J . Phys. Chem. 1988, 92, 6379-6381
of the opposing forces for cluster ion growth and destruction as described by reactions 2-4. In order to test this specific possibility, additional experiments were performed in which the pressure in the first region of the mass spectrometer vacuum envelope was intentionally raised from the lowest possible value of 1.5 X to 5.0 X Torr by partially closing the butterfly valve that connects this region to its diffusion pump. With He as the buffer gas, this change in background pressure caused no detectable change in the observed ion intensities. If reaction 4 had been operative and served to cancel a tendency for cluster growth in the jet by reactions 2 and 3, one might have expected this tripling of background pressure to have led to an increase in the relative intensity of the smaller cluster ions. (This result is, in fact, observed when this experiment is performed with nitrogen as the buffer gas.) Therefore, it does not appear that the appearance of accurate ion sampling in He is due merely to cancellation of these opposing effects.
II
L L
7 0.'51
v
c
c
6379
0.10
0.05 -
He, 2 0 0 ° C
Conclusion
(5) involved and the partial pressure of water. The measurements shown are those for which the ions involved constituted at least 3% of the total ion signal. A variation in water pressure of almost 1 order of magnitude was possible for measurements of K3,4,and a variation of a factor of 3 was possible for measurements of K4,5. The redundancy of measurements at a given partial pressure of water shown in Figure 8 results from the different combinations of dry and humidified carrier gas flow rates possible that provide the same final water content. The measured equilibrium constants for clustering shown in Figure 8 are clearly independent of the magnitude of water concentration used. Also, the magnitude of each measured constant is essentially equivalent to that measured by Kebarle et al.I3 at this temperature; K394= 0.15 Torr-] and K4,5= 7.4 X Torr-] (the small differences between Kebarle's and our measurements are easily within that expected due to measurement uncertainties associated with each method). In spite of the evidence provided above suggesting the lack of sampling perturbations whenever helium or hydrogen is used as the buffer gas at the higher ion source temperatures, the possibility nevertheless remains that the appearance of accurate ion sampling under these conditions is due merely to an accidental cancellation
Although the physical conditions used for ion sampling in APIMS are in gross violation of the criteria normally considered necessary for the accurate ion sampling of a high-pressure ion source, we have provided evidence here which suggests that accurate ion sampling by APIMS may nevertheless be possible with specific selections of the buffer gas and ion source temperature. By use of helium or hydrogen carrier gas and ion source temperatures in excess of about 125 OC, we have shown that accurate measurement of equilibrium distributions of hydrated hydronium ions can be made by an APIMS if the diameter of its aperture is on the order of 20 pm and is made in 10-pm stainless steel. An obvious extension of this study would be to vary both the dimensions and the metallic composition2' of the aperture. Extrapolation of the known effects of aperture size to even smaller apertures than used here may further facilitate the ease with which the contents of an atmospheric pressure ion source can be accurately sampled.
Acknowledgment. This work was supported by the Chemical Analysis Division of the National Science Foundation under Grant NO. CHE-8711618. Registry No. H', 7732-18-5; HzO, 12408-02-5 (21) Sigmond, R. S. In Gaseous Dielectrics III: Christophorou, L. G., Ed.; Pergamon: New York, 1982; pp 92-96.
Energetics of Acetylene-Addition Mechanism of Diamond Growth D. Huang, M. Frenklach,* and M. Maroncellit Department of Materials Science and Engineering, Pennsylvania State University, University Park, Pennsylvania I6802 (Received: March 17, 1988)
A semiempirical quantum mechanical (MNDO) method was applied to investigate the energetics of a recently proposed elementary-reaction mechanism of epitaxial diamond growth at low pressures. The mechanism consists of surface activation by H atom abstraction of a hydrogen atom from a surface carbon followed by the addition of acetylene molecules. The computed potential surface indicated that the propagation steps, those of acetylene addition, proceed without any energy barriers.
Introduction L ~growth of crystalline ~ diamond films ~has become ~ a subiect of intensive research.'-7 It has been demonstrated that high-huality diamond films can be produced employing different experimental techniques: microwave and radio frequency plasmas, 'Department of Chemistry.
0022-3654/88/2092-6379$01.50/0
not filament, UV-assisted deposition, e t c 7 A variety of hydroin these experiment^.^^^ carbons ~ were used ~as starting material ~ ~ ~ (1) Derjaguin, B. V.; Fedoseev, D. V. Sci. Am. 1975, 233, 102. (2) Fedoseev, D. V.; Derjaguin, B. V.; Varshavskaya, I. G.;SemenovaTyan-Shanskaya, A . S. Crystallization of Diamond; Nauka: Moscow, 1984 (in Russian). (3) Derjaguin, B. V . ; Fedoseev, D. V. Russ. Chem. Rev. 1984, 53, 435.
C 1988 American Chemical Society
~
6380 The Journal of Physical Chemistry, Vol. 92, No. 22, I988 Most works, however, have been carried out with CH,-H2 mixtures, typically on the order of 1% of methane. Although a large number of publications have been appearing on the subject,6 few concentrate on the mechanism of growth. Derjaguin, Fedoseev, and c o - ~ o r k e r s ~ -discussed ~ * * * ~ the growth of diamond layers in terms of surface processes of “hydrocarbon complexes”. However, no specific proposals as to the nature of these complexes, their hydrogenation and dehydrogenation reactions, or the way they “incorporate themselves into the lattice of the crystal“ have been made. At one point,2 it was proposed that diamond may form “at least partially via metastable radicals CH,”. The need for hydrogen was e ~ p l a i n e d ~ ~by ~ *the * - ’for~ mation of hydrogen atoms, which in their superequilibrium state suppress the formation of graphite but not that of diamond. Tsuda et al.11J2searched for the lowest energy path of diamond growth using quantum chemical computations (the M I N D 0 / 3 methodI3 was used for potential energy calculations). Assuming that only C, radicals and ions can be the growth species in CH,-H, plasma, the authors reported the following two-step reaction sequence.” In the first step, the (1 l l ) plane of the diamond surface is covered by the methyl groups either via methylene insertion or hydrogen abstraction followed by methyl radical addition. Then, following the attack of a methyl cation, three neighboring methyl groups on the ( 1 11) plane are bound to form the diamond structure. In the subsequent publication, Tsuda et a1.12extended their analysis and concluded that the epitaxial growth of a diamond film is sustained provided the surface maintains a positive charge and there is a supply of methyl radicals. Frenklach and SpearI4 proposed that the main monomer growth species is acetylene and the reaction mechanism consists of two alternating steps: surface activation by H atom abstraction of a hydrogen atom from a surface carbon and the addition of one or two acetylene molecules. This proposal was motivated by the results of a similar reaction mechanism identified for the formation and growth of polycyclic aromatic hydrocarbons in hydrocarbon pyrolysis and c o m b u s t i ~ nand ~ ~ the realization that acetylene should be the main gaseous species present in hydrocarbon plasma. The acetylene-addition mechanism was found to be consistent with numerous experimental facts.I4 In this work n e further test the soundness of the acetylene hypothesis by subjecting the proposed mechanismL4to energy analysis using semiempirical quantum mechanical methods.
Method The energies were obtained by using the MNDO all-valence electron parametrization of the NDDO SCF approximation.16 All calculations were of restricted Hartree-Fock type with the half-electron method being used for radical species.l’ With hydrocarbons of the sort considered here, such an approach typically reproduces heats of formation to within f 6 kcal/mol (4) Derjaguin, B. V.; Fedoseev, D. V. Diamonds Wrought by Man; Mir: Moscow. 1985. ( 5 ) Matsumoto, S.; Sato, Y.; Kamo, M.; Setaka, N. Jpn. J . Appl. Phys. 1982, 21, L183. (6) DeVries, R. C. Ann. Rev. Mater. Sci. 1987, 150, 161. (7) Messier, R.; Badzian, A. R.; Badzian, T.; Spear, K.E.; Bachmann, P.; Roy, R. Thin Solid Films 1987, 153, 1. (8) Derjaguin, B. V.; Bouilov, L. L.; Spitsyn, B, V. Arch. Nauk. Macer. 1986, 7, I 1 I . (9) Varnin, V . P.; Fedoseev. D. V.; Teremetskaya, I . G . Arch. Nauk. Mater. 1986, 7 , 121. (IO) Spitsyn, B. V.; Bouilov, L. L.; Derjaguin, B. V. J . Cryst. Growth 1981, 52. 219. ( I I ) Tsuda. M.; Nakajima. M.; Oikawa, S. J . A m . Chem. Sor. 1986,108, 5780. (12) Tsuda, M.; Nakajima, M.; Oikawa, S. Jpn. J . Appl. Phys. 1987, 26, LS27. (13) Bingham, R. C.; Dewar, M. J. S.; Lo, D. H . J . Am. Chem. SOC.1985, 92, 1285. (14) Frenklach, M.; Spear, K. E. J . Mater. Res. 1988, 3, 133. ( I 5 ) Frenklach, M.; Clary, D. W.; Gardiner, W. C., Jr.; Stein, S. E. Symp. (fnt.) Combust. [Proc.] 1985, 20, 887. (16) Dewar, M. J. S.; Theil, W. J . Am. Chem. Soc. 1977, 99, 4899. ( I 7) See, for example: Sadlej, J. Semi-Empirical Methods ofQuantum Chemistry: translated by I . L . Cooper: Ellis Horwood: Chichester, 1985.
Huang et al.
Figure 1. Model compound assumed for the initial structure. The black circles designate carbon atoms, and the white circles designate hydrogen
atoms. for closed-shell systems and to within roughly twice this figure for radicals.Is The computations were performed with the AMPAC computer program developed by Dewar and co-worker~;’~ they were done using a Cray X-MP/48 supercomputer of the National Center for Supercomputing Applications and required a total of approximately 35 CPU hours. Following the ideas of Tsuda et al.,” the model compound, shown in Figure 1, was chosen such that it contains the smallest number of atoms required to reproduce the H-abstraction/ C2H2-additionreaction sequence of Frenklach and Spear.I4 Tsuda et al.”J2 reported that the computed energetics of the surface reaction were not very sensitive to the size of the “background” molecule. We assumed that similar situation should apply to our case as well. The energies of the stable molecular and radical species in the present work were minimized with respect to variation of all bond lengths and angles. For the transition states (TS), the geometry of the background structure and the lengths of the TS carboncarbon bonds were assumed to be fixed at optimal values, and the energy was minimized with respect to variation of TS bond lengths and angles.
Results and Discussion The results obtained in this work are shown in Figure 2. As mentioned above, molecular compounds A and G and surface radicals C and E were computed with full structural optimization; in the energy computations of transition structures B, D, and F only partial optimization was used. Enlarged diagrams are given in Figures 3 and 4,to identify clearly the transition states D and F, respectively. Inspection of Figure 2 indicates that the reaction sequence beginning with the formation of surface radical C proceeds with a continuous decrease in potential energy, that is, spontaneously. The energy barrier for the initiation, H-abstraction reaction C(,,-H (A)
+H
+
C(sl’ + H2
(C)
is computed to be 17.4 kcal/mol, which is slightly higher than the value of 13.5 kcal/mol computed with an ab initio method C H 3 H2.20*21The higher computed for reaction CHI + H energy for the transition-state B is probably obtained because of only partial optimization of the TS geometry: the C(s,-C(s)and C(,)-H bond lengths and angles of the background structure were assumed to be equal to the optimal values obtained for A; H-H and C(q-H bond lengths of B were fixed at 0.919 and 1.464 A, respectively, the corresponding bond lengths in the H3C-H-H transition state;*Othe energy of B was minimized with respect to variation of the TS bond and twist angles.
-
+
(18) Dewar, M. J. S.; Theil, W. J . Am. Chem. SOC.1977, 99, 4907. (19) Available from the Quantum Chemistry Program Exchange (Chemistry Department, Indiana University) as QCPE Program 506, 1985. (20) Schatz, G. C.; Walch, S. P.; Wagner, A. F. J . Chem. Phys. 1980, 73, 4536. (21) Schatz, G. C.; Wagner, A . F.; Dunning, T . H., Jr. J . Phys. Chem. 1984, 88, 221.
The Journal of Physical Chemisfry, Vol. 92, No. 22, 1988 6381
Acetylene-Addition Mechanism of Diamond Growth
B
-
D *
l
F
120.4
t H +2Cz Hi
94.4
G 64.2
+H2+CiH2
+H*
44.)
43.R
+HiHz 27.6
Figure 2. Energy diagram for the proposed reaction sequence of epitaxial diamond growth. The numbers are the sums of enthalpies of formation of corresponding surface structures and gaseous species (H, H,, and C,H, as indicated) in kcal/mol.
9
Figure 3. Transition structure D
The reaction sequence in Figure 2 contains a smaller number of steps than was originally proposed in ref 14. The results of the present computations revealed that the transformations from C to E and from E to G are energetically more favorable if they each proceed as a single step via corresponding transition states D and F than via a sequence of reactions as proposed previously.'4 Although the formation of a surface radical by the addition of acetylene to C or E (Figure I C and f in ref 14) results in a reduction in potential energy, further progress of the surface reaction (steps c d and f g in Figure I of ref 14) requires a substantial activation energy. In comparison with our results, which were an energy barrier of 17.4 kcal/mol for the initiation reaction and a continuously decreasing potential energy surface for the propagation steps, the initiation step of the reaction sequence proposed by Tsuda et al." is computed" to be 30.59 kcal/mol endothermic (31.04 kcal/mol if computed with the method used in the present study) and the propagation of the epitaxial growth of the diamond surface in-
- -
P
0
0 Figure 4. Transition structure F.
k
cludes reactions with 4-6 kcal/mol energy barriers. The fact that the growth of diamond surface is a slow process (a maximum reported rate is on the order of 100 *m/h)'-" indicates that it is surface reaction that controls the net growth rate. We conclude, therefore, that the computational results reported here not only further support the proposed H-abstraction/C,H,-addition reaction ~ e q u e n c eof ' ~ epitaxial diamond growth but also provide evidence that this reaction mechanism should be more favorable under thermal and plasma conditions than the mechanism of Tsuda et al.'','2 driven by methyl ions and radicals.
Acknowledgment. The work was supported in part by the Office of Naval Research, Contracts No. N00014-86-K-0283 and N00014-86-K-0443. The computations were performed by using the facilities of the National Center for Supercomputing Applications at Urbana, IL. Registry No. H, 12385-1 3-6: C,H,, 74-86-2: diamond, 7782-40-3.
