J. Phys. Chem. 1992, 96, 10848-10855
10848
termine that at temperatures below 310 K,we observe evidence of oscillatory AVCFs and that these oscillations become more pronounced as the liquid is cooled further. From the functional form of the extracted AVCF’s, we have inferred that inhomogeneity of local structuresin the liquid contributes dominantly to the process of librational dephasing. These results join and strengthen a large body of work on numerous molecular liquids, indicating that the transition to oscillatory AVCFs upon cooling is in fact a general phenomenon. Finally, we have discussed the puzzling absence of corroboration for this picture in MD simulations and stressed the importance of investing a renewed effort in understanding this discrepancy. Acknowledgment. We are indebted to Prof. K.A. Nelson and G. P. Wiederrecht for enlightening discussions and warm hospitality. We thank Dr. E. Mastov for technical assistance. S.R. thanks the Israeli Council for higher education for an Allon Fellowship. This work was supported by the Israel America Binational Science Foundation and the James Franck program for light-induced processes. The Farkas Center is supported by the Bundesministerium fur Forschung and the Minerva Gesellschaft fur die Forschung. Registry No. Benzene, 71-43-2.
References and Notes (1) Statistical Mechanics; McQuarie, D. A,, Ed.; Harper and Row: New York, 1976. (2) Rothchild, W. G. Dynamics of molecular liquids; Wiley: New York, 1984. (3) Steele. W. A. Adv. Chem. Phys. 1976, 34, 1. (4) Gordon, R. G. J. Chem. Phys. 1965, 43, 1307. (5) McTague, J. P.; Birnbaum, G.Phys. Rev. Lerr. 1968, 21, 661. (6) Frenkel, D.; McTague, J. P. J. Chem. Phys. 1980, 72, 2801. (7) Madden, P. A.; Tildsley, D. J. Mol. Phys. 1985. 55, 969. (8) Madden, P. A.; Tildsley, D. J. Mol. Phys. 1983, 48, 129. (9) Kluk, E.; Monkos, K.; Pastemy, K.; Zerda, T. Acta Phys. Pol. A 1979, 56, 109. (10) Cox, J. I.; Battaglia, M. R.; Madden, P. A. Mol. Phys. 1979, 38, 1539.
(11) Bansal, M. L.; Deb, S. K.; Roy, A. P. Chem. Phys. Lett. 1981,83, 83. (12) Dill, J. F.; Litovitz, T. A.; Bucaro, J. A. J. Chem. Phys. 1975, 62, 3839. (13) Evans, G. T.; Evans, M. W. J. Mol. Liq. 1983, 25, 177. (14) Linse, P.; Engstrom, S.; Jonsson, B. Chem. Phys. Lett. 1985,115,95. (15) Steinhauser, 0. Chem. Phys. Lett. 1981,82, 153. (16) Geiger, L. C.; Ladanyi, B. M. J. Chem. Phys. 1987,87. 191. Geiger, L. C.; Ladanyi, B. M. J. Chem. Phys. 1988,89, 6588. (17) Greene, B. I.; Farrow, R. C. Chem. Phys. Lett. 1983, 98,273. (18) Halbout, J. M.; Tang, C. L. Appl. Phys. &It. 1982,40, 765. (19) (a) Ruhman, S.; Kohler, B.; Joly, A. G.; Nelson, K. A. IEEE J. Quant. Electron. 1988, 24, 470. (b) Ruhman, S.; Joly, A. G.;Kohler, B.; Williams, L. R.; Nelson, K. A. Reu. Phys. Appl. 1987, 22, 1717. (20) McMorrow, D.; Lotshaw, W. T.; Kenney-Wallace, G.A. Rev. Phys. Appl. 1987,22,443. McMorrow, D.; Lotshaw, W. T. Chem.Phys. Lett. 1990, 174, 85. (21) Hattori, T.; Terasaki, A.; Kobayashi, T.; Wada, T.; Yamada, A,; Sasaba, H. J. Chem. Phys. 1991, 95, 937. (22) Hattori, T.; Kobayashi, T. J. Chem. Phys. 1991, 94, 3332. (23) Yan, Y.-X.; Cheng, L. T.; Nelson, K. A. In Advance in Nonlinear Sepecroscopy; Clarke, R. G. H., Hester, R.E., Eds.;Wiley: New York,1987. (24) Etchepare, J.; Grillon, G. J.; Chambaret, P.; Hamoniaux, G.; Onzag, A. Opt. Commun. 1987, 63, 329. (25) Ruhman, S.; Nelson, K. A. J . Chem. Phys. 1990, 94, 859. (26) Kohler, B.; Nelson, K. A. J. Phys. Condens. Matter. 1990, 2, 109. (27) Etchepare, J.; Grillon, G.;Chambaret, J. P.; Antonetti, A.; Orszag, A. Rev. Phys. Appl. 1987, 22, 1749. (28) Dardy, H. D.; Volterra, V.; Litovitz, T. A. J. Chem. Phys. 1973,59, 4491. (29) Yan, Y.-X.; Nelson, K. A. J. Chem. Phys. 1987,87, 6240. (30) Kubo, R. In Fluctuation, Relaxation and resonance in Magnetic System; ter Harr, D., Ed.; Oliver and Boyd: Edinburgh, 1992. (31) Deb, S. K. Chem. Phys. 1988, 120, 225. (32) Lynden-Bell, R. M.; Steele, W. A. J. Phys. Chem. 1984,88, 6514. (33) Sizer, T. J.; Kafka, D.; Duling, I. N.; Gabel, C. W.; Mourou, G. A. IEEE J . Quanr. Electron. 1983, 19, 506. (34) Chesnoi, J.; Fini, L. Opt. Lett. 1986, 11, 635. (35) Dawson, M. D.; Maxson, D.; Boggess, T. F.; Smirl, A. L. Opt. Lett. 1988, 13, 126. (36) Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; Vettering, W. T. Numerical Recipes in C; Cambridge University Press: New York, 1992. (37) Kohler, B.; Nelson, K. A. J . Phys. Chem., in press. (38) Hegemann, B.; Jonas, J. J. Chem. Phys. 1985.82, 2845. (39) Geiger, L. C.; Ladanyi, B. M. Chem. Phys. Leu. 1989, 159, 413.
Mechanlsm of the Thermally Induced Gas-Phase Decomposition of Silane: A Revlsltation M. A. Ring* and H.E.O’Neal* Department of Chemistry, San Diego State University, San Diego, California 92182 (Received: February 3, 1992)
Modeling of the SiH4 thermal decomposition (640-703 K, 80-320 Torr)ia revisited here since new kinetic data now invalidate our prior modeling. The new data are for silylene insertion reactions, for silylene-disilene isomerizations, and for the H2 elimination from Si2&. Three possible sink reactions as balance for silylene productiom were examined: (1) reactive intermediate polymerization followed by wall deposition, (2) reactive intermediate decomposition to a nonreactive species followed by wall deposition, and (3) direct reaction of polysilanes (Si3H8 and larger) on the walls. Using rate constants consistent with all present data, the modeling demonstrated that fits to the experimental data could only be achieved with polysilane-wall decompositions as sink reactions. Rate constants for these wall processes were obtained directly from our published Si3H8 decomposition data. In addition, the modeling indicated that best fits to the experimental data were realized with negative activation energies for all silylene Si-H bond insertion reactions in accord with new data on the SiH, SiH4 reaction (Walsh et al.),
+
Introduction In 1985 we proposed a mechanism for the silane decomposition under static system conditions: temperatures between 640 and 703 K and total pressures between 80 and 320 Torr.’ This mechanism, the essential features of which are shown in Scheme I not only explained all of the unusual kinetic behaviors of the silane system but also quantitatively fit the rather demanding product yield observations of Pumell and W&h2 (PBtW). These were as follows: a 3 / 2 order in silane initial reaction stage from
0 to 1% silane conversion, a rate accelerated transition stage from 3 to 10% reaction, a first order in silane middle stage from 10 to 30% silane conversion, and a f d inhibition stage at conversions above 3096, also R = (DS),.,/(S)o = 0.0274 f 0.0011, R’= (TS),,,ax/(S)o= 0.00474 f 0.00023, and MA = [(DS)I/(S)(TS)Imax= 0.20 f 0.01, where S, DS, and TS represent silane, disilane, and trisilane, and subscripts 0 and max refer to the initial and maximum yield conditions, respectively. From the vantage point of nearly a decade of experimental and theoretical inves-
0022-3654/92/2096-10848$03.00/00 1992 American Chemical Society
The Journal of Physical Chemistry, Vol. 96, No. 26, 1992 10849
Decomposition Mechanism of Silane tigations on a large number of the elementary reactions of this system, it is evident that some of the features of the original treatment remain valid; others require modification. SCHEME I: Ropolca (1985) Mechanism of the Silane
col)ol/tjo. Initiations: SiH4 SiH4
+ (M)
--
De-
+
SiH2 H2 + (M)
+ wall-PSi:
- -+ + + - +
SiH2SiH2+ H2
SiH3SiH
Sink Reactions: SiH2SiH2 SiH2SiH2
+ SiH4
(SiH2SiH2)2
wall-P
wall-Si:
wall-P H2
(where wall-P indicates wall-held polymer of stoichiometry (SiH2)x) In the former category are the interpretations of the initial and final reaction stages under P&W reaction conditions. That the initial, 3 / 2 order in SM, reaction stage corresponds to a region where the silane decomposition is solely homogeneous, unimolecular, and pressure dependent is now generally accepted (i.e., the reaction is SiH4 + (M) A SiH2 H2 + (M) fmt-order in silane and roughly half order in total pressure). Also, there is consensus on the cause of the reaction’s final stage: high hydrogen product concentrations cause rate inhibition as silylene back reactions with hydrogen compete with their reactions with silane.’ With regard to the important higher silane reactions, subsequent investigations of the disilane, trisilane, and tetrasilane decompositions have confirmed their homogeneous reaction channels and produced only minor changes in their Arrhenius parameters (seeTable I). Potentially important new observations here were that the disilane decomposition is slightly pressure dependent under static system conditions and that the trisilane and tetrasilane decompositions are nonstoichiometric with respect to their gas-phase products. The latter observations are critical to our present treatment (see later). The transition and middle stages of the decomposition, with 1) and near doubling in silane loss rates, their order change (3/2 are still not fully understood. Our earlier proposal’ still provides a reasonable and quantitative explanation for this unusual behavior. Thus we attributed the order change to the onset of a surface initiation promoted by (SiH2)xproduct depositions. A possible mechanistic representation for this is shown below. An
-
wall
-
Si:
A
wall;
+ Hz;
Si:
A
wall
+ SiH,
-
XHSiH3 wall
--C
SH,
A
+ SH2
wall
observation consistent with this interpretation is that in silane decompositions where silylene scavenging is complete, the kinetics remain those of the initial reaction stage over the entire course of reaction.’ Wall initiation kinetics were estimated’ using the order dependence observed by Robertson, Hills, and Gallaghe+ (RHG) for the surface reaction of silane at low pressures. When coupled with the P&W homogeneous gas-phase initiation kinetics, an overall second stage initiation was obtained which effectively displayed the observed fmt-order behavior over the pressure range = kpaw + kRHG = of the static system studies. Thus kinitintion (1015.18 x ,-559W/RT[S]0.5 + 107.82 x e-43800/RT[S]4Js-l).l,S In the following paper in this issue, Beccera and Walsh6 provide an
ref 8 9 10 9 11 12 11 11 11 11 11 11 11 11 11
- -
alternative explanation for the rate increases of the transition and middle reaction stages, namely a silylene promoted chain involving chemically activated disilane: SiH2+ S DS* SiH3SiH + H2,SiH3SiH+ S TS S M 2 + DS. This intuitively appealing alternative is based on recent RRKM calculations of Moffat et al.’ For the purpose of modeling the silane reaction, either our dual channel initiation or the B&W6 homogeneous P&Winitintion plus silylene chain can be used. We have employed the former and have deferred discussion of the pros and cons of the two approaches until later in this paper. Relative to our prior treatment, in the ‘no longer valid category”, are two highly significant kinetic changes: rate constants of silylene Si-H insertion reactions and rate constants of silylene/disilene isomerizations. Formerly, there were no data on these proctsses. Now, absolute rate measurements using laser absorption and laser induced fluorescence methods have shown that silylene insertionsinto Si-H bonds occur at rates two or more orders of magnitude faster than previously believed.13-14These reactions also appear to have negative activation energies,15 a characteristic which appears to be important to reaction behavior (seelater). Also,refined ab initio calculations of the silylsilylene -1314disilene isomerizations produce activation energies much lower than those used earlier (Le., E13 = 9 f 3I6l8 rather than 26 kcal,’ and E,, = 19 f 3 rather than 38 kcal’). These calculated activation energiesI6J8-” are supported by modeling studied8 of systems critically dependent on their values. The faster rates of silylene insertion and isomerization reactions (set Table 11) have profound mechanistic implications. Specifically, they necessitate revisions in ‘sink” reaction assignments, and the determination of the real sink reaction(s) of the silane decomposition is the major objective of this paper. An instructive way of viewing the silane decomposition is through s o w and sink reactions, where source reactions are those generating silylene and disilene reaction intermediates, and sink reactions are processes directly or indirectly removing reaction intermediates. In the former treatment, the sink reactions were assumed to be wall depositions of disilene polymers (see Scheme I), and the reaction controlling the sink reactions was the disilane decomposition, Si2H6 H2 + SiH2=!3H2. Our modeling’ showed that to fit the experimental observations, hydrogen elimination from disilane had to be 1,Zhydrogen (as shown), not 1,l-hydrogen (to form SiH3SiH, silylsilylene).’6.2’The modeling also required an activation energy for disilene isomerization to silylsilylene of at least 39 kcal. These conditions prevented system feedback of disilene intermediates,via the reactions S i H 2 S i H 2 SiH’SiH and SiH’SiH + SiH, Si3H8,and guaranteed polymerization and eventual wall deposition of all disilenes produced by the disilane/hydrogen elimination reaction. Modeling was successful on this basis for two reasons: the 52 kcal activation energy of the source reactions of the second stage matched the activation energy of the 1,Zhydrogen elimination from disilane (Le., the effective sink reaction of the system with E = 55.3 2.2 kcalg), and the much slower rates of silylene insertion resulted in artificially high intermediate concentrations which in turn greatly overemphasized the importance of polymerization reac-
--
SiH2SiH2 (SiH2SiH2)2 (SiH2)x (SiH2)x wall
-
- --
Main Gas-Phase Product Forming Reactions:
+ Si2H6 SiH2 + Si2H6* Si3H8
-
--
wall-PSiH2 + SiH2
SiH2 SiH,
TABLE I: Decomposition Kinetics of the Higher Silrncs reaction log A E kM7@-I) Si2H6 SiH,+ SiH2 14.5 49.2 2.39 14.4 48.8 2.56 15.75 52.20 4.41 Si2H6 SiH3SiH+ H2 15.3 55.3 0.15 16.45 57.8 0.32 Si3H8 SiH4+ SiH,SiH 14.68 49.94 2.06 15.41 51.17 4.38 Si3H8 Si2H6+ SiH2 15.69 52.99 2.12 15.70 53.20 1.85 7.55 Si3H8 all products 15.60 51.03 i-SiPHIO SiH4+ SiH3SiSiH3 15.2 50.3 5.22 1.27 Si3HB+ SiH2 15.8 >54.0 n-Si4+H,,,SiHl+ SiH3SiH2SiH 15.5 49.9 14.1 2.13 Si& + SiH3SiH 15.5 52.4 2.49 Si3H8+ SiH2 15.6 6 3 . 5
-
-
-
*
Ring and O'Neal
10850 The Journal of Physical Chemistry, Vol. 96, No. 26, 1992 TABLE II: Pertinent Kinetic and Tbenaochedcd Data
reaction SiH2 SiH4
+
SiH2
(A) Silylene Insertions prior modeling exptl k" (M-I S-I) kb (M-I s-I) 3.1 X IO8 6.6 X 1O'O
+ Si2H6
T (K)
rep
298 298 298
13 14 14
1.3 X 10" 2.0 X 10"
2.1 X IO9
(B) Hydrogen Elimination from Disilane prior calcdd or modeling exptid reaction (all singlet) Ec (kcal) E (kcal) Si2H6 SiH,SiH H2 high 55Sd Si2H4 H2 52.2 86.1d
--
+
ref
+
16 16 17
85.7d
(C) Silylsilylene-Disilene Isomerizations E,C Ed
-
reaction SiH,SiH Si2H4
-
Si2H4
(prior)
(calcd)
ref
29.2
9.0d 5.3 2e 13.0d
16 18 17
SiH,SiH
*
39.2
(D) Heats of Formation (kcal/mol) and Reaction Enthalpies (kcal) species SiH,SiH
AH?/
species
7 2 . 8 ' ~ ~SiH2SiH2 ~ 75 .X'JO
74.9'3 73.5cJi
H2SiSi:
6X.9eql
+. ---
reaction SiH,SiH SiH2SiH2 H2SiSiH2 HSiSiH H 2 SiH,SiH HSiSiH + H 2 H2SiSiH2 H2SiSi H 2 H2SiSi Si(H2)Si
+
+
MtJ
species
64.9'$16 HSiSiH 67.2'320 . .62.9'3'7 101.5'*20 Si(H2)Si 108.2'-'7
AHtJ 111.2'q20 95.6'J7
M(ca1cd) -7.9,16 -8.6:' -12.0" 44.020 35.420 34.2,20 45.317 -12.6''
Rate constant from prior modeling.' Rate constant from current literature. cActivation energy from prior mode1ing.l Ab initio calculated activation energies. e Estimated activation energy or reaction enthalpy. /Ab initio calculated heats of formation.
tions. With the new, faster silylene insertion rates (observed), faster silylsilylene/disilene interconversionrates (calculated), and exclusive 1,l-hydrogen elimination from disilane16.21 (calculated), it is no longer possible to tit the experimental observations of the silane system by our prior mechanism (see later). Successful modeling of the silane reaction requires identification of the real sink reaction(s) of the system. Whatever their nature, because of the constant R and MA ratios, they must have (or the reactions controlling them must have) activation energies in the 52 kcal range. In the following we offer an experimentally based answer to the sink reaction puzzle and support this answer with modeling results.
Mechanism of tbe Silane Decomposition The mechanism employed in our modeling is shown in Scheme 11. Most of the reactions are those of our former treatment. There is one signifhnt difference: reaction 5, hydrogen elimination from disilane, is now shown as a 1,l-elimination. Our test criteria for the modeling were the R, R', and MA ratios at maximum conversion, with special attention to their T and P dependencies. Product/time modeling was not a specific objective, but, as we have shown in our former modeling and demonstrate again here later, gas-phase product/time curves can be modeled successfully (as long as the product maximum conditions of the reaction's middle stage are met) by starting the surface channel of the dual channel initiation at about the 2.5% conversion point. Reactions 1-25 of Scheme I1 are all the reactions initially considered other than sink reactions. Arrhenius parameters shown for reaction 1 are a composite for the dual channel initiation (Le., parameters derived from rate constants obtained as the sum of the P&W
TABLE III: RRKM Adjusted Rate Constants and Arrbenius Parameters" PT = 80 PT = 160 PT = 320 Torr Torr Torr reaction lop, A E loa A E loa A E 26 3 4c 5 13dJ 14'J
8.62 14.69 9.78 14.91 9.21 10.15
0 49.61 -3.48 54.15 2.60 12.54
8.84 14.95 10.03 15.12 9.45 10.82
0 50.21 -2.82 54.64 2.76 13.93
9.05 15.15 10.10 15.31 9.83 11.19
0 50.65 -2.67 55.09 3.20 14.25
High-pressure Arrhenius parameters are given in Scheme 11. bThese parameters assume E = 0 and are based on the Inoue and Suzuki" determination of k4 = 6.6 X 1Olo M-l SKI,our determination of k 2 / k 3= 0.02 at 678 K and 184 Torr,I and RRKM fall-off calculations on the disilane and silane decompositions. cReaction 4 parameters were based on the RRKM fall-off calculation for reaction 3 to yield (k/k&xn3as a function of pressure at 667.2 K. By microscopic reversibility, these ratios also apply to reaction 4, therefore with (k..)rxn4 from Walsh et aI.,l5 we obtained k4 as a function of P at 667.2. Activation energies as a function of pressure were estimated from the two highest temperature data lines in the Walsh et al.I5 table. Reaction 13 parameters are based on RRKM calculations using the Becerra and Walshl* estimate of kl3 = 1.0 X IO7 s-I at 298 K and 200 Torr. CReaction 14 parameters are based on RRKM calculations using the Becerra and WalshIs estimate of k14 = 0.10 s-I at 298 K and 200 Torr. /Reaction 21 and 29 parameters were set equal to those of reaction 13, while those of reactions 22 and 30 were set equal to those of reaction 14. It was demonstrated that the modeling output of Scheme I1 was not affected when kll and kZ2were increased by a factor of 3 and k29 and k30 were increased by a factor of 9.
homogeneous initiation channel and the RHCG heterogeneous channel), and the Arrhenius parameters given for reactions 2-5, 13, and 14 are their high pressure values. The RRKM generated parameters used in the modeling of these pressure dependent reactions are provided in Table 111. The remaining reactions, headed as case A (reactions 26-40), case B (reactions 41 and 42), and case C (reactions 43-45) represent the three termination mechanisms considered: termination by gas-phase polymerization of silylenes and disilenes with wall depositions of these species and their polymers; termination by disilene and/or silylsilylene decomposition to some chemically inert species (presumably Si(H2)Si); and termination by wall adsorption/decomposition of trisilane and all heavier silanes, respectively.
Mscussion and Modeling Results The R, R', and MA ratios reach maximumvalues near the 13% conversion level, hence steady-state conditions of the middle reaction stage are reached early in the reaction. At the yield maximum, intermediate production and removal rates are equal. The reactions of intermediate production (Le., either our dual channel or the B&W approach discussed earlier) for modeling purposes can be considered as known. The task is to characterize the intermediate removal channels. Logically, these sink reactions are processes occurring at the reactor walls, since gas-phase product yields other than hydrogen are all quite low. We can think of only three possible sink reaction scenarios: case A (polymerization and wall deposition of disilenes and silylenes, the mechanism of our former treatment), case B (disilene or silylsilylene decompositions to disilaacetylenes, species presumed to be chemically inert and to eventually deposit on the walls), and case C ("higher" silane adsorptions and decompositions at the walls). The sole reaction of wall attached species is presumed to be release of hydrogen to the gas phase. Case A Termination: Disilene and Silylene Polymerization and Wall Deposition. This most obvious sink reaction possibility is consistent with the P&W findings that the initial stoichiometry of the wall deposits is Si,Hh? The main condition for fitting the experimental observations with case A sink reactions is that the intermediate generated in the hydrogen elimination from disilane (now known to be silylsilylene) must react almost exclusively by these reactions. There can be no significant system feedback.
The Journal of Physical Chemistry, Vol. 96, No. 26, 1992 10851
Decomposition Mechanism of Silane Thus silylsilylene must isomerize to disilene before it reacts with silane (the new isomerization activation energy data support this condition), and disilene must polymerize before it equilibrates with silylsilylene. The only adjustable parameters to the modeling are the rate constants of disilene and silylene polymerization and the rate constants of polymer wall deposition. We have modeled the silane reaction with polymerization and wall deposition rate constants ranging from reasonable (k, = 0.1 s-I, k, = lo6 M-l s-I) to their theoretical upper limits (k, = lo4s-I, k = 10” M-I s-l), see Scheme 11. Calculated R ratios, see Table I&, were only sensitive to the wall capture rate constants, and they were all much too high. It is evident that no reasonable combination of kp and k, can prevent feedback of the disilene and silylsilylene intermediates (via reaction lo), hence the case A termination mechanism is incompatible with the experimental observations. Force fits to the R ratios with these sink reactions (at any given temperature and pressure condition) can be realized, but only by raising the disilene to silylsilylene isomerization activation energy to values in excess of 30 Kcal. This implies an SiH3SiH SiH2SiH2isomerization enthalpy higher than 23 Kcal, much higher than the calculated values (see Table 11). Further, R and MA ratios obtained with such unreasonably high isomerization energies increase strongly with increasing temperature. Case B Termination: Disilene andlor Silylsilylene Decompositions. Feedback of disilene and silylsilylene can be prevented by fast decompositions of these species to some inactive species. There appear to be two reasonable reactions of this type: SiH2=SiHZ H2SiSi: H2, followed by H2SiSi: Si(H2)Si, and SiH3SiH HSiSiH, followed by HSiSiH Si(H2)Si. The modeling shows that R ratio fits can be achieved with these sink reaction decompositions (Scheme I1 reaction 41 or 42), but only if their activation energies are less than 13 kcal. The ab initio enthalpy calculations of Table I1 cannot support such low values. Case C Termination: Wall Capture and Reaction of Higher Silanes. Scott, Estes, and JasinskiZ2(SE&J) examined the question of homogeneous and heterogeneous thermal reactions of SiH4over a silicon surface. They concluded that heterogeneous reactions of silane under the P&W conditions were unimportant, and they demonstrated a relationship between silicon deposition and Si2& concentration. The former is consistent with our original views, and the latter is consistent with our assertion that the rate controlling step in the silane decomposition after reaching steady state is hydrogen elimination from disilane. An interesting suggestion of SE&J was that silicon deposition in the steady state may involve higher hydrides as well as higher silylenes and disilenes. The possibility of termination by higher hydrides was one not previously examined. On the qualitative level, there are results which support this possibility. Gates23reported that Si2H6and Si3Hschemically adsorb on Si( 1 1 1) surfaces to a much greater extent than SiH4,and it is evident that adsorbed silane does deposit silicon at P&W reaction temperature conditions. Consequently, higher silanes should also react on the walls to deposit silicon. The question is ‘How fast?” under the P&W reaction conditions. To provide an answer, we reexamined our results on the decomposition kinetics of Si2H6,Si3H8,and Si4HI0. All three reactions were studied statically over silicon and hydrogenated silicon surfaces at slightly lower temperatures but at comparable pressures to those of the silane decomposition. In the case of Si2H6,SiH4 product yields in excess butadiene were equal to the loss of Si2H6,I1indicating a homogeneous system with good mass balances. However, in the trisilane and tetrasilane decompositions under the same conditions of excess butadiene, reactant losses were always significantly greater than the sum of the yields of the gas-phase product yields.” In the particular case of trisilane, where the data were more accurate and extensive, reactant losses were always larger than SiH4 and Si2H6yields, and no other products attributable to the trisilane decomposition were detected. Hence, the possibility of trisilane reaction at the walls to give surface bound species (eventually reacting to silicon by hydrogen release) seemed likely. To put the possibility into a quantitative framework, we assumed that the stoichiometric discrepancies observed between trisilane loss and silane and disilane productions” were due to
-
--
+
--
TABLE I V Case A Modeling Resultsu for Siylene and Disilew Polymerizationsband Wall Depositions‘ as Sink Reactions kp (M-I s-I) 106 1 06 10” 10”
kw
(s-l)
0.1 104 0.1 104
R
10’‘ 8.02 6.95 8.02 6.95 X
R ’ X lo3 39.0 29.7 39.0 29.7
% rxn at max 29.4 27.6 29.4 21.6
“Results are for T = 667.2 K, PT = 160 Torr. bThe polymerization reactions of Scheme I1 (reactions 26-28 and 31-37) were assigned the indicated k, values. ‘The monomer and polymer silylene and disilene wall depositions of Scheme I1 (reactions 38-40) were assigned the inRexptl= 0.0274. R’ = dicated k, values. d R = [Si2H6]max/[SiH4]0; [Si3H8],,x/[SiH4]o; = 0.000474.
a trisilane “wall” reaction, hence kslnk(=) = kTS,loss - [ks + kDSlfomtlons.Calculations of the rate constants and corresponding Arrhenius parameters of this presumed sink reaction gave kainCcxp = lOI322 X e-46270*630/RT s-l. Similar and possibly faster rate constants would be expected for the wall reactions of tetrasilanes and pentasilanes, etc. Fitting the R , R‘, and MA Data. The silane reaction was modeled with the case C sink reactions (i-e.,Scheme 11, reactions 1-40 and 43-45) and with kslnkas calculated above. The R and MA ratios results, columns 3-5, Table V, were in close agreement with observation, particularly for T = 667 K, but deviated slightly from observation at the other temperatures. Only slight adjustments in the experimentally based kslnk values &e., less than 24% at 640 K, 7% at 667 K, and 19% at 703 K, all well within the errors of their estimation) were needed to produce the much improved agreements between observed and calculated ratios shown in the brackets of columns 6-8,Table V. The Arrhenius parameters for these “best fit” sink rate constants are kslnk,.& = 101527 x e-52622/RT s-1. Negative Activation Energies of Silylene Insertions. Our initial modeling assumed zero activation energies for all silylene Si-H insertion reactions (Scheme 11, bracketed parameters). After access to a preprint of work by WalshI5 on the temperature dependence of the SiH2/SiH4reaction, it seemed of interest to see what effect negative activation energy assignments to Si-H insertion reactions would have on the modeling. consequently, k4 parameters, shown in Table 111, were estimated (as described in footnote c, Table 111) as a function of total pressure from RRKM calculations on the disilane decomposition and from the Walsh insertion data. Assignments for the higher silylene insertions reactions (reactions 8, 10, 16,and 18) were made by analogy to reaction 4. Modeling results using these revised iqertion reaction rate constants, after additional small adjustments in the sink reaction rate constants, are shown as the nonbracketed values of columns 6-8 in Table V. It is evident that negative activation energy assignments to the silylene insertion reactions did result in improved agreements in the R , R’, and MA ratios, and this provides some support for such activation energies. A Minimal Reaction Scheme. Scheme I1 contains a large number of intermediate association, decomposition, and wall deposition reactions as well as silyleneldisilene type isomerization reactions between large species, which are not essential to the modeling. Thus if all these reactions are eliminated (Le., reactions of case A termination and reactions 23-25) no change in the R ratios exceeding 1% results. This means that the only reactions of significance for modeling the R, R’, and MA ratios of the silane decomposition under the P&W conditions are reactions 1-22 plus reactions 43-45. To fit hydrogen production curves, reactions 46-48 must be added. Reaction Initiation and Rate Acceleration-Other Modeling Tests. Figure 1 shows the gas-phase product production in time for the 703 K, 154 Torr condition with our mechanism (reactions 2-22 and 43-45 plus reactions 46-48 for hydrogen release from Si,Hh-wall bound species). Initiation was by the P&W homogeneous kinetics up to the 2.5% level and then via our dual channel kinetics beyond that point. It is clear that agreements between modeling and observation of the gas-phase products are as good
Ring and ONeal
10852 The Journal of Physical Chemistry, Vol. 96, No. 26, 1992 SCHEME II: Mechenism of the Surae Decomposition parameter@
-
reactions
1
SiH4 + M
SiH2 + H2 + M
3
(M) + Si2H6
5
7
Si3H8
8
9
Si3H8
10
H3SiSiH + H2 ( 5 , 6 ) Si2H6+ SiH2
SiH3SiH + SiH4
+ I1
Si3H8 (M)
SiH4 + SiH2 + (M)
I2
SiH3SiH2SiH+ H2
SiH3SiH
13 14
Si2H4+ (M)
15
Si4Hlo SiH3SiH2SiH+ SiH4 16
lb
3c 4c 5c
6 7 8
9 10 11 12 13c 14c 15 16
18
17 18
-
19 20
17
19
Si4H,o SiH2 + Si3&, 20
210
+ SiH3SiH2SiH22'
-
Si5HI2
23
SiH3SiHPSiH2+ (M)
SiH2 + Si4Hlo
24
Si5HI2 SSNY + SiH4 25
-
2SiH2-% SiH3SiH 27 SiH, + Si2H4 SiH3SiH2SiH SiH2 + SiH3SiH+iH2 28 SSNYb SSNY
SNYYc (29, 30) 304
SiH2 + SNYY -% SSNY 2Si2H4-% SSNY Si2H4+ SiH3SiH=SiH22SSNY Si2H4+ SNYY -% SNYY 2SiH3SiH=SiH2 2 SSNY SiH3SiH=SiH2+ SNYY 36 SSNY
12.76
51.53
1
sce Table I11 15.75 11.12 (10.82 15.90 11.23 15.70 10.60 (10.83 15.41 10.60 (10.91 15.25 1 1.23 12.74 13.42 15.64 10.60 (10.78 15.50 10.60 (10.91 15.80 10.60 (10.83
52.12 0.19
0.00) 56.64 2.20 53.20 -2.60 -0.91) 51.17 -2.60 0.00) 54.64 2.20 6.95 19.39 50.30 -2.60 0.00) 49.90 -2.60 0.00) 53.50 -2.60 4.91)
see Table I11 see Table 111
21 22 23 24 25
ref
E. (kcal)
log A
2c
-
Si4H,o Si2H6+ SiH3SiH
(M)
rxn no.
f f 16, 19 16, 19 11 15 11 15 11 15 g 8
50.30 50.30 0.00
14.64 15.60 10.63
10 15 13, 14 9, 16 11 11 15 3 11 15
Case A: Polymerization-Wall Deposition of Silylenes and Disilenes 26 6.0, 11.0 0.00
h h h i
27
6.0, 11 .O
0.00
i
28
6.0, 11.0
0.00
i
see Table 111 see Table 111
29 30 31
6.0, 11.0
0.00
i
32 33
6.0, 11 .O 6.0, 11.0
0.00 0.00
i
34
6.0, 11.O
0.00
i
35
6.0, 11.0
0.00
i
36
6.0, 11.0 6.0, 11.0
0.00 0.00
i
8 8
i
SNYY + SNYY 2 SNYY
37
Si2H4
38
-1.0, 4.0
0.00
i
39 40
-1.0, 4.0 -1.0, 4.0
0.00 0.00
i i
38
~all-Si~H~~ SNYY -% wall-SNYYd 40 SiH3SiH=SiH2 ~all-Si~H~~
--
-
SiH2SiH2 Si2H2+ H2 SiH3SiH 2 Si2H2+ H2 41
Si3H8 Si,H6-wall + H2 44 SilHIO Si4H8-wall+ H2 45 Si,H12 Si5Hlo-wall+ H2 43
Si,H6-wall
41 42
Case B: Disilene and silylsilylene Decompositions 14.48 53.00 15.11
55.10
Case C: Wall Termination of Trisilane and Higher Silanes 43 scc Table V 44 scc Table V
sce Table V
45
i
i i
11
11 11
46
Si3(.) + 3 H2
46
0.03
1, i
41
Si4(,,+ 4 H2
47
0.03
1,j
48
0.03
1,j
Si4H8-wall
Si5Hlo-wall
48
Si&)
+ 5 H2
The Journal of Physical Chemistry, Vol. 96, No. 26, 1992 10853
Decomposition Mechanism of Silane Sckme I1 (continued)
parametersu reactions
SiH2 + SiH,
2 SiH3SiH + H 2
rxn no.
log A
49
Silylene Induced Hot Molecule Chain see ref k
E. (kcal)
ref
k
"Units are s-I or M-' s-I for A, kcal for E. bComposite parameters of initiation calculated as the sum of kPrW and kRHG,see text. CParameters shown are for pressure condition. For pressure fall-off parameters of these reactions, see Table 111. dSSNY represents a silylene containing four or more Si atoms. 'SNYY represents a disilene containing four or more Si atoms. 'Parameters assigned by analogy to reactions 5 and 6. #Parameters assigned by analogy to reactions 13 and 14. *Parameters assigned by analogy to the reactions of the tetrasilane decomposition. 'See text for assignment rationale. 'Reactions represent several reactions in sequence each eliminating one H2 with a rate constant value as shown. 'The rate constant for the hot molecule chain induced by the reaction of silylene with silane was calculated from the fractional amount of the SiH2 SiH, reaction leading to SiH,SiH at 700 K and the pressure of interest, calculated by Moffat et al.,' and the rate constant of reaction 4 at that Same pressure. At 80. 160 and 320 Torr, the values of k49 are estimated to be 7.53 X lo9, 5.95 X lo9,and 4.58 X lo9 M-I 5-l at 80, 160 and 320 Torr, respectively.
+
40
35
30
25
20
w
v
15
10
5
seconds
Figure 1. Modeling results of gas-phase product production at 703 K and 154 Torr. Addenda: Plots are product pressure (Torr) vs time (s). The solid lines are the experimental curves as obtained by P&WG2Triangles represent trisilane product levels in Torr; circles represent disilane product levels in Torr;squares represent hydrogen product levels in Torr.
as those obtained by B&W6 with their all homogeneous, silylene induced chain reaction treatment. At this time it is not possible to say by this product modeling test which of the two approaches arc correct, but we have made several other modeling tests of the system which are interesting. We have modeled the reaction at 703 K and at 80, 160, and 320Torr with three different intermediate generation approaches: the P&W2 homogeneous initiation alone, the B&W6 approach (PCW homogeneous initiation2plus hot molecule silylene chain), and our dual channel initiation. Reaction 49 was added to the modelin# to incorporate the hot m o l d e ' induced silylene chain. Rate constants for this reaction at the temperature and pressures of intereat wcrc estimated from the calculations of Moffat et a1.2 as described in foot note k of Scheme 11. Results of these calculatim relative to the R, R', and MA ratios are shown in Table
VI. Fairly good R and MA values were obtained by all three aproaches, but the R'values were poor in the P&W case alone and showed strong dependencies with pressure in the B&W6case. With regard to the transition stage rate accelerations, both the R&O dual channel and the B&W hot molmle silylene chain generate the striking changes in silane loss rates which are experimentally observed (see Figure 2). Even the P&W initiation shows a small rate acceleration at the 3% point, indicating a small amount of ynormal" reaction 5 induced silylene chain; however, it is a much smaller acceleration than observed. A particularly interesting modeling test of the intermediate production mechanism involves the kinetic order changes of the initial and middle reaction stages. According to the data of PLW, initial slopes of fint-order silane loss plots, e.g., Figure 2, should increase with P'lz, while the slopes at conversions beyond the rate transition
Ring and O”ea1
10854 The Journal of Physical Chemistry, Vol. 96, No. 26, 1992
TABLE V Modeling Results for Case C Wall Adsorption-Decomposition of Tririlane a d Larger Silrws as the Sink Reactioas results for ksink,erp(l results for ksintadjwtd’ T (K) PTOV R X lo2‘ R’X MA‘ R X R ‘ X 103d 640.2 80 2.63 3.67 0.222 2.85 4.65 [2.76 4.46 160 2.53 3.75 0.205 2.76 4.76 [2.79 4.58 320 2.47 3.81 0.192 2.71 4.83 12.81 4.67 667.2 80 2.88 4.46 0.225 2.88 4.46 [2.89 4.44 160 2.78 4.61 0.207 2.78 4.61 [2.89 4.61 320 2.72 4.70 0.192 2.72 4.70 12.92 4.71 703.2 80 3.34 5.99 0.233 2.99 4.54 [3.08 4.46 6.22 0.214 2.89 4.14 160 3.25 [3.07 4.67 6.43 0.197 2.82 4.87 320 3.16 [3.06 4.83
MA‘ 0.213f 0.20218 0.196 0.20018 0.182J 0.20018 0.22si 0.22618 0.207f 0.21718 0.1921 0.21518 0.23g 0.25518 0.220, 0.24418 0.2011 0.23518
+
O k n i n k = kTS- (kDS k,) = 10’3.22X e46270/RT s-l, where TS = trisilane, DS = disilane, and S = silane (see text). *kSindjwtrd = 10’5.37X e-52851/Rr s-I for modeling with negative activation energies for silylene Si-H insertion reactions. krink,ad,ua,d - 10’5.27X e-52622/Rps-1 for modeling with zero = 0.0274. d R ‘ = [Si3H8]/[SiH4l0;R’eap,l 0.00474. ‘MA activation energies for silylene Si-H insertion reactions. R = [Si2H6]/[SiH4]0;RFapp‘l [Si2H612/[Si3H8][SiH,]; MAsaptl= 0.20. /Results with negative activation energies for all silylene insertion reactions; Scheme I1 no brackets for double listed parameters. g Results with zero activation energies for all silylene insertion reactions; Scheme I1 with brackets for double listed pa-
rameters.
-5.6
-5.65
-5.7
-5.75
-
-
-
-5.8
0
20
40
80
60 t
100
in seconds
120
140
160
I
Figure 2. Modeling results of silane loss rate acceleration with three different intermediate production modes (PBW, BBW, and RBO) for the 700 K, 168 Torr condition. Addenda: Plots are all In[SiH4] vs 1; concentrations in M, time in s. The curve labeled P B W corresponds to initiation via the Purnell and Walsh initial stage kinetics alone; the curve labeled BBW corresponds to initiation via the h r n e l l and Walsh initial stage kinetics plus the hot molecule chain initiated by the reaction, SiH2 + SiH4 (Si2H6): SiH3SiH + H2; the curve labeled R&O corresponds to initiation via the Purnell and Walsh initial stage kinetics plus a surface initiation by (SiH,), polymers starting at 30 s.
-
should be total pressure independent. In Table VI1 we show the 3 / 2 order and first-order rate constants calculated from the modeling for the initial and second stage regions of the silane decomposition, respectively, at 700 K and total pressures of 80, 160, and 320 Torr for the three types of processes considered. All three approaches give the proper initial reaction kinetics as one would expect, i.e., kuni/Pi/2 = constant. However, pressure independence of the rate constants of the second stage is best produced by the dual channel initiation (less than 8% deviation from constancy in the k‘s). For the B&W approach, rate constant variations over the pressure range are close to 20%.
-
A very important modeling test of the B&W approach will be the effect of temperature on the R,R’,and MA ratios. Unfortunately, this test cannot be made until the hot molecule RRKM calculations on reaction 4 are extended to other temperatures. Since the silylene chain only operates from molecules well out on the Boltzmann tail, it is difficult to believe that temperature will not have a significant effect on the ratios. Finally, it is important to note that the hot molecule calculations of Moffat et ala7depend strongly on the true value of the silylsilylene heat of formation. The value consistent with our modeling is wf(SiH,SiH) = 74.1 kcal/mol, a value close to the lowest reported. For any signifi-
The Journal of Physical Chemistry, Vol. 96, No. 26, 1992 10855
Decomposition Mechanism of Silane TABLE VI: Comparisoacl of PBW? BbW," and Dual Channel' Intermediate Production Mechrnisms Relative to R , R', and MA
Ratios'
R
R'
MA
0.0226 0.0257 0.0299
0.00281 0.00526 0.00454
0.215 0.162 0.239
PCW only BCW RCO
160 Torr 0.0251 0.0271 0.0289
0.00367 0.00586 0.00474
0.207 0.160 0.220
P CW only BCW R&O
320 Torr 0.0277 0.0290 0.0282
0.00469 0.00658 0.00483
0.199 0.164 0.235
pressure and approach
80 Torr
PCW only BCW (PCW chain) RCO (dual channel)
+
"Results are for T = 700 K. Termination was by case C reactions and with adjusted krinkwith negative activation energies for silylene insertion reactions.
enhanced termination of the B&W approach is more difficult to rationalize. In summary, while there are still questions concerning the cause of the rate accelerations of the transition and middle stages of the silane reaction under P&W reaction conditions, all present data and knowledge of the system points to termination via trisilane, tetrasilane, and higher silane adsorptions and subsequent decompositions on the walls. Reliable data now exist for most of the relevant reactions of the silane decomposition system, but additional data are still needed on the kinetics of the silylsilylene to disilene isomerization, the kinetics of the disilane decomposition to silylsilylene and hydrogen, and the heat of formation of silvlsilvlene. Acknowledgment. We are indebted to the National Science Foundation for financial support of this work (Grant CHE8719843). We also thank Dr. R. Walsh for his helpful comments and critique. Registry No. SiH4, 7803-62-5.
References and Notes TABLE MI: Initial Stage and Middle Stage Rate Constants for the P 0 W, B & W, and Dual Channel Intermediate Production Mechanisms' initial stage middle stage P (Torr) k/[S]1/2 (M-'l2 s-I) k @-I) approach PCW only 80 1.08 x 10-2 7.15 X lo4 160 1.14 X 1.03 x 10-3 1.34x 10-3 320 1.17 X BCW 80 1.22 x 10-2 1.58 x 10-3 (homogeneous 160 1.41 X 1.72x 10-3 plus chain) 320 1.31 X 1.96 x 10-3 RCO 80 1.08 X 1.27 x 10-3 (dual channel) 160 1.14 X 1.36x 10-3 320 1.17 X 1.38 x 10-3 'Calculations were made for the 700 K condition with case C terminations and with negative activation energies for silylene insertion reactions.
cantly higher value (e.g., as little as 2 kcal/mol), the calculations indicate that hot molecule effects are far too small to produce the required rate accelerations. Surface Effect Implications. The absence of surface effects in the silane decomposition*has important implications for both our and the B&W6 approach. Because of the RHG surface component of the dual channel initiation, one would expect to see reaction acceleration with increasing surface. However, the termination routes proposed here (and favored also by B&W) are surface reactions,hence a cancellation of surface effects is possible. Surface insensitivity for the homogeneous initiation and surface
(1)White, R. T.; Espino-Ria, R. L.; Rogers, D. S.;Ring, M. A.; ONeal,
H.E. Int. J. Chem. Kinet. 1985, 17, 1029. (2) Purnell, J. H.; Walsh, R. Proc. Roy. SOC.Ser A. 1966, 293, 543. (3)Erwin, J. W.; Ring, M. A.; O'Neal, H. E. Int. J . Chem. Kinet. 1985, 17, 1067. (4)Robertson, R.; Hils, D.; Gallagher, A. G. Chem. Phys. Lerr. 1984,107, 397. (5)O'Neal, H. E.;Ring, M. A. Chem. Phys. Lett. 1984, 107,442. (6)Becerra, R.; Walsh, R. J . Phys. Chem., following paper in this issue. (7)Moffat, H. K.; Jensen, K. F.; Carr, R. W. J . Phys. Chem., in press. ( 8 ) Bowery, M.; Purnell, J. H. Proc. Roy. Chem. SOC.Ser A. 1971,321, 341. (9)Dzarnoski, J.; Rickborn, S . F.; ONeal, H. E.; Ring, M. A. Organometallics 1982, I , 1217. (10)Martin, J. G.; Ring, M. A.; ONeal, H.E.Int. J . Chem. Kiner. 1987, 19,715. (1 1) Martin, J. G.; ONeal, H. E.; Ring, M. A. h t . J. Chem. Kinet. 1990, 22,613. (12) Vanderwielen,A. J.; Ring, M. A.; ONeal, H. E. J. Am. Chem. Soc. 1975, 97,993. (13) Inoue, G.; Suzuki, M. Chem. Phys. Leu. 1985, 122,361. (14)Jasinski, J. J.; Chu, J. 0. J . Chem. Phys. 1988,88,1678. (15)Becerra, R.; Frey, H. M.; Mason, B. P.;Walsh, R.; Gordon, M. S. J . Am. Chem. Soc., submitted for publication. (16)Gordon, M. S.;Truong, T. N.; Bonderson, E. K. J . Am. Chem. Soc. 1986, 108, 1421. (17)Ho, P.;Melius, C. F. J. Phys. Chem. 1990, 94, 5120. (18)Bercerra, R.; Walsh, R. J . Phys. Chem. 1987, 91,5765. (19)Boatz, J. A.; Gordon, M. S.J . Phys. Chem. 1990, 94,7331. (20)Sax, A. F.; Kalcher, J. J . Phys. Chem. 1991, 95, 1768. (21)Nares, K. E.;Harris, M. E.; Ring, M. A.; O'Neal, H. E. Organometal. 1989, 8, 1964. (22)Scott, B. A.; Estes, R. D.; Jasinski, J. J. J . Chem. Phys. 1988, 89, 2544. (23) Gates, S. M. Surf. Sci. 1988, 195,307.
