202 6.16 1031 0.3 2.07 101 5.44 1208 3.55 1015 1 7.25 101 5.44 1223 1.16 1014 SiH2þ H ! SiH3(k2a) k1 3.24 1011 0.47 84 5.05 1010 k0 7.62 1024 3.51 1158 2.32 1034 0.3 3.05 105 4.54 1135 1.64 1018 1 1.11 104 4.54 1132 5.76 1018 10 1.38 103 4.56 1131 6.44 1017 760 1.91 101 4.61 1128 6.7 1015 SiH2þ H ! SiH þ H2(k2b) 10 3 –104b 4.95 1010 0.07 229 4.93 1010 103–104c 2.61 104 1.60 1849 SiH2þ H ! SiH þ H2(kTS4) 1.05 1015 1.82 100 7.03 1011 SiHþ H2! SiH3 k1 1.28 1018 2.04 1379 2.59 1014 k0 3.42 10 23 2.96 813 6.47 1032 0.3 2.08 104 4.05 1645 8.56 1017 1 7.38 104 4.06 1847 1.94 1016 SiHþ H !1SiH 2(k3a) k1 5.71 1012 0.36 52 4.83 1011 k0 5.74 10 27 2.40 354 9.01 1034 0.3 1.67 108 3.40 355 5.21 1018 1 5.60 108 3.40 355 1.74 1017 10 5.38 107 3.40 354 1.72 1016 760 2.40 105 3.34 406 9.97 1015 SiHþ H !3Siþ H 2(k3b) via CP 103–103 1.73 1010 0.71 375 9.41 1013 SiHþ H !1 Siþ H2(k3c) 103–103 1.84 1010 0.18 222.9 3.70 1011 SiHþ H !3Siþ H 2(kTS5) via TS5 103–104b 1.71 109 0.32 299 1.26 1010 103–104c 2.42 107 0.95 915 SiHþ H !3Siþ H 2(kTS6) 1.20 1015 1.65 4.8 3.43 1011
[a] k(T)¼ ATnexp (-E
a/RT) predicted for various temperature in units of cm3molecule1s1for k and k1and cm6molecule2s1for k0at 300–2000 K
given in Figure 1a. The predicted rate constants for both prod-uct channels at 300–2000 K temperature range and various pressures including the high- and low-pressure limits are sum-marized in Table 4, and the rate constants are also graphically presented in Figures 3a and 3b. The calculated pressure-de-pendent rate constants for competing product formation at 500 K are displayed in Figure 3c. These results clearly show that the formation of SiH4 by collisional deactivation is
strongly P-dependent and cannot compete with the H2
elimi-nation process at pressure less than 106 Torr because of its low energy barrier and the small molecular size. At 500 K, the decomposition reaction is more than 107 times greater than the deactivation process under practical experimental condi-tions. This finding indicates that under PECVD conditions (e.g., P \ 1 Torr at 500 K), the SiH3þ H reaction rapidly generates
SiH2, and the SiH2 þ H2 reverse process is too slow to
com-pete. Our calculated rate constant for SiH3 þ H ! SiH2 þ H2
at 300 K is 2.1 1010 cm3molecule1s1, which is close to the value predicted by Barbato et al.,[23]1.2 1010cm3 mol-ecule1s1from their reported expression, 1.15 1011T0.736 exp(134.8/T(K)) cm3 molecule1 s1, using the kinetic Monte Carlo method to solve the master equation in their RRKM cal-culation based on PES computed at the CCSD(T)/CBS//B3lyp/ aug-cc-pvtz level of theory for 300–2000 K and 103–75 Torr pressure. Experimentally, Loh and Jasinski[44] investigated the Hþ SiH3reaction using the modeled SiH3densities generated
Figure 3. Arrhenius plots of rate constants for Hþ SiH3! SiH4 a), Hþ
SiH3! SiH2þ H2b) at different pressures and predicted rate constants at
T ¼ 500 K as functions of pressure for H þ SiH3 producing SiH4 and
SiH2þH2c).
Figure 4. Arrhenius plots of rate constants for SiH4 ! H þ SiH3 a) and
SiH4!1SiH2þ H2b) at different pressures. [Color figure can be viewed in
at various time profiles following photolysis of HCl/SiH4 at
room temperature and low pressure using infrared diode laser spectroscopy; they reported an unusually small rate constant for the exothermic radical–radical reaction, 2 1 1011cm3 molecule1s1, which an order of magnitude smaller than the computed values mentioned earlier. The rate constant for the direct H-abstraction yielding 3SiH2 þ H2 has been calculated
using TST with the Eckart tunneling corrections as shown in Figure. 3b. The rate constant is seen to be several orders of magnitude smaller than the association/decomposition process via the singlet surface due to the 4.2 kcal/mol barrier.
The result for the thermal decomposition of SiH4 by
colli-sional activation producing SiH3 þ H and SiH2 þ H2 is
pre-sented in Figure 4 for comparison with available experimental and theoretical data.[7b,10,22b,23] The decomposition reaction is dominated by the latter product channel because of its lower
energy barrier. As shown in the figure and the rate constant expressions summarized in Table 5 obtained by least-squares fitting to the predicted values, both reactions have positive-pressure dependence reflecting the nature of collisional activa-tion. At 500 K, the production of SiH2at the high-pressure limit
is predicted to be 14 orders of magnitude greater than that of SiH3, and the disparity becomes even greater at low pressures
under collision-controlled conditions due to the much higher energy requirement for the formation of the latter product (see Table 5). The calculated rate constant is in good agreement with all theoretical[10,22b,23]and experimental[7b]data measured by Matsui and coworkers using a shock tube at 33 1 Torr Ar pressure in the temperature range of 1250–1570 K. Their values lie within our results predicted for 10 and 100 Torr Ar pressure. The predicted rate constants for the1SiH2 þ H2! SiH4
reac-tion presented at various pressures are shown in Table 4.
Table 5. Arrhenius parameters[a]for unimolecular decomposition of SiHx(x 5 1–3) at various pressures including high-pressure limit (k‘) and
low-pressure limit (k0). P (Torr) A n Ea/R (K) kP(500 K) SiH4! SiH3þ H (k1c) k1 1.01 1017 0.26 46,155 1.56 1024 k0 1.23 1012 4.86 47,295 6.68 1043 0.3 3.74 1030 5.87 47,343 3.54 1027 1 1.38 1031 5.88 47,394 1.08 1026 10 1.70 1032 5.91 47,558 7.91 1026 760 1.96 1033 5.71 48,152 9.28 1025 SiH4!1SiH2þ H2(k1d) k1 2.78 1012 0.67 27,707 1.48 1010 k0 3.10 109 4.6 29,348 3.36 10 29 0.3 8.98 1027 5.6 29,353 1.93 1013 1 3.18 1028 5.6 29,368 6.32 1013 10 4.17 1029 5.6 29,470 5.49 1012 760 6.50 1030 5.46 30,013 8.69 1011 SiH3!1SiH2þ H (k2c) k1 1.28 1015 0.15 35,159 8.71 1016 k0 2.54 104 3.14 35,641 8.70 1036 0.3 1.02 1023 4.18 35,709 4.79 1020 1 3.96 1023 4.20 35,751 1.52 1019 10 4.47 1024 4.21 35,805 1.39 1018 760 4.59 1026 4.26 36,079 6.24 1017 SiH3! SiH þ H2(k2d) k1 5.97 109 1.23 23,120 9.52 108 k0 7.97 102 3.04 22,206 2.39 10 25 0.3 1.22 1022 4.26 23,090 3.15 1010 1 5.91 1022 4.31 23,311 7.12 1010 10 1.01 1024 4.38 23,773 3.04 109 760 8.18 1025 4.40 24,749 3.03 108 1SiH 2! SiH þ H (k3d) k1 5.19 1013 0.31 38,635 9.46 1020 k0 1.28 102 1.57 38,402 3.22 1040 0.3 3.69 1016 2.57 38,402 1.86 1024 1 1.24 1017 2.57 38,404 6.2 1024 10 1.28 1018 2.57 38,418 6.07 1023 760 1.05 1020 2.59 38,757 2.23 1021 3 SiH2!3Siþ H2(k3e) k1 7.17 1011 0.50 22,548 4.02 107 k0 1.04 101 2.91 21,209 4.80 10 26 0.3 1.98 1019 3.84 22,270 3.44 1011 1 6.33 1019 3.83 22,430 8.41 1011 10 5.37 1020 3.80 22,749 4.45 1010 760 3.20 1022 3.76 23,359 1.01 108 1SiH 2!1Siþ H2(k3f) k1 2.17 1013 0.11 32,075 5.5 1015 k0 1.19 102 1.64 32,074 5.8 1035 0.3 3.64 1016 2.65 32,080 3.37 1019 1 1.18 1017 2.65 32,079 1.12 1018 10 1.23 1018 2.65 32,092 1.1 1017 760 7.50 1019 2.64 32,388 4.09 1016
[a] k(T)¼ ATnexp (-E
Bimolecular association of H with SiH2and
decomposition of SiH3
As aforementioned, the association reaction of H atom with
1
SiH2producing SiH3 with more than 68.5 kcal/mol of internal
energy occurs without a well-defined transition state; the
disso-ciation of SiH3 can take place with 21.0 kcal/mol of excess
energy above its transition state (TS3) producing H2 and the
SiH radical. The predicted values of k2aforming SiH3at various
pressures between 0.3 and 760 Torr along with its high-pres-sure limit in the temperature range of 300–2000 K are graphi-cally presented in Figure 5a and are also listed in Table 4. In the table, the value for the low-pressure limit is also given for kinetic modeling. The values of k2a decrease as the increasing
from 300 to 2000 K. When the pressure increases from 0.3 to 760 Torr, k2a increases proportionally, as clearly illustrated in
Figure 5a, reflecting the need for collisional deactivation of the excited SiH3. The predicted rate constants for the Hþ SiH2!
SiHþ H2(k2b) is a pressure-independent process under
practi-cal conditions as shown in Figure 5b, and their rate constant values are given by the three parameter expression covering the temperature range of 300–1000 and 1000–2000 K at 103– 104 Torr in Table 4. For H-abstraction reaction (kTS4), the rates
are smaller at low temperatures; however, as the temperature increases, they become more competitive (Fig. 5b). Accordingly,
Figure 5. Arrhenius plots of rate constants for Hþ SiH2! SiH3a), Hþ SiH2
! SiH þ H2b) at different pressures and predicted rate constants at T¼ 500
K as functions of pressure for Hþ SiH2producing SiH3and SiHþH2c).
Figure 6. Arrhenius plots of rate constants for SiH3 ! H þ SiH2 a) and
SiH3! SiH þ H2b) at different pressures. [Color figure can be viewed in
the rate constants for production of SiH3 (k2a) and SiH þ H2
(k2b) at 500 K covering the wide pressure range are shown in
Figure 5c. These results clearly show that the formation of SiH3
by collisional deactivation cannot compete with the H2
elimina-tion process at pressures less than 106Torr because of its low energy barrier and the small molecular size involved.
The thermal decomposition of SiH3under similar conditions
as given earlier for the association process produces predomi-nantly SiH þ H2 due to its lower energy barrier comparing
with that for SiH2þ H. As shown in Figures 6a and 6b and the
rate constant expressions summarized in Table 5 obtained by least-squares fitting to the predicted values, both reactions have positive-pressure dependence reflecting the nature of collisional activation. At 500 K, the production of SiH at the high-pressure limit is predicted to be eight orders of magni-tude greater than that of SiH2 production and the disparity
becomes even greater at low pressures under collision-controlled conditions due entirely to the much higher energy requirement for the formation of the latter product (see Table 5). It is worth noting that, at the high-pressure limit, Walch and Dateo[21]calculated the rate constant for SiHþ H2
formation based on the PES computed at the CCSD(T)/ a-cc-PVTZ with an extrapolation to the basis-set limit at the MP2 level; their rate constant agrees closely with our result throughout the temperature range overlapped with ours, 400–2000 K (see Fig. 6b).
Figure 7. Arrhenius plots of rate constants for Hþ SiH !1SiH 2 a), Hþ
SiH! Si þ H2at pressure 103–103Torr except H-abstraction b), and
pre-dicted rate constants at T¼ 500 K as functions of pressure for H þ SiH producing1,3SiH2and1,3SiþH2c). [Color figure can be viewed in the online
issue, which is available at wileyonlinelibrary.com.]
Figure 8. Arrhenius plots of rate constants for1SiH2! H þ SiH a) and 3
SiH2 !3Siþ H2b) at different pressures. Predicted rate constant (solid
line) for1SiH
2!1Siþ H2(k3e) at 1 Torr pressure in comparison with the
experimental data at 1–10 Torr pressure from Ref. [46], shown in circular dots ‘‘*.’’
Bimolecular association of H with SiH and decomposition of SiH2
The rate constants of H þ SiH reactions via singlet and triplet paths have been calculated using the molecular parameters and the energies presented in Table 2 and Figure 1c, respectively. The results for Hþ SiH !1SiH2(k3a), Hþ SiH !
1 SiH2*! 3 Siþ H2(k3b) via CP, Hþ SiH ! 1 SiH2*! 1
Siþ H2(k3c) and the
reac-tion via the triplet transireac-tion state TS5 are plotted in Figures 7a and 7b in the temperature range of 300–2000 K covering 0.3– 760 Torr pressure. As seen from Figure 7a, the rate constant for the formation of the1SiH2product by collisional deactivation is
strongly pressure dependent and is negligibly small under prac-tical PECVD conditions. At pressures below 104Torr, formation of
3
Si þ H2 from H þ SiH reaction via the chemically activated 1,3
SiH2 *
intermediates is predominant and pressure independent due to the noncompetitive quenching process as shown in Fig-ure 7b along with the direct H-abstraction process via TS6. Com-paring the contributions from the four separate paths, the for-mation of3Siþ H2via
3
SiH2 *
and TS5 directly from Hþ SiH is dominant. At 500 K, the rate constant for this product channel is about 1–2 orders greater than those from the singlet-state path through CP and the direct abstraction via TS6 (kTS6), respectively
(see Fig. 7b and Table 4). The crossing probability of1SiH2! 3
Si þ H2spin-forbidden reaction is predicted to be 0.01–0.001 for
the energy from 10 to 1000 cm1by a nonadiabatic TST calcula-tion.[34,35] The predicted crossing probability is lower than that of Matsunaga et al.[45]who used a different method from Har-vey’s[35]and also used a different basis set for performing the CASSCF calculation in this energy range. The direct triplet prod-uct channel via3SiH2
*
is about three times larger than the forma-tion of the singlet products1Siþ H2via
1
SiH2 *
. The calculated rate constant expressions for all the reaction product channels obtained by three-parameter fitting in the 300–2000 K tempera-ture range at 0.3–760 Torr pressure are given in Table 4. The pressure-dependent rate constants for the bimolecular reactions of H þ SiH forming various products calculated at 500 K are shown in Figure 7c. Apparently, at high pressure, the3SiH2
prod-uct rate constants are predicted to be around 1 order of magni-tude faster than those of the singlet-state products.
The rate constant for the unimolecular decomposition of
1
SiH2 producing SiH þ H and that for the decomposition of 3
SiH2 via TS5 giving 3
Si þ H2 predicted at the
above-men-tioned reaction conditions are shown in Figure 8. From the fig-ure, one sees that the experimental rate constant of the 1SiH2
! 1Si þ H2 reaction reported by Johannes and Ekerdt [46]
is considerably smaller comparing with that of3SiH2 !
3
Siþ H2
due to the much larger endothermicity of the former process. Predicted rate constant for 1SiH2 !
1
Si þ H2 (k3f) at 1 Torr
pressure in comparison with the experimental[46] data at 1–10 Torr pressure are shown in Figure 8b and in good agreement.
Conclusions
The mechanism for the reactions of H atoms with SiHx (x¼ 1–
3) radicals and their related unimolecular decomposition proc-esses have been investigated with ab initio MO calculations
with the CCSD(T)/CBS extrapolation. The results show that, the reactions of H þ SiHx (x ¼ 1–3) leading to SiH4, SiH3, and 1,3
SiH2occurs with no intrinsic barriers. The excited
intermedi-ates can decompose predominantly via transition stintermedi-ates, TS1 for SiH4!
1
SiH2þ H2, TS3 for SiH3 ! SiH þ H2, and TS5 for 3
SiH2! 3
Siþ H2, with the predicted barriers of 56.7, 47.5, and
44.3 kcal/mol, respectively. The dissociation path1SiH2 ! 1
Si þ H2was computed to be endothermic by 62.5 kcal/mol
with-out an intrinsic barrier; however, we found a singlet–triplet sur-face CP locating at 16.9 kcal/mol below the1Siþ H2products
(or 45.6 kcal/mol from 1SiH2) with the bending geometry of
ffHASiAH ¼ 32.9. The Hþ SiHx reactions can also take place
by direct H-abstraction, the energy barriers for these processes were found to decrease according to the order, SiH3(4.2 kcal/
mol) [ SiH2 (1.3 kcal/mol) [ SiH (1.0 kcal/mol), consistent
with the strengths of the corresponding SiAH bonds.
The enthalpies of the formation DfHof SiH3, SiH2, and Si at
0 K have been predicted by using the computed enthalpies of reaction DrH
0, including the isodesmic reactions (SiHxþ CH4¼
SiH4 þ CHx) at the same level. The results are in good
agree-ment with previous experiagree-mental values. Furthermore, the rate constants for the bimolecular and unimolecular decomposition reactions for all the product channels have been calculated using the VTST method and/or the RRKM theory by solving the master equation involved over a wide range of P,T-condi-tions covering those used in a typical PECVD process.
Acknowledgments
M.C.L. also acknowledges the support from Taiwan Semiconductor Manufacturing Co. for the TSMC Distinguished Professorship and the NSC for the distinguished visiting professorship at National Chiao Tung University in Hsinchu, Taiwan. The authors are grateful to the National Center for High-performance Computing for com-puter time and facilities.
Keywords: ab initio calculation
silane chemistryreaction mechanismrate constantHow to cite this article: P. Raghunath, Y.-M. Lee, S.-Y. Wu, J. S. Wu, M. C. Lin, Int. J. Quantum Chem. 2013, 113, 1735–1746. DOI: 10.1002/qua.24396
Additional Supporting Information may be found in the online version of this article.
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Received: 13 September 2012 Revised: 12 December 2012 Accepted: 21 December 2012 Published online on 22 February 2013
![Table 5. Arrhenius parameters [a] for unimolecular decomposition of SiH x (x 5 1–3) at various pressures including high-pressure limit (k ‘ ) and low-](https://thumb-ap.123doks.com/thumbv2/9libinfo/7496106.115851/8.918.87.833.136.770/arrhenius-parameters-unimolecular-decomposition-various-pressures-including-pressure.webp)
