95
J. Phys. Chem. 1994,98, 95-99
Ab Initio Molecular Orbital Study of the Strengths of the Gallium-Carbon Bonds in Ga(CH3), n = 1-3 Charles W. Bock' and Mendel Trachtman Chemistry Department, Philadelphia College of Textiles and Science, Philadelphia, Pennsylvania 19144 Received: July 22, 1993'
Ab initio molecular orbital calculations at a variety of levels are used to investigate the strengths of the Ga-C bonds in trimethyl-, dimethyl-, and monomethylgallane. The calculations show that the Ga-C bond is strongest in trimethylgallane and weakest in dimethylgallane. Computational support for the observed polymerization of monomethylgallane is found in a favorable 10 kcal/mol dimerization energy for monomethylgallane.
-
The decomposition of DMG to MMG
Introduction Metaloogranicvapor-phaseepitaxy (MOVPE) is a widely used method for the preparation of thin films of group 111-V (13-1 5) semiconductors,such as gallium arsenide, GaAs, because it offers both high productivity and versatility.' In the preparation of GaAs using MOVPE, gaseous precursors, e.g., trimethylgallane (TMG) and arsine, are passed over a heated substrate, initiating a complex series of homogeneous and heterogeneous chemical reactions.2 Despite many advances in the use of this technique for the fabrication of GaAs films,' the fundamental reactions involved in the deposition process are still not well ~nderstood.~ Recently Tirtowidjojo and Pollard5 have developed a comprehensive mathematical model for the deposition of GaAs from TMG and ASH, on a (1 1l)Ga substrate using MOVPE. The model includes multicomponent heat and mass transport, fluid flow for an impinging jet system, and reaction kinetics for elementary processes in the gas phase and at the growing surface. Sixty distinct species and in excess of 230 reactions in the gas phase, together with 19 separate species and more than 100 reactions at the surface were included in the model. The rate constants required for this vast array of processes were estimated using statistical mechanics, transition-state theory, and bond dissociation enthalpies."* The model subsequently identified approximately 25 major elementary processes involved in the deposition. The important gas-phase reactions include the decomposition of TMG to dimethylgallane, DMG, and the subsequentdecompositionof DMG to monomethylgallane,MMG. The formation of DMG from TMG is an important component in the overall MOVPE fabrication of GaAs and may occur either in the gas phase or after adsorbtion of TMG on the ~ u r f a c eIn .~ the gas phase, the reaction Ga(CH,),
-
Ga(CH,),
+ CH,
(1)
appears to havea significantbarrier. In their study of the pyrolysis of TMG in the temperature range 740-840 K, Jacko and Priceg reported an activation barrier of 59.5 kcal/mol, a value which was subsequently adopted by Tirtowidjojo and Pollard5 in their model. In a statistical reevaluation of these experimental results, using the complete set of data points reported by Jacko and Price? Oikawa et a1.10 obtained a revised value of 59.2 f 5.5 kcal/mol. However, after eliminating two suspiciouspoints from the original Jacko and Price9data, Oikawa et al.1° suggested a higher value for the barrier, 64.3 f 4.3 kcal/mol. Interestingly, ab initio molecular orbital calculations at the PMP4/HUZSP*//UHF/ HUZSP* level find the Ga-C bond strengths in the compounds ethylgallane and trans-methylgallomethylarsineto be 66.0 and 68.1 kcal/mol,I1J2 respectively, in reasonable agreement with the revised results for TMG. Abstract published in Aduance ACS Abstracts, December 15, 1993.
0022-3654/94/2098-0095$04.50/0
Ga(CH,),
GaCH,
+ CH,
(2) is also very important for the fabrication of GaAs films, since MMG is probably one of the dominant species adsorbed on the growing ~ u r f a c e Jacko . ~ and Price9 also studied this decomposition and obtained a Ga-C bond energy of 35.4 kcal/mol, significantly lower than the Ga-C bond energy for Ga(CH3)'. Although no direct computational results for reaction 2 have been reported in the literature, Bala~ubramanian,'~ using multiconfigurationSCF calculations with a relativistic effective core potential, has shown that removing a hydrogen atom from GaH, requires -80.9 kcal/ mol, while removing a hydrogen atom from GaH2 requires significantlyless energy, -40.6 kcal/mol, in qualitativeagreement with the results of Jacko and Price9 for the methyl analogs. The further decomposition of MMG into .CH3 and Ga is nqt one of the dominant gas-phase reactions predicted by the Tirtowidjojo and Pollard5 model. One possible explanation is that the barrier for this decomposition in the gas phase is quite large. In their study of the pyrolysis of TMG, Jacko and Price9 found that at temperatures above which two-thirdsdecomposition occurred, gallium was found quantitatively in the reaction vessel as a thin, apparently nonmetallic, film suggesting that GaCH3 does not decompose but rather deposits in the reaction vessel as the polymer (GaCH3)". Taking the total strength of the three Ga-C bonds as 172.4 kcal/mol,13 Jacko and Price9 estimated the energy of the Ga-C bond in MMG to be -77.5 kcal/mol, which is significantly higher than the value they obtained for the energy of the Ga-C bond in TMG, 59.5 kcal/mol. In this connection, Bala~ubramanianl~ computed the energy to remove an H atom from Ga-H to be -64.8 kcal/mol, which is significantly lower than the energy computed to remove an H atom from GaH3. One might expect that the stepwise removal of H atoms from GaH3 would correspond more closely to the stepwise removal of methyl groups from Ga(CH3)'. In fact, calculations at the PMP4/ HUZSP*//UHF/HUZSP* level suggest that the strengths of the Ga-C and Ga-H bonds in trans-methylgallomethylarsine and ethylgallane are very similar.Ql3 In the present paper ab initio molecular orbital methods are utilized to determine the energies required to break the Ga-C bonds in TMG, DMG, and MMG. The calculations are performed at a variety of computational levels in order to assess the effects of including polarization functions and electron correlation in determining the strength of these bonds. The possible polymerization of MMG9 is also investigated computationally by considering the dimerization of MMG. Computational Methods Ab initio calculations were carried out using the GAUSSIAN 92 series of programs15 on the Cray Y-MP/832 computer at the Q 1994 American Chemical Society
96
Bock and Trachtman
The Journal of Physical Chemistry, Vol. 98, No. 1 , I994
Pittsburgh Supercomputer center and on IRIS 4D/35 and VAX 8250 computers located in Philadelphia. Equilibrium structures were initially computed using all-electron, nonrelativistic, singledeterminant Hartree-Fock (HF) theory with the Huzinaga (4,3,3,21/4,3,21/4,*) basisset for gallium, which includesa splitvalence shell and one d-type polarization function.16 The basis sets for C and H were taken directly from the standard 6-31G* set." For convenience, this combined basis set will be referred to as HUZSP*.I8 Electron correlation was included using frozen core (FC) Moller-Plesset perturbation theoryIg up to the MP4SDTQ(FC)HUZSP**//HF/HUZSP* level, with p functions on the H atoms and using spin-projected energies for the DMG and *CH3radicals.20 Frequency calculations were performed at the HF/HUZSP*//HF/HUZSP* level to verify that the computed structures were indeed stable states. TOassess the effects of electron correlation on the geometries of TMG, DMG, and MMG, optimizations were then performed using frozen core second order Moller-Plesset19 perturbation theory with the basis set for the valence shells and p orbitals on the Ga atom completely uncontracted, Le., (4,3,3,111/4,3,111/4,*). If p functions are included on the H atoms, this combined basis set will be referred to as HUZSP(3)**. To determine the effects of increasing the flexibility of the basis set for the completely filled third shell of gallium, additional single-point calculations were performed with the 3d-function split, Le., (4,3,3,111/4,3,111/3,1*), using the MP2(FC)/HUZSP(3)** optimized geometry. We will refer to this hybrid basis set when p functions are included on the H atoms as HUZSP(4)**. Isolated calculations were performed with the Ga atom third shells and p functions also split; however, reaction energies were not significantly changed with this increase in the flexibility of the basis set. Single-point calculations were also carried out with multiple polarization functions on both the Ga and C atoms, as well as expanded versions of the (7,3/7) Huzinaga basisset16ontheC atom,using theMP2(FC)/HUZSP(3)** geometry, to assess the importance of more flexible basis sets in the description of the Ga-C bonding.16 Recent calculations on related Ga and A1 compounds can be found in refs 21 and 22, and calculations on heavier analogs can be found in ref 23. An excellent discussion of the approximations and limitations inherent in calculations a t these levels can be found in ref 24.
Results and Discussion The computed structures of all the molecules involved in the present study are shown in Figure 1, and the corresponding total molecular energies at a variety of computational levels are listed in Table 1. Complete geometries in the form of Z matrices are given in Table 1 s of the supplementary material (see paragraph at end of paper). The computed reaction energies for the decompositions of TMG, DMG, and MMG are given in Table 2 a t 298 K, and at higher temperatures in Table 2 s of the supplementary material.
TMG, DMG, MMG, and the Ga-C Bond Strength As expected, the symmetries of TMG, DMG, and MMG are and C3,, respectively. As can be seen from Figure 1, the Ga-C bond length increases along the series TMG, DMG, and MMG a t both the HF/HUZSP*//HF/HUZSP* and the MP2(FC) /HUZSP( 3) * *//MP2( FC)/HUZSP( 3) * * levels. The C-Ga-C angle in DMG is slightly less than 120.0° at both levels of optimization, a likely consequence of the repulsion between the nonbonded electron and the two methyl groups. The computed geometry of TMG is in excellent agreement with that calculated by Graves and Scuseria25 using Dunning's 14sl lp5d primitive basis set contracted to (7s5p2d). Mulliken population analysis at the HF/HUZSP*//HF/HUZSP* level suggests that the net positive charge on the Ga atom decreases along the series TMG, C3hr C,,
H H
i
1.085 11 13.0'1
t0.175
ll.09ll
0.122
II
H IGaCH31,
Figure 1. Optimized geometries of Ga(CH,),, Ga(CH3)2, GaCH3, and
[GaCHo]2. All distances are in angstroms, and all angles in degrees. Optimized parameters are at the HF/HUZSP*//HF/HUZSP* level, and if available, the MP2(FC)/HUZSP(3)**//MP2(FC)/HUZSPS(3)** optimized parameters are given in square brackets. The positive and negative values refer to atomic charges on the respective atoms. DMG, and MMG, with the largest variation occurring between TMG and DMG, see Figure 1. A H 2 9 8 for the decomposition of TMG into the DMG and 'CH3 is given iin Tables 2A and 2B at a variety of computational levels which include single polarization functions on the Ga and C atoms. Additional results are given in Tables 3 s and 4 s of the supplementary matterial. Correlation effects are extremely important for the description of the decomposition of TMG and typically increase the enthalpy change for this process by some 25 kcal/mol. However, increasing the order of the perturbation correction from PMP2(FC)/HUZSP** to PMP4(FC)/HUZSP** a t the RHF/HUZSP* geometry decreases AH298 by less than 0.8 kcal/mol. Estimated values for A H 8 5 0 are not significantly different from AH298 and are given in Table 2 s of the supplementary material. The computed values of AH298 listed in Table 2B lie in a narrow range from 72.6 to 73.4 kcal/mol, but are significantly higher than the original experimentalvalue reported by Jacko and Price,g 59.5 kcal/mol, and also higher than the revised experimental value suggested by Oikawa et al.,1° 64.3 f 4.3 kcal/mol. It is important to note that splitting the 3d function changes A H 2 9 8 by less than 0.4 kcal/mol, see Table 2B, and a further split of the 3s and 3p functions changes A H 2 9 8 by less
The Journal of Physical Chemistry, Vol. 98, No. 1 , 1994 97
Gallium-Carbon Bonds
TABLE 1: Total Molecular Energies (au) and Zero-Point Vibrational Energies (kcal/mol) Ga(CW3 Ga(CHd2 WCHd CH3 Ga -2 040.256587 -2 000.611 44 -1 961.011 518 -39.558 992 -1 921.395562 HF/HUZSP*//HF/HUZSP*" -2 040.272 875 -2 000.623445 -1 961.016982 -39.567 424 -1 921.397314 PUHF/HUZSP**//UHF/HUZSP* -2 040.806685 -2 000.988 301 -1 961.230604 -39.694 602 -1 921.441 107 PMP2(FC)/HUZSP**/HF/HUZSPLb -2 040.876 218 -2 001.037815 -1 961.265 368 -39.715847 -1 921.455301 PMP4(FC)/HUZSP**/HF/HUZSP* PMP2(FC)/HUZSP(3)**//MP2(FC)/HUZSP(3)' -2 040.853485 -2 001.035054 -1 961.277423 -39.694 621 -1 921.487570 PMP2(FC)/HUZSP(4)**//MP2(FC)/HUZSP(3)**d*e -2041.031 248 -2001.213 425 -1 961.456695 -39.694621 -1 921.667279 PMP2(FC)/HUZSP(3)[*)*//MPZ(FC)/HUZSP(3)** -2 040.880948 -2 001.059699 -1 961.299555 -39.694621 -1 921.507604 PMP2(FULL)/HUZSP(3)[*lS//MP2(FC)/HUZSP(3)**f&-2 040.940 022 -2 001.112 283 -1 961.346247 -39.699 458 -1 921.548260 PMP2(FULL)/HUZSP(3)(2d,p)//MP2(FC)/HUZSP(3)**Jh -2 040.988713 -2 001.144797 -1 961.363031 -39.708 886 -1 921.548260 PMP~(FULL/HUZSP(~,~)(~~,P//MP~(FC)/HUZSP(~)**' -2 041.053706 -2 001.188692 -1 961.386230 -39.731 627 -1 921.548260 PMP~(FULL/HVZSP(~,~)(~~,P//MP~(FC)/HUZSP(~)**~ -2 041.300071 -2 001.422925 -1 961.608 130 -39.747 895 -1 921.756680 PMP~(FULL/HUZSP(~,~)(~~,P//MP~(FC)/HUZSP(~)**~ -2 041.314585 -2 001.432 574 -1 961.612975 -39.752 514 -1 921.756 680 71.0 46.8 zero-point energy (kcal/mol) 22.5 19.4 a HUZSP*Ga: (4,3,3,21/4,3,21/4,*) C: 6-31G*. FC = frozencore. e HUZSP(3). Ga: (4,3,3,111/4,3,111/4,*),Ga: 9 = 0.207C: 6-31G*. dIf A H 2 9 8 for TMG DMF + CH3 is 73.2kcal/mol. HUZSP(4)* = (4,3,3,111/ the s and p functions are also split, Le., (4,3,21,111/4,21,111/3,1,*), 4,3,111/3,1,*). JFULL = all orbitals active. 8 [*I* indicates two d functions only on the Ga atom Ga: 9 = 0.091,0.336. Two sets of d functions on all heavy atoms Ga: 9 = 0.091,0.336.Ga: HUZSP(3)*, see c above; C: 9 = 0.288,1.355(52,111/511)from (7,3/7);see ref 16. Ga: HUZSP(4)*, see e above C: 9 = 0.288, 1.355(52,111/3211)from (7,3/7);see ref 16. Ga: HUZSP(4)*, see e above C: 9 = 0.288,1.355(322,111/31111)from (7,3/7);see ref 16.
-
TABLE 2
-
-
AE and AH Values for the Decomposition of TMG, DMF, and MMG (kcalhnol) TMG DMG DMG + CHI M M G + CH3 AE AH AE AH
MMG CH3
+
-
Ga
A E A H
energy for three Ga-C bonds
2A
HF/HUZSP*//HF/HUZSP*b
54.06 51.46
49.76 47.16
25.68 24.50
21.23 20.04
35.74 32.78
32.55 29.59
103.54 96.79
PMP2(FC)/HUZSP**/HF/HUZSP*bc PMP4(FC)/HUZSP**/HF/HUZSP* PMP2(FC)/HUZSP(3)**//MP2(FC)/HUZSP(3)**d PMP2(FC)/HUZSP(4)**//MP2(FC)/HUZSP(3)**eJ
77.67 76.90 77.69 77.31
73.37 72.60 73.39 73.01
39.59 35.52 39.53 38.98
35.13 31.06 35.08 34.52
59.54 59.12 59.76 59.48
56.35 55.93 56.56 56.29
164.85 159.59 165.03 163.82
2c PMP2(FC)/HUZSP(3)[*] *//MP2(FC)/HUZSP(3)**
79.46
75.16 76.19 80.44
41.12 41.78 45.75
36.66 37.32 41.29
61.08 61.83 66.46
57.88 58.63 63.26
169.70 172.14 184.99
79.40 76.84 76.96
44.45 41.98 42.10
39.99 37.52 37.64
66.73 65.11 65.12
63.53 61.79 61.93
182.92 176.15 176.53
PUHF/HUZSP**//UHF/HUZSP* 2B
PMPZ(FULL)/HUZSP(3)[*] +//MP~(FC)/HUZSP(~)**~T~ 80.50 PMP2(FULL)/HUZSP(3)(2d,p)//MP2(FC)/HUZSP(3)**8 84.75 2D
PMP2(FULL/HUZSP(3,1)(2d,p//MP2(FC)/HUZSP(3)**J 83.70 PMPZ(FULL/HUZSP(4,2)(2d,p//MPZ(FC)/HUZSP(3)**k 81.11 PMP2(FULL/HUZSP(4,3)(2d,p//MPZ(FC)/HUZSP(3)**' 81.25 All thermalcorrtctionsweremadeattheHF/HUZSP*//HF/HUZSP* level.
HUZSP' = (4,3,3,21/4,3,21/4,*). e FC = frozencore. HUZSP(3)* = (4,3,3,111/4,3,111/4,*).Ifthesandpfunctionsarealsosplit,i.e.,(4,3,21,111/4,21,111/3,1,*), AH298forTMG-DMG+CH3 is73.2kcal/mol. fHUZSP(4)' = (4,3,3,111/4,3,111/3,1,*). 8 FULL = all orbitalsactive. [*I* indicates two d functionsonly on the Ga atom. Two sets of d functions on all heavy atoms. j Ga: HUZSP(3)*,see c above; C: 9 = 0.288,1.355(5,2,111/511)from (7,3/7)see ref 16. Ga: HUZSP(4)*, see e above; C: q = 0.288,1.355(5,2,111/3211) from (7,3/7)see ref 16.'Ga: HUZSP(4)*, see e above; C: 7 = 0.288,1.355(322,111/31111)from (7,3/7)see ref 16.
than 0.2 kcal/mol. A single-point calculation at the QCISD/ HUZSP(3)**//HF/HUZSP* level, which generally yields the most accurate dissociation energies, finds A H 2 9 8 to be 72.8 kcal/ mol, in good agreement with the corresponding PMP2 and PMP4 calculations listed in Table 2B. For comparison purposes, we note that A H 2 9 8 at the MP2(FC)/HUZSP(3)**//MP2(FC)/ HUZSP(3)** level for the removal of a hydrogen atom from GaH3is 73.1 kcal/mol. This is in good agreement with the result of Bala~ubramanian,'~ if our thermal corrections are applied to his results. The computed values of A H 2 9 8 for the decomposition of DMG to MMG and 'CH3, which include only single polarization functions on the Ga and C atoms, are also given in Tables 2A and 2B at a variety of computational levels. Correlation effects increase the enthalpy change for this decomposition by some 1&15 kcal/mol. In this case, increasing the order of the perturbation correction from PMP2(FC)/HUZSP** to PMP4(FC)/HUZSP** using the RHF/HUZSP* geometry lowers the enthalpy change for the decomposition by -4 kcal/mol. The computed values of A H 2 9 8 in Table 2B lie in the range 3 1.1-35.1 kcal/mol. All of these values are in reasonable agreement with the experimental value of Jacko and Price? 35.4 kcal/mol, if the experimental error is similar to the value suggested by Oikawa,
et a1.I0 for the decomposition of TMG, Le., f5.5 kcal/mol. In any event, the experimental and computational results agree that the barrier for breaking the Ga-C bond in DMG is significantly lower than that for breaking the Ga-C bond in TMG. A H 2 9 8 values for the decomposition of MMG to a Ga atom and 'CH3 are also given in Tables 2A and 2B. Correlation effects increase the enthalpy change for this decompositionby -25 kcal/ mol. The computed values for A H 2 9 8 in Table 2B for the decomposition of MMG lie in the narrow range from 55.9to 56.6 kcal/mol. These values are significantly lower than the value proposed by Jacko and Price? 77.5 kcal/mol. It is also important to note that the computed values of A H 2 9 8 for the removal of the methyl group from GaCH3 are significantly lower than the corresponding computed values for the removal of a methyl group from Ga(CH&. This is in disagreement with the results of Jacko and Price? but in qualitative agreement with the computational results of Bala~ubramanianl~ for the removal of H atoms from GaH and GaH3. The above discrepancies between the computed and experimentalvalues for theabsolute and relativestrengths of thevarious Ga-C bonds in TMG, DMG, and MMG led us to recalculate the total energy for the formation of three Ga-C bonds usiing more recent experimental thermochemical A H 2 9 8 for the
98 The Journal of Physical Chemistry, Vol. 98, No.
reaction Ga(CH3)3(g)
-
+ 3CH3(g)
(3)
is a measure of the total bonding energy for the formation of three Ga-C bonds. Earlier calculations26of the heat of reaction 3 used a value of 32.5 kcal/mol for the heat of formation of 'CH3, which leads to a value of approximately 173.0 kcal/mol for the formation of the three Ga-C bonds. More recent measurements*' and high-level calculations28suggest a significantly higher value for the heat of formation of 'CH3, 35.6 f 0.2 kcal/mol. Using the experimental value of -9.9 f 1.5 kcal/mol for AHof of trimethylgallium(g),29and 65.0 f 0.5 kcal/mol for AHvBp of Ga(g),z7 the computed dissociation energy for the three galliumcarbon bonds is 181.7 f 2.6 kcal/mol. This is -9.0 kcal/mol greater than the value used by Jacko and Price9 and, in conjunction with their original experimental values for the Ga-C bond strengths in TMG and DMG, would suggest that the strength for the Ga-C bond in MMG is -87 kcal/mol, which is nearly 30 kcal/mol greater than their value for the Ga-C bond in TMG. Furthermore, their experimentalvalue for the Ga-C bond strength in TMG, 59.5 kcal/mol, would now be less than the revised mean Ga-C bond strength of -60.6 kcal/mol, which would be rather unusual.l3 The last column in Table 2B lists the sums of the computed bond strengths of the Ga-C bonds in TMG, DMG, and MMG at various computational levels which include correlation effects and single polarization functions on the heavy atoms. The values lie in the range 159.6-165.0 kcal/mol, considerably below the experimental value of 181.7 f 2.6 kcal/mol obtained above from reaction 3. This suggests that the level of computation and/or the basis sets employed in these calculations underestimate the strengths of Ga-C bonds. Thus, additional calculations were performed which include two d-type polarization functionsI6on the Ga atom, with both the frozen core and full options, using the MP2(FC)/HUZSP(3)** optimized geometries. Employing this more complete basis set increases the strengths of the Ga-C bonds in all three structures, and their sum now ranges from 169.7 to 172.1 kcal/mol; see Table 2C. However, these values are still some 10 kcal/mol below the experimental value noted above. Expanding the basis set further to include two d functions on both the gallium and carbon atoms, single-point MP2( FULL) calculations were performed at the MP2(FC)/HUZSP(3)** optimized geometry. This raises the total bond strength to 185.0 kcal/mol, which is in reasonable agreement with the above experimental value. Thus, it seems necessary to include multiple polarization functions on both the carbon and gallium atoms to adequately describe the Ga-C bonding using the HUZSP(3) basis set. Since the 6-31G basis set for carbon is rather inflexible, we performed additional calculationsusing various expanded versions of a (7,3/7) Huzinaga basis set for carbon,*6 see Table 2D, including two d functions on both the Ga and C atoms. This lowers the strength of the Ga-C bonds in each of the structures TMG, DMG, and MMG a few kcal/mol, compared to the results in Table 2C, reducing the total bond strength to about 176.5 kcal/mol, some 5 kcal/mol below the experimental value noted above. However, thestrength of the Ga-C bond in TMG remains significantlyhigher than the experimentalvalue obtained by Jacko and Price.g It is important to note that the Ga-C bond in TMG is found to be 17 kcal/mol stronger than the Ga-C bond in MMG at all the levels of computation reported above; see Tables 2A, 2B, and 2C. This is in stark contrast to the experimental results of Jacko and Priceg in which they suggest that the Ga-C bond in MMG is 18 kcal/mol stronger than the Ga-C bond in TMG. However, our computed results are in qualitative agreement with the calculations of Balasubramanian14 on GaH3 and GaH, in which the Ga-H bond in GaH3 was found to be 16 kcal/mol stronger than the Ga-H bond in GaH.
-
-
-
Bock and Trachtman
I, 1994
Conclusions At temperatures below 773 K, the mathematical model developed by Tirtowidjojo and PollardSfor the MOVPE of GaAs suggests that the deposition rate of GaAs is dictated primarily by the kinetics of surface reactions, and that the homogeneous decomposition of TMG is relatively unimportant. The results of the above ab initio calculations strongly support this conclusion, and suggest that it may be more difficult to decomposeTMG into DMG and 'CH3 in the gas phase than previously thought. The calculations confirm the experimental results of Jacko and Price9 that the Ga-C bond in TMG is substantially stronger than the Ga-C bond in DMG but find the Ga-C bond in MMG to be weaker than the Ga-C bond in TMG, in disagreement with Jacko and Price.9 It is interesting to note that removing 'CHs from H3As:Ga(CH3)3at the PMP2/HUZSP*//HF/HUZSP* level requires approximately the same energy, A H 2 9 8 = 74.0 kcal/mol, as removing 'CH3 from isolated Ga(CH3),.30 Thus, it seems that a simple adsorption onto an electron donating site on the surface would do little to alter the strength of the Ga-C bond in TMG. On the other hand, model calculations by Tsuda et al.31 suggest that interactions of an alkyl group on gallium with neighboring As-H bonds may significantly lower the activation energy for this decomposition. Jacko and Pricegalso suggested that MMG may not decompose but rather polymerize according to (4)
To investigate this possibility, we computed the dimerization energy of MMG at the MP2(FC)/HUZSP**//RHF/HUZSP* level. Indeed this reaction is exothermic, A H 2 9 8 = -10.0 kcal/ mol, which lends some support to their assertion. Although there are clearly many points in which the experimental and computational results on the pyrolysis of TMG are in agreement, neverthelessinconsistenciesconcerning the absolute and relative strengths of the Ga-C bonds in TMG, DMG, and MMG remain. Additional calculations at the MCSCF level, as well as further experiments on the complete pyrolysis of trimethylgallane would certainly help to clarify this situation, and at the same time provide more accurate informationfor future modeling.
Supplementary Material Available: Tables of selected Z matrices, values for decomposition and AE of TMG, DMG, and MMG, total molecular energies, zero-point vibrational energies (5 pages). Ordering informationis given on any current masthead page. References and Notes (1) Coleman, J. J.; Dapkus, P. D. In Gallium Arsenide Technology; Ferry, D. K., Ed.;Sams: Indianapolis, IN, 1986; p 89. (2) (a) Putz, N.; Heinecke, M.; Balk, P.; Weyers, M.; Luth, H. J. Cryst. Growth 1986,74,292. (b) Chiu, T. H.; Cunningham, J. E.; Robertson, Jr., A.; Malm, D. L. J. Cryst. Growth 1990, 105, 155. (c) Piocos, E. A.; Ault, B. S. J. Am. Chem. Soc. 1989, I I ! , 8918. (3) Cowley, A. H.; Benac, B. L.;Ekerdt, J. G.; Jones, R. A.; Kidd, K. B.; Lee, J. Y.; Miller, J. E. J . Am. Chem. Soc. 1988, 110, 6248. (4) (a) Tirtowidjojo, M.; Pollard, R. J. Cryst. Growrh 1989,98,420. (b) Omstead, T. R.; Van Sickk, P. M.; Lee,P. W.; Jensen, K. F. J. Cryst. Growth
1988, 93, 20. (5) Tirtowidjojo, M.; Pollard, R. J . Cryst. Growth 1988,93,108. Other models can be found in: Sherman, A. J. Electron. Mater. 1988, 17, 413. Arora, A.; Pollard, R. J. Electrochem. Soc. 1991,138, 1523. Frenklach, M.; Wang, H. Phys. Rev. 1991, 43, 1520. (6) Benson,S.W. ThcrmochcmfcalKfnerfcs, 2nded.; Wiley: New York, 1976. (7) Laidler, K. J. Chemical Kinetics, 3rd ed.; Harper and Row: New York, 1987. (8) Kondrat'ev, V. N. Chemical Kinetics of Gas Reactions; Pergamon: Oxford, 1964. (9) Jacko, M. G.; Price, S. J. W. Can. J. Chem. 1963.41, 1560. (10) Oikawa, S.;Tsuda, M.; Morishita, M.; Mashita, M.; Kuniya, Y. J. Cryst. Growth 1988, 91, 471.
Gallium-Carbon Bonds
The Journal of Physical Chemistry, Vol. 98, No. 1, 1994 99
(11) Bock. C. W.;Trachtman, M.J. Phys. Ch" 1993,97, 3183. (12) Bock, C. W.;Trachtman. M. 1. Phys. Chem. 1992, 96,8048. (13) Long, L. H. Pun Appl. Chem. 1%1,2,61. (14) Balasubramanian. K. Chem. Phys. Lctr. 1989, 164, 231. ( 15) Gaussian92, Revision A; Friach, M.J.; Trucja, 0. W.;Had-Gordon, M.;Gill, P. M.W.; Wong, M.W.;Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.;Robb, M. A.; Reploglc,E.S.;Gompcrt~,Re;-, J. L.; Raghavachari, K.; Binkley, J. S.;Gonzalez, C.; Martin, R. L.; Fox, D.J.; Defrcg, D.J.; Baker, J.;Stmart, J. J.P.;Pople, J.A.;Gaurrian,Iao.: Pittsburgh,PA, 1992. (16) Huzinaga, S.; Andzslm, J.; Klobukowaki,M.;Radzio-Andzclm, E.; Sakai, Y.;Tatmah, H. Gaussian Basis Sets for Molecular Calculations; Elsevier: Amsterdam, 1984. (17) Hariharan, P. C.; Pople, J. A. Theor. Chim. Acta 1973, 28, 213. (18) Bock. C.; Trachtman, M.; Murphy, _ - C., Muschert, B.; Mains, G. J. Phys. Chem. 1991,95,2339. (19) Moller, C.; Pl-t, M. S . Phys. Rev. 1934,16, 678. (20) Schlenel. B. H. 1. Chem. Phvs. 1986.84.4530. (21) van dir Woerd, M.J.; Lf"crtsma,~K.;Duke, D.J.; Schafer 111, H.F. J. Chem. Phys. 1991,95, 1160.
(22) Jin,S.Q.;Xie,Y.;Schacfer111,H. F. J . Chem. Phys. 1991,95,1834. (23) Balasubramanian. K.; Tao, J. X. J. Chem. Phys. 1991,94,3000. (24) Hehre, W. J.; Radom, I.; Schleyer, v. R.; Pople, J. A. Ab Initlo MOlecular Orbital Theory; John Wiley & Sons: New York, 1986. (25) Graves, R. M.;Scwria, G. E.J. Chem. Phys. 1992,915,3723, (26) Long, L. H.;Sackman,J. F. Trans. Faradaday Soc. 1958,54,1797. ( 2 7 ) (a) Lias, S.;B a r t " , J. E.;Liebman, J. F.; Holmes, J. L.; Levin, R. D.;Mallard, W.G. J. Phys. Chem. Ref.Data 1988,17, Suppl. No.1. (b) JANAF Themochemical Tables, 3rd ul.; Chasc, Jr M. W.; Davies, C. A.; Downey, Jr. J. R.; Frurip, D. J. McDonald, R. A.; Syverud, A. N. J. Phys. Chem. Ref.Data 1985, 14, Suppl. No. 1. (28) Curtiss, L. A.; N o h , R. H.; Pople, J. A.; Radom, L. J. Phys. Chem. 1992, 97, 6766. (29) Pulley, J. B.; Rylance, J. Sussex-N.P.L. Computer Analysed Thermochemical Datu; Brighton, University of Sussex, 1977. (30) Bock. C. W., unpublished results. (31) (a) Tsuda, M.;Morishita, M.;Oikawa, S.; Mashita, M. J. Appl. Phys. 1988,27, L960. (b) Tsuda, M.; Oikawa, S.;Morishita, M.;Mashita, M. J. Cryst. Growth 1990.99, 545.
.--I
