J. Phys. Chem. 1994, 98, 8-1 1
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Elementary Reaction Mechanism of Diamond Growth from Acetylene Sergei Skokov, Brian Weiner,+and Michael Frenklach' Department of Materials Science and Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802 Received: October 21, 1993; In Final Form: November 17, 1993'
Kinetically and thermodynamically plausible reactions that can explain the growth of diamond from acetylene are introduced. This class of reactions includes the addition of acetylene to a biradical with a t least one of its sites being either a (100)-(2X1) dimer carbon or a secondary carbon, so that the admolecule can undergo a series of H-additions, H-abstractions, and P-scissions leading to incorporation of its carbon atoms into a diamond lattice. Several examples are presented and supported with the results of semiempirical quantum-chemical and transition-state-theory calculations. Among those considered, the most favorable reaction pathway is initiated by the addition of an acetylene molecule that forms a bridge between adjacent dimer rows.
Introduction: Previously Proposed Mechanisms Ever since the initial proposal that acetylene can be a major growth species in chemical vapor deposition (CVD) of diamond,' the subject has been surrounded with controversies. Until very recently, numerous experimental studies have been reported claiming that acetylene cannot possibly be an efficient growth species.2 The new evidence presented by Loh and Cappelli3 demonstrates unambiguously that high-quality diamond can be grown from acetylene as a sole hydrocarbon source and with a ratecomparable to that from methane. Similar results have been also reported by Martine4 Part of the problem has been associated with the difficulty of visualizing a plausible reaction mechanism that can convert a presumably unreactive acetylene molecule into a diamond lattice. Several reaction mechanisms have been proposed, each being criticized and none so far accepted universally. The initial mechanism of Frenklach and Spear,' proceeding through sequential H-abstraction and acetylene-addition reaction steps, was found to possess substantial potential energy barriers.s8 A similar reaction pathway via concerted transition states5 appeared to encounter no energy barriers but was criticized for its first step being highly reversible and estimated to proceed in the reverse direction under the conditions of diamond CVD.9Jo Instead, Belton and HarrislO suggested that acetylene adds to the same siteas proposed by Frenklach and Spear1but with both its carbon atoms, not just one as in the original proposa1,l dehydrogenated. Although such addition resolves the thermodynamic stability of the chemisorbed acetylene, in that its desorption rate-the reverse of the addition-is negligible, the difficulty resides in its kinetic stability,ll i.e., in the relatively short lifetime of the adsorbate in the presence of bombardment by H atoms, as compared to the time required to incorporate the chemisorbed acetylene into the diamond lattice. The proposal of Belton and Harris10 continues with a similar addition that places another acetylene molecule just near the first one, and the two chemisorbed molecules are converted into a diamond lattice by a reaction with atomic hydrogen. Besler, Hase, and H a s 7 found, performing semiempirical quantumchemical calculations, that such conversion can proceed as molecular addition between the neighboring chemisorbed acetylenes, without the mediating role of hydrogen. Thus, the minimum requirement for this growth mechanism is that the first chemisorbed acetylene remains adsorbed until the second acetylene adsorption takes place. t Department of Physics, The Pennsylvania State University, DuBois, PA
15801.
*Abstract published in Advance ACS Absrracfs, December 15, 1993.
The per-site rate for the adsorption of acetylene at a biradical site is R c ~ H = ~r2k~2~2[C2H2], where r = kab/kadd is the rate constant ratio of H-abstraction to H-addition and accounts for the probability of a C-H surface site to be dehydrogenated (Le., to be a radical),12 [CzHz] the concentration of acetylene in the deposition zone, and kCIHl the rate coefficient for the addition of acetylene to a surface radical. Considering typical CVD conditions13-temperature 1200 K, r 0.1, [CZHZ]= [HI l k 9 mol/cm3, the conditions adopted for the rest of the paper-and assigning a conceivable upper limit of 10" cm3 mol-' s-l to kC2H2, we obtain R Q Hof~ the order of lo2 s-I; with kC2Hl = 3 X lo9 cm3 mol-l s-1, as estimated by Belton and HarrislO for 1200 K, the acetylene adsorption is even slower, R c ~ H = ~0.03 s-I. Let us now consider a situation when one C2H2 molecule has already been adsorbed and a second C2Hz molecule is being lo2 s-I. During this adsorbed with the per-site rate of R c ~ H ~ time, however, the initially adsorbed C2H2 is being continuously bombarded by H atoms, and some of them are added to the chemisorbed acetylene. We estimate the per-site rate for this addition as RH 104 s-1, basing it on a rate constant14 of 1013 cm3 mol-l s-1 for H addition to C2H4. The surface radical formed is unstable and undergoes rapid thermal decomposition
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with a rate of lo7s-I (at 1200 K), typicalI4 for such /3-scissions of c-c bonds; here Cd represents a carbon atom of a diamond surface. The resulting chemisorbed vinyl desorbs either through thermal decomposition, with a ratel4 of -0.1 s-1, or through the addition of H to the inner carbon of the vinyl group followed by &scission of CzH4, with respective rates of lo4 and lo7 s-I. Comparing these rates with the much lower rate of acetylene addition, R c ~ Hwe~ must , conclude that, during the time required for the adsorption of the second C2H2, the first one is likely to desorb. The same conclusion still holds if instead of the H-addition reactions we would invoke 10-fold slower H-abstraction steps. The above analysis points out the general feature-the kinetic instability of acetylene bonded to two isolated lattice carbons. This places a prohibitive restriction on many of the proposed mechanisms, besides that of Belton and Harris,'" for example, on two-center acetylene addition of Huang et al.;s addition of C2H,1,8JSC2H3,'"6 or other C2H, compounds; combination of chemisorbed CH2 groups;l7 and many other CH3-based reaction mechanisms.17J* Recent kinetic Monte Carlo simulations demonstrated that the growth rate of diamond can be accounted for by considering combined CH3and C2H2 additions, in which twocenter additions of acetylene are disallowed and only three-center additions permitted." This may resolve the prohibition of two-
0022-3654/94/2098-0008$04.50/0 @ 1994 American Chemical Society
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The Journal of Physical Chemistry, Vol. 98, No. 1, 1994 9 H \
Figure 1. Reaction pathway for acetylene addition between dimers of adjacent rows: top reaction sequence, addition of acetylene leading to the formation of H*C=C- bonded to a dimer carbon; bottom reaction sequence, dimer opening.
center reactions discussed above; however, serious doubts still remain regarding the detailed mechanism proposed for the threecenter acetylene addition. Although the transition state determined for this reaction in semiempirical quantum-chemical calculations of Huang et al.5 was found to possess no potential energy barrier, it is not clear that such a concerted transition state can be attained dynamically with sufficient frequency. Furthermore, calculations confined to a more realistic geometry of the surface appeared to produce substantial barriers.Ig
quencies from small-cluster calculations. The vibrational frequencies were computed using standard MOPAC ~ubroutines.2~ Low frequencies that originated from internal rotations were substituted by appropriate free rotations with rotational constants evaluated from the computed moments of inertia. We will illustrateour ideas with twospecific reaction pathways, the addition of C2H2 to a dehydrogenated (100)-(2X 1) dimer,
H
/
'C
'L" H, c=c
A New Hypothesis
In a search for plausible reactions that can explain the growth of diamond from acetylene, we discovered several possibilities that overcome the kinetic and thermodynamic limitations discussed above and thus open new, yet unexplored avenues. We present these ideas below and support them with the results of quantum-chemical and transition-state-theory calculations. The quantum-chemical calculations were performed on two kinds of model clusters. The first kind was either a C50H64 or a C40H50 cluster described with the PM3 semiempirical Hamiltonian20 and embedded into a corresponding 550- or 320-atom surrounding cluster described by an empirical potential fitted to PM3.2' Minimum-energy configurations were obtained by unrestricted Hartree-Fock (UHF) calculations with a combinedforce molecular dynamics method described and tested by us previously in a study of diamond (100) surface reconstructions.21 The use of these large-size clusters is beneficial in the determination of potential energy minima, as the cluster size effect on such calculations is well d o c ~ m e n t e d . ~ J ~ However, , ~ I - ~ ~ vibrational frequencies cannot be established reliably for these clusters. To obtain normal frequencies, the calculations were repeated using a small cluster model, C9H12, the same cluster which was used in the works of Badziag and V e r ~ o e r and d ~ ~Tsuda et alez5 and also examined in our previous study.21 All atoms were allowed to relax during these calculations. Transition-state geometries for both large and small models were found to be very close to each other. On the basis of this, we computed reaction rate coefficients using nonvariational transition-state theory,26 for which potential energies of ground and transition states were taken from large-cluster calculations and corresponding fre-
/"
and betweendimers of the adjacent rows. As will be shown below, the latter case is thermochemically most favorable, and hence this entire reaction sequence is depicted in Figure 1. The feasibility of having the biradical surface sites, the prerequisite for these reactions, follows from our recent analysis,21 performed with the same molecular dynamics technique and the same potentials as those used in the present study. The analysis of (100)-(2X 1) diamond surfaces indicated21 that the equilibrium state of the dehydrogenated dimer is a singlet biradical. The formation of a double bond for such a dimer comes at the expense of overstretching other C-C lattice bonds. The same rationale underlies the stability of a monohydride (100)-(2Xl) dimer radical, the constituent of the "in-between" biradical precursor to the reaction sequence depicted in Figure 1. Unlike the case of free hydrocarbon radicals, there is no energetic compensation for @-scissionfrom a (100)-(2Xl) surface dimer radical due to formation of a double C-C bond. Indeed, the C-H bond energy on the present level of theory is 90.2 kcal/mol, and its rate of thermal decomposition is 4 X 10-2 s-I, much slower than the 106s-I rate of a typical C-H @-scissionrea~ti0n.t~ The thermal decomposition of the dimer C-H bond is also much slower than H-abstraction under the conditions of diamond CVD. All the above arguments imply that the two carbon sites of a (100)( 2 x 1) dimer behave kinetically rather independently of each other, similar in this respect to dimers on (100) silicon surfaces.28 Hence, the probability of having a (100) biradical site, either as an
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10 The Journal of Physical Chemistry, Vol. 98, No. 1, 1994
TABLE 1: Potential Energy Barriers, E, Rate Coefficients, k, and Changes in Cibbs Free Energy, ACO, for the (100)-(2X1) Dimer Opening Reactions first step
second stepb
source AGOlm(kcal/mol) k12w (s-I) E (kcal/mol) adspecies E (kcal/mol) 7.5 3.5 x 109 -1.1 -15.8 this study 6.5 X 10" 8.8 H2C43.8 12.3 6.5 x 109 -14.6 this study 1.6 X 1Olo 15.3 H2& 4.3 8.8 5.0 X 1011 -21.2 ref 31 1.0 x 1013 c oc H2& a &scission of dimer C-C bond; e.g., the first step of the bottom reaction sequence in Figure 1. Formation of C-C bond with the admolecule; e.&, the second step of the bottom reaction sequence in Figure 1. These parameters were not calculated in ref 3 1 but assigned values with origin not specified. AGOlzw (kcal/mol)
k m t ~(s-I)
*
individual dimer or composed of two adjacent dimers, is the same as having two independent surface radical sites, which is kinetically not formidable for diamond CVD.10J2 (We note that the thermal stability of a monohydride (100)-(2Xl) dimer radical which follows from the above considerationsalso serves as a justification for the methyl addition reaction,30~~~ which was not previously addressed.) Both of the reaction pathways, "on-topdimer" and "in-between dimers", begin with the addition of acetylene to one of the radical sites, with a potential energy barriers of 6.9 and 8.4 kcal/mol and the rate coefficients of 4.4 X 1011 and 2.4 X 1011 cm3 mol-' s-l, respectively. Thecomputed barriers are lower than the 13.6 kcal/ mol, obtained by Besler et al.' for acetylene addition to a tertiary diamond (1 11) radical site at a similar level of theory. The differenceis caused by lower repulsion exerted on hydrogen atoms during the addition of C2H2 to a (100)-(2X1) dimer radical. The second steps of acetylene additions in both cases are not rate limiting, with potential energy barriers of 2.3 and 0.7 kcal/mol and rate coefficients of 1.6 X 101' and 3.1 X 1011 cm3 mol-' s-1, respectively. The formed acetylene adducts are thermodynamically stable, with chemisorption energies of 74.9 and 95.0 kcal/ mol, respectively, in close agreement with 73.8 and 87.6 kcal/ mol obtained in ASED-MO calculations of Mehandru and Andersonz9 for the two structures. The overall reactions of acetylene additions are essentially irreversible, with the equilibriumconstantsof -lO*forthefirststepsand -106and -1O'O for the second steps, respectively. Incorporation of the chemisorbed acetylene into a diamond lattice, in both cases, can be initiated by H atom addition to an sp2 carbon atom, which will immediately (with the per-site rate of lo7 s-I) be followed by @-scission,similarly to reaction 1. However, under the present circumstances, the formed CzH3 group, chemisorbed to one of the (100)-(2X1) dimer sites, undergoes a rapid *insertion" reaction upon either H-abstraction from its inner C atom, H addition to its outer C atom, or H-migration to a neighboring radical site. For the conditions stated, T = 1200 K and [HI = mol/cm3, H-migration is estimated to be the fastest. The migration of H for the "on-top" initial configuration,
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is estimated to occur .with the rate of 1.2 X 106 s-1 (barrier 33.4 kcal/mol), Le., about 500 times faster than the abstraction of the inner H from the adsorbed C2H3 and about 50 times faster than the addition of an H to the dimer radical site. In the case of the "in-between" initial configuration, the inner H atom of the chemisorbed C2H3 migrates to a carbon radical of the adjacentrow dimer (Figure 1) with an even faster rate of 1.4 X 109 s-1 (barrier 16.5 kcal/mol). The reverse migration of H is estimated to be 10-fold slower than the forward reaction in each case. We note that, for reasons discussed earlier in the text, the thermaldesorptionofC2H3froma (100)-(2xl)dimerisestimated to be relatively slow, 1.3 X 102 s-1, compared with the -107 s-l
ti Figure 2. Transition-statestructure calculated with the present method for the second step of the dimer opening shown as the bottom sequence in Figure 1. The numbers are distances in angstroms.
rate of a typical @-scissionreaction. The UHF-PM3 energy of the bond between the dimer C and chemisorbed vinyl is calculated to be 76.5 kcal/mol, more like a regular C-C bond than one undergoing @-scission. The (100)-(2Xl) dimer with the H2C=& group formed at one of its sites undergoes a rapid dimer opening, shown as the bottom reaction sequence in Figure 1. These reactions are similar to those for a methylene adspecies, identified in molecular dynamic simulationsof Garrison et s~.,~O but with an additional "advantage" of ending with the chemisorbed =CH2 group, which can also be incorporated into a diamond lattice when it neighbors an appropriate site. The thermochemical parameters for the two steps of this dimer opening are listed in Table 1, where they are compared with similar parameters for methylene calculated with the present method and with an ab initio method reported by Harris and G o o d ~ i n . ~Inspection ' of these data indicates that the kinetics and thermodynamics of the dimer opening reactions with the H 2 C 4 - and H&- adspecies are relatively close to each other but not exactly the same. The first step in the case of H 2 C 4 - is kinetically and thermodynamicallymore favorable than that of H2&. For the second step, whose transition-state structure is shown in Figure 2, the energy barrier is lower for the H2C=& case, but its higher rotational entropy counterbalances this energetic advantage. We observe that the prediction of the potential energy barrier for the second step of the methylene case calculated with the semiempirical PM3 Hamiltonian, 12.3 kcal/ mol, is respectfully close to the ab initio result, 8.8 kcal/mol.sl Similarly close are our predictions for the Gibbs free energy changes to those reported in ref 31. The difference in the rate coefficients of the second step is caused by the higher energy barrier and lower preexponential factor, 1 X 1012 s-1, computed with our PM3-based method. We note, however, that all the rate coefficients in Table 1 are very large, compared to the rate of the initial acetylene addition, indicating that the dimer opening reactions provide no overall kinetic limitation. Assuming that the initial addition of acetylene to a radical site is rate-limiting, as our results seem to suggest, leads to the event probability of the order of Multiplying the latter by r = 0.1, the probability for the neighboring site to be a radical, we obtain 10-3, which is within the range tested in recent dynamic Monte Carlo simulationsll and close to the experimental sticking probability determined by Loh and Cappelli.32 The proposed mechanism for acetylene addition is also consistent with recent experimentalfindings of Thomas et al.33 that acetylene chemisorbs
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The Journal of Physical Chemistry, Vol. 98, No. 1, 1994 11
onto a room-temperature diamond surface after it was subjected to adsorption of oxygen followed by thermal desorption of carbon monoxide. Thelatter should leave behinddehydrogenated radical sites,34 some of which may be biradical. The analysis performed in the course of the present study for the on-top acetylene adduct formed in reaction 2 indicated that the rate coefficient for @-scissionof dimer C - C bond is much larger, 3 X 10" s-', than that of Cdimer-C2H3bond considered above. The dimer bond cleavage leads to an interesting and kinetically feasible possibility,
Acknowledgment. The work was supported by the Innovative Science and Technology Program of the Ballistic Missile Defense Organization via the U.S.Office of Naval Research, under Contract N00014-92-5-1420.
H
H
\
I
*C-C-H
I
Cd-Cd
\
/ \ / \
-
H
H\
I
*C-C-H
I
/C(
\ ;ct
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C*
\ /
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. )
if the >Cd=& and >Cd=CH2 groups formed in (4) have appropriate neighboring sites for the addition. However, at the PM3 level of theory, the energy differences for the reaction steps in (4) are positive, not negative, thus indicatingthat these reactions should run in reverse. The latter results may be an artifact of the PM3 Hamiltonian, which underpredicts the energy of cyclobutane by 10.6 kcal/mol and overpredicts that of ethylene by4.1 kcal/mol, errors which do not cancel but add up for reaction 4. Also, Besler et ala7reported a 15-20 kcal/mol difference between PM3 and ab initio results for the potential energy barrier of an ethylene self-reaction. Thus, the direction of reaction 4 and hence the fate of the on-top acetylene adsorption must await more accurate evaluation of the thermodynamic properties. The conversion into diamond of acetylene adsorbed at biradical sites may be initiated not only by the H addition discussed above but also by the H abstraction, which after a corresponding @-scissionleads to an adsorbed ethynyl. Addition of an H atom to an outer carbon atom of this ethynyl forms the same adspecies, H2C=C-, followed by the dimer opening. Another possibility, along the lines discussed in this Letter, is the addition of acetylene to two adjacent radicals of the same dimer row. Finally, the addition of an acetylene molecule to a (1 10) surface biradical site with one of its carbons being secondary (Le., having an H attached to it) may lead to diamond growth reactions similar to those introduced in the present work, although probably slower due to the higher barrier for the acetylene addition.'
Conclusion The reaction possibilitiesintroduced anddiscussed in the present study can be generalized to the addition of acetylene to a biradical with at least one of its sites being either a (100)-(2X1) dimer carbon or a secondarycarbon, so that the admoleculecan undergo a series of H-additions, H-abstractions, and @-scissionsleading toincorporationofoneortwocarbonatomsintoadiamond lattice. A specific reaction pathway depicted in Figure 1 is estimated to have the most favorable kinetic and thermodynamic parameters.
References and Notes (1) Frenklach, M.; Spear, K.E. J. Muter. Res. 1988, 3, 133. (2) For example: Martin, L. R.; Hill, M. W. J. Muter. Sci. Lett. 1990, 9,621. DEvelyn, M. P.; Chu, C. J.; Hauge, R. H.; Margrave, J. L. J . Appl. Phys. 1992,71,1528. Johnson, C. E.; Weimer, W. A.; Cerio, F. M.J . Muter. Res. 1992,7,1427. Harris, S.J.; Weiner, A. M. ThinSolid Films 1992,212, 201. Yarbrough, W. A.; Tankala, K.;DebRoy, T. J. Muter.Sci. 1992,7,379. (3) CappeUi,M. A.;Loh,M.H.Presentedat the4thEuropeanConference
on Diamond, Diamond-like and Related Materials, Albufeira, Portugal, Sept 1993. (4) Martin, L. R. J . Muter. Sci. Lett. 1993, 12, 246. (5) Huang, D.; Frenklach, M.; Maroncelli, M. J. Phys. Chem. 1988,92, 6379. (6) Huang, D. Homogeneous Nucleation of Diamond Powder and Growth
Mechanisms. Ph.D. Thesis, The Pennsylvania State University, University Park, PA, 1993. (7) Besler, B. H.; Hase, W. L.; H a s , K . C. J . Phys. Chem. 1992, 96, 9369. (8) Chang, X.Y.; Thompson, D. L.; Raff, L. M. J. Phys. Chem. 1993, 97, 10112. (9) Harris, S. J.; Belton, D. N. Jpn. J. Appl. Phys. 1991, 30, 2615. (IO) Belton, D. N.; Harris, S. J. J . Chem. Phys. 1992, 96, 2371. (1 1) Frenklach, M. J . Chem. Phys. 1992, 97, 5794. (1 2) Frenklach, M. Phys. Reu. E 1992, 45, 9455. (13) Hsu,W. L. Appl. Phys. Lett. 1991, 59, 1427. (14) For recent recommendations see references in: Mallard, W. G.;
Westley, F.; Herron, J. T.; Hampon, R. F.; Frizzell, D. H. NIST Chemicul Kinetics Dutubuse 5.0; National Institute of Standards and Technology: Geithersburg, MD, 1993. (15) Cappelli, M. A.; Paul, P. H. J. Appl. Phys. 1990, 67, 2596. (16) Frenklach, M.; Wang, H. Phys. Rev. E 1991,43, 1520. (17) Huang, D.; Frenklach, M. J . Phys. Chem. 1991,95, 3692. (18) Butler, J. E.; Woodin, R. L. Philos. Truns. R . Sa.London, A 1993. 342, 209. (19) Huang, D.; Frenklach, M. J . Phys. Chem. 1992, 96, 1868. (20) Stewart, J. J. P. J. Comput. Chem. 1989, 2, 209. (21) Skokov, S.; Carmer, C. S.;Weiner, B.;Frenklach, M. Phys. Rev. E.,
in press.
(22) Liu, J.; Feyereisen, M. W.; Amlof, J.; Rohlfing, C. M.; Saebo, S. Chem. Phys. Lett. 1991,183,478. (23) Yang, S. H.; Drabold, D. A,; Adams, J. B. Phys. Reu. B 1993, 48,
5261. (24) Badziag, P.; Verwoerd, W. S.Surf.Sci. 1987, 183, 469. (25) Tsuda, M.; Oikawa, S.;Furukawa, S.;Sekine, C.; Hata, M. J . Electrochem. Soc. 1992, 139, 1482. (26) For example: Steinfeld, J. I.; Francisco, J. S.;Hase, W. L. Chemicul Kinetics and Dynamics; Prentice Hall: Englewood Cliffs, NJ, 1989. (27) Stewart, J. J. P. Quuntum Chemistry Program Exchange, No. 455. (28) Carmer, C. S.;Weiner, B.; Frenklach, M. J . Chem. Phys. 1993,99, 1356. (29) Mehandru, S.P.; Anderson, A. B. Surf.Sci. 1991, 248, 369. (30) Garrison, B. J.; Dawnkaski, E. J.; Srivastava, D.; Brenner, D. W. Science 1992, 255, 835. (31) Harris, S.J.; Goodwin, D. G. J. Phys. Chem. 1993, 97, 23. (32) Loh, M. H.; Cappelli, M. A. InProceedingsofthe Thirdlnternutionul
Symposium on Diamond Muteriuls; Dismukes, J. P., Ravi. K. V., Us.The ; Electrochemical Society: Pennington, NJ, 1993; p 17. (33) Thomas, R. E.; Posthill, J. B.; Rudder, R. A,; Markunas, R. J.; Frenklach, M. In ref 32, p 71. (34) Frenklach, M.; Huang, D.; Thomas, R. E.; Rudder, R. A,; Markunas, R. J. Appl. Phys. Lett. 1993,63, 3090.
