10112
J. Phys. Chem. 1993,97, 10112-101 18
Minimum-Energy Paths for Elementary Reactions in Low-Pressure Diamond-Film Formation XiaoYan Chang, Donald L. Thompson, and Lionel M. Raff Department of Chemistry and Diamond Research Group, Oklahoma State University. Stillwater. Oklahoma 74078 Received: March 23, 1993; In Final Form: July 8, 1993'
We have determined minimum-energy paths on the Brenner empirical hydrocarbon potential-energy hypersurface for a number of important elementary reactions that include hydrogen atom abstraction and migration, C2H2, CzH, and hydrogen atom addition to a carbon radical site, and six-membered, carbon ring closure. Our results show that the reaction barrier for addition of CzH2 or C2H via C,-C single-bond formation at some radical site is within range of the expected thermal energies. Although both addition processes are exothermic, the energies released are very different. For C2H2 addition, hE is -0.66 eV, whereas AE = -3.5 eV for C2H addition if the end carbon atom forms the bond. If C2H chemisorbs via the C-H carbon, AE = -1.58 eV. The reaction profiles show that the formation of a second C - C bond for chemisorbed C2H2 to an adjacent radical site is a near barrierless, exothermic process. However, if hydrogen atom migration is a prerequisite to formation of the second C-C bond, the overall process is associated with a barrier that can be as large as 1.62 eV (37.4 kcal/mol). The potential barrier for creation of a radical site via hydrogen atom abstraction at an sp3 carbon is 0.53 eV (12.2 kcal/mol). Consequently, radical sites required for C2H2 addition or ring closure are more likely to be created by abstraction reactions than by hydrogen atom migrations. Ring closures between two radical sites are found to be near barrierless processes. If, however, hydrogen atom release accompanies the ring closure, the overall process is associated with a barrier of at least 1.34 eV (30.9 kcal/mol). Chemisorption of ethynyl radicals (C2H) is found to lead to a more stable surface species that is less likely to undergo desorption than is the case for acetylene addition. In addition, the ethynyl radical provides a second radical site for subsequent reactions which may obviate the need for hydrogen migration or abstraction. The results indicate that hydrogen abstraction is very likely the rate-determining step in low-pressure, diamond-film growth.
I. Introduction In recent years, the low-pressure synthesis of diamond films has received increased attention. Experimental advances include high-temperature activation, microwave-assisted plasma discharge, laser-assistedchemical vapor deposition (CVD), and oxy/ acetylene flame-assisted methods.1-3 Growth rates of up to 150 mm/h have been reported.c8 It is generally accepted that the growth of diamond is sustained by the addition of gaseous hydrocarbon species to surface radicals which are formed by the abstraction of hydrogen atoms from an otherwise hydrogenated surface. Measurements of the concentration of gas-phasespeciespresent in a filament-assisted,diamond growth experiment suggestthat the two most likely growth species are methyl radicals and a~etylene.~ One-dimensional,flow-field calculations of filament-assisted diamond growth have been reported by Goodwinlo and by Goodwin and Gavillet." These studies assume that each hydrocarbon species has a constant probability of chemisorption on the substrate surface which is accompanied by simultaneous desorption of all hydrogen atoms in molecular form. The results indicate that only CH3, C2H2,or CH4 have sufficient abundance at the surface to be solely responsiblefor themeasured growth rate. However, other species such as CH2, C2H4, C ~ H SC2H6, , C3H2, C3H3, C3H4, C3H5, and C are predicted to have maximum growth rates sufficientlylarge that some combination of these species could account for the observed diamond-film growth rate. There is no general agreement on the underlying reaction mechanism responsible for diamond growth. There have been several hypothetical mechanisms suggested on the basis of assumed reaction rates under the physical conditions present during diamond-film growth.12-'8 Huang, Frenklach, and Maroncelli (HFM)15 have proposed an elementary reaction mechanism in which the main monomer growth species is Abstract published in Advance ACS Abstracts, September 1, 1993.
0022-3654/93/2097- 10112$04.00/0
acetylene. The reaction mechanism involves (1) surface activation via hydrogenatom abstraction, ( 2 )additionofacetylenemolecules to the surface via the formation of one C-C single bond at the radical site, and (3) a series of hydrogen atom migrations coupled with the formation of more C - C bonds via successive addition of acetylene molecules. The details of the HFM mechanism are shown in Figure 2. The surface activation step is represented by the process structure A
+H
-
structure B
+ H2
Acetylene addition via the formation of a single C,-C bond then leads to structure C. Structure C is converted to structure D via a simultaneous hydrogen atom transfer process coupled with ring closure. A second C2H2 addition via single C,-C bond formation leads to structure E. Finally, the combination of one hydrogen atom transfer and a second hydrogen atom release or abstraction permits the formation of two additional C-C bonds which result in two ring closures to give structure F. Abstraction of the remaining hydrogen atoms produces the tetrahedral diamond lattice. Frenklach and Spear16have proposed a similar growth mechanism for vapor-deposited diamond films. The HFM hypothesishas been criticizeddue to the revcrsibility of the acetylene addition.18 Belton and Harris18 suggested that, under typical conditions of diamond CVD, acetylene pressures of 0.01-0.1 Torr around 1200 K,the C2H2 addition reaction should be spontaneous in the direction of desorption because the exothermicity of this addition is counterbalanced by the decrease in entropy. This suggestion is supported by the molecular dynamics studies reported by Peploski et aI.l9 which show that whenever acetylene chemisorbs to a radical site on the surface, the probability of subsequent desorption is large unless the newly formed ethenyl radical is able to subsequently form a second C-C bond to the surface. To circumvent the problem of desorption, Belton and Harris's (BH) proposed a model in which the acetylene moiety adds not 0 1993 American Chemical Society
Low-Pressure Diamond-Film Formation to a single-radical site, as in the HFM case, but to a diradical site, forming a chemisorbed ethylene moiety. After a similar addition places another acetylene molecule on an adjacent absorption site, the two chemisorbed ethylenes cross-link and are then converted into diamond by reaction with atomic hydrogen. While the BH model obviates the problem of acetylene desorption, it has been criticized on the basis that the series of selective attacks required by the mechanism should substantially lower the rate of the pro~ess.1~ The resolution of this point requires accurate values for the rates of hydrogen atom abstraction, acetylene chemisorption, and C2H2 desorption. We have recently reported extensive calculations of hydrogen abstraction rates from different types of chemisorbed moieties.20 Molecular dynamics computations are presently in progress to obtain rate coefficients for the chemisorption and desorption of a variety of hydrocarbon species on a diamond-like substrate. When these data are in-hand, a quantitative evaluation of the BH mechanism will be possible. The recent development of a semiempirical potential-energy function by Brenner,21which fits known hydrocarbon interaction energies very closely, permits more quantitative molecular dynamics and Monte Carlo simulations to be carried out. Garrison et a1.22 have used this potential function in a molecular dynamics study of dimer opening on a diamond (001) surface. Peploski et al.19 have studied the reactions of C2H2 and C2H with a (1 11) diamond substrate using molecular dynamics on the Brenner potential-energy surface (BPES). Their calculations show that if acetylene is involved directly in the growth process, it probably incorporates into the lattice by the formation of two C-C bonds. The results indicate that the ethynyl radical (C2H) may be an important growth species in that the chemisorption probability is probably two or more orders of magnitude greater than that for acetylene. In addition, half of the hydrogen has already been removed from the ethynyl radical relative to acetylene. This point is discussed in more detail below. Xing and Scott23 have performed a kinetic Monte Carlo simulation of diamond-film growth on a C( 111) substrate from acetylene and hydrogen vapor deposition. In their calculations, Monte Carlo steps are accepted or rejected on the basis of a Kawasaki algorithm24 computed using the BPES. This is the first reported simulation that examines atom-by-atom growth of diamond films using kinetic Monte Carlo methods. The results show that acetylene binding to a clean C( 111) surface is favored. Consequently, (n+ 1)-layergrowth does not start until the n-layer growth is substantially complete. While these Monte Carlo studies yield significant information related to the microscopic reactions involved in the growth process, they contain no information on growth rates, since the actual time scales of the various Monte Carlo steps are unknown. Such information is unavailable unless the rates for the various reactions can be computed or measured. All of the proposed mechanisms for diamond-film growth have one step in common, abstraction of surface hydrogen by gasphase hydrogen atoms. We have recently computed the reaction probabilities, cross sections, rate coefficients, frequency factors, and activation energies for hydrogen atom abstraction from a hydrogen-covered C ( 111) surface using quantum wave packet and classical trajectory methods on the BPES.20 Upper bounds for the abstraction rates, activation energies, and frequency factors have been obtained for six different chemisorbed moieties on a C(111) diamond surface using a classical variational transitionstate method. For the hydrogen-covered surface, the results of the wave packet/trajectory calculations give k(T) = 1.67 X 1014 exp[-0.46 eV/kb7'l cm3/(mol.s). Thecomputed frequency factor is 1.33 times the value reported by Westbrook et a1.2s for the gas-phase abstraction of the hydrogen atom from the tertiary carbon of isobutane. The activation energy computed using the BPES is about 0.14 eV (3.2 kcal/mol) higher than the measured gas-phase result for isobutane.25 Our variational calculations show that the activation energies for hydrogen atom abstraction
The Journal of Physical Chemistry, Vol. 97,No. 39, 1993 10113 a
.-
L
6
Chair
b
b
Boat
d
.-L
6
Figure 1. Conformation of initial structures: (a) chair-chair; (b) boatboat; (c) boat-chair; (d) chair-boat.
vary from 0.0 to 1.063 eV depending on the bonding environment.20 We have therefore suggested that phenomenological growth models which assume either an equilibrium distribution between surface hydrogen and H2 or a common abstraction rate for surface hydrogen atoms are unlikely to be correct.20 Understanding the underlying mechanisms of the growth of diamond-like films a t low temperatures and pressures is essential for expanding the practical aspects of the technology. In this paper, we employ the BPES to examine minimum-energy paths for several of the elementary reactions which have been proposed by various research groups to play a crucial role in low-pressure diamond-film formation. These include hydrogen abstraction, C2H2, C2H, and H atom addition reactions a t a carbon radical site, formationof a second C-C bond subsequent to chemisorption of C2H2 or C2H, six-member ring closure processes, and hydrogen atom diffusion between various chemisorbed moieties. 11. Reaction Models and Numerical Procedures
The elementary processes listed in the previous section are investigated starting with the model structure originally employed by HFM to describe their suggested growth m e c h a n i ~ m .This ~~ structure includes 10 carbon and 18 hydrogen atoms, which are sufficient to construct two hydrogen-saturated, six-membered carbon rings as shown in Figure 1. One of these rings represents the diamond surface while the second is a chemisorbed moiety on the surface.
Chang et al.
10114 The Journal of Physical Chemistry, Vol. 97, No.39,1993 TABLE I: Stationary Moieties (SMs) for Various Elementary Processes on Diamond Surfaces DrOCtSS
hydrogen atom abstraction C2H2 addition C2H addition C,--C, bond formation requiring hydrogen atom migration C,--C,bond formation not requiring hydrogen atom migration
SM
G--Ha- -H, G-'C2H2 G--C2H G--H- -G
&cf2Gt Abstraction
G--G
The twocarbon rings can exist in the four distinct conformations shown in Figure 1a d . These four initial conformationsare labeled chair-chair (Figure la), boat-boat (Figure 1b), boat-chair (Figure IC),and chair-boat (Figure Id). Our calculations have been carried out on the chair-chair structure. However, some of the discussion will refer to the other structures. The empirical hydrocarbon potential developed by Brennerzl has been employed in all of the calculations. This potential is based on Tersoff's covalent bonding formalism with additional terms that correct for overbinding of radicals and nonlocal environmental effects. Nonlocal effects are included using an analytic function that defines conjugation in terms of the coordinationof carbon atoms that neighbor carbon-rbon bonds. Minimum-energy reaction profiles are obtained by computing the potential energy after allowing all atoms in the structure to relax in the field of stationarymoieties (SMs) to the configuration corresponding to the nearest potential minimum. The atoms in the SM depend on the elementary reaction under consideration. For example, in the case of hydrogen abstraction, the SM is C,--H,--H,, where the subscript s denotes an atom chemisorbed on the surface structure. Table I gives the SM for each of the processes considered. Relaxation of the atoms of the structure is achieved by using a damped-trajectory method.26.27 In this procedure, the kinetic energy of each atom is set to zero and the Hamiltonian equations of motion for all atoms, save those in the SM, are integrated until the total kinetic energy attains a maximum. At this point, the integration is halted and the momentum components of all atoms are once again set to zero. This procedureis repeated until thesystemconvergesto the nearest local minimum potential.
D Atom Transfer C-C Bond Formation
" I
+ C2H2
C2H2Addition
Atom Transfer +
-
E
+
Hydro en Release + 2 C-C%onds Formed
H
F
- -
--
Figure 2. HFM reaction mechanism (see ref 15). A B is hydrogen abstraction. B C and D E are acetylene additions. C D is hydrogen migration/ring closure. E- F is hydrogen relcast/ringclosure. The overall prOCtSS B C D is termed 'two-ccnter" addition by Frenklach.14 The process D- E- Fis termed"thrcc-CtntCt"addition."
a
A
E
Entrance Channel
>
III. Results and Discussion A. Hydrogen Abstraction. All of the proposed mechanisms for diamond-film growth have one step in common, abstraction of surface hydrogen by gas-phase hydrogen atoms. For example, in the HFM growth mechanism shown in Figure 2, the initiation reaction is such an abstraction which converts structure A to structure B, forming gaseous H2 in the process. The potentialenergy contour map for collinear abstraction is shown in Figure 3a. The contours are determined by taking the three-atom C,-Ha--H, system as the SM and running damped trajectories as described above. The coordinate rl is the H,--H, distance, and r2 is the Cr-H,distance. Consequently,the reactant configuration space lies in the lower right-hand region of the map while the product space is the upper-center of the plot. The minimumenergy path is illustrated by the dot-dashed line labeled S in Figure 3a. Figure 3b shows the corresponding reaction profile. As can be seen, this hydrogen atom abstraction is an exothermic process with a reaction barrier of 0.529 eV (12.2 kcal/mol). We have previously found20 that this value is typical of barriers on the BPES for abstraction of hydrogen from sp3 carbon atoms. B. CtHt, Cfi, and H Addition to a CarbonRadical Site. The reaction profile for CzHz addition to a diamond surface carbon radical site via a single Ca-C bond is shown in Figure 4. The reaction coordinate is the distance between C, and the nearest carbon atom of the incoming CzHz molecule. The reaction bamer for this process is 0.021 eV (0.48 kcal/mol), which is within the range of the thermal energies usually available in diamond CVD
n
-0.2 0
20 40 Reaction Coordinate S
60
Figare 3. (a) Collinear contour plot for hydrogen atom abstraction. (b) Potential energy along the minimumenergy reaction pth, S.
experiments. The addition is exothermicby 0.66 eV (1 5.22 kcal/ mol). These results support the hypothesis suggested by Huang et al.15 that CzH2 addition to a radical site via single G-C bond formation is barrierless. In their phenomenologicalmodeling study, Belton and Harrisl8 used kinetic data on acetylene addition to a tert-butyl radical to estimate the rate coefficient for chemisorption of C2H2 on a diamond surface. This procedure gives an activation energy for chemisorption of 0.34 eV (7.7 kcal/mol). The results obtained using the BPES indicate that this value is too large. If a nearzero activation energy had been employed, Belton and Hamsla
Low-Pressure Diamond-Film Formation
The Journal of Physical Chemistry, Vol. 97, No. 39, 1993 10115
C2H2 Addition to a Radical Site via a Single C-C Bond
T
H Adsorption to a Radical Site
I
1 .O
L
0
3.0
.
.
’
.
1
,
. . .
1
.
1.o Reaction Coordinate (Angs)
2.0
.
’>
Figure 4. Reaction profile for C2H2 addition to a carbon radical site uiu single C,-C bond formation. The reaction coordinate is the distance between a carbon atom of C2H2 and the carbon radical site. C2H Addition to a Radical Site Via a Single C,-C Bond
A
!
1.o
.C-C-H
:/
i
2* 0.0l.O: 1
P
E -1.0-
Lu
-2.0-
ii,
-3.0-3.0 -3.0
W,&,> 2.0 ,
3.0
2.5 1.5 1.0 Reaction Coordinate (Angs)
I . .
/viacarbon Radical
‘,\.J .
I
.
.
.
I
.
.
.
.
I
1.o Reaction Coordinate (Angs)
3.0
2.0
. . .>
Figure 5. Reaction profiles for a C2H addition to a carbon radical site uiu single C,-C bond formation. The dot-dashed line is for C2H addition fromthemiddlecarbonatom. Thesolidlineistheresult forchemisorption at the carbon atom shown in the lower right corner. The reaction coordinate is the distance between the carbon atom of C2H undergoing chemisorption and C,.
Figure 7. Reaction profile (solid curve) for the concerted processes of hydrogen migration/ring closure [C + D in Figure 21. Points u, 6,and c represent the transition state, an intermediate metastable state, and the product state, respectively [see Figure 81. The dot-dashed curve is the reaction profile when ring closure occurs between two radical sites so that hydrogen migration is not required. Thereactioncoordinateisthedistance between C, and C in both cases.
might have found hydrogen abstraction to be the rate-controlling step in the overall process. The analogous reaction profile for C2H addition to a carbon radical site oia single C,-C bond formation is shown in Figure 5 . Since the two carbon atoms in the C2H molecule are not equivalent, we denote the one bonded to the hydrogen atom as C,+ The second carbon containing the unpaired electron is denoted Cg. The reaction profiles for C,-C, and C,-Cg chemisorption are shown by the dot-dashedand solid lines, respectively, in Figure 5 . When C2H is bonded to the diamond surface radical site at carbon atom A, the reaction barriers and reaction exothermicity are 0.031 eV (0.71 kcal/mol) and 1.58 eV, respectively. For the case of C.4, chemisorption of C2H, the reaction barrier and exothermicity are 0.027 eV (0.62 kcal/mol) and 3.5 eV, respectively. Although the reaction is a near barrierless process for both C2H2 and C2H addition via single C,-C bond formation, the significant difference between the exothermicity for these two adsorbates shows that C2H addition leads to a much more stable product than C2H2 addition. This is in accord with the molecular dynamics results of Peploski et al.19which show that C2H radical addition to a chemisorbedacetylene moiety proceeds with a much higher probability and, once chemisorbed, C2H is much less likely to undergo desorption than is the case for C2H2. Figure 6 shows the reaction profile for gas-phase hydrogen atom addition to a carbon radical site. The reaction coordinate is the distance between the gas-phase hydrogen atom and the surface carbon atom. The chemisorption is a barrierless process with a predicted exothermicityof 3.76 eV. These results support the substrate-heating mechanism by hydrogen atom recombination observed by severalgroup in diamond growth systems.2~30 Tankala et al.,a for example, found that the substrate was hunreds of degrees hotter in a hydrogen than in a helium environment. The difference was attributed primarily to the exothermic recombination of hydrogen atoms on the substrate.
C. Hydrogen Atom Migration and Ring Closure. After C2H2 (or C2H) addition to the carbon radical site via a single C,-C bond to form structure C in Figure 2, the HFM mechanism15 suggeststhat a second c8-Cbond between C2H2 and the diamond surface is formed via the migration of a hydrogen atom from the lower surface layer to the upper layer. The process leads to structure D in Figure 2. Frenklach” has termed the processes involving (1) addition to C2H2 followed by (2) hydrogen atom migration and ring closure ”two-center” acetylene addition. In his recent Monte Carlo, ballistic simulations of diamond-film growth, Frenklach” assigned an overall event probability of 0.01 to the “two-center” process. We have obtained the minimum-energy pathway for such a ring closure by executing a series of small displacements that move the carbon atom on acetylene toward the carbon atom in the lower layer by an amount Aq. The hydrogen atom bonded to the lower layer is then allowed to rotate within a fixed range, which is adjusted to maintain a favorable bonding configuration and stretch freely along its bond until the nearest local potential minimum is found. The C,--H--C group is then treated as the stationary moiety while permitting the remaining atoms to relax using the damped-trajectory procedure described in Section 11. The minimum-energy path thus obtained is shown by the solid line in Figure 7. The reaction barrier for the diffusion/ring closure reaction is 1.62 eV (37.4 kcal/mol). The exothermicity is 1.45 eV. As can be seen in Figure 7, there is a local stationary point b after the reaction barrier a. Examination of the potential derivatives shows that the configuration corresponding to state b is a metastablestructure. The relative positionsof the H-H-H--C, moiety for the configurations corresponding to points a, b, and c are shown in Figure 8. The metastable structure corresponding to b resembles the hydrogen-bridged compounds that are often found for Si,H, systems. For the diamond system,
10116 The Journal of Physical Chemistry, Vol. 97, No. 39, 1993
a
6 b
C
F i p e 8 . Configurationsof the (a) transition state, (b) metastable state, and (c) product state for the concerted process of hydrogen migration/ ring closure whose reaction profile is given by the dot-dashedcurve shown in Figure 7.
however, the depth of the potential well is significantly less than those usually observed for silicon systems. On the BPES, the hydrogen atom migration/ring closure process that converts structure B into structure C in Figure 2 is not a barrierless process as suggested by Huang et a1.15 The magnitude (37.4 kcal/mol) of the barrier to the “two-center” addition suggests that theevent probability assumed by Frenklach (0.01) in recent Monte Carlo simulationsI7 is much too large. We have previously shown20 that the event probability may be expressed as
P(T) = [reaction rate]/[collision rate] = k(T)N/u,(T)N (1)
where N is the number of acetylene molecules per unit volume in the gas phase, k( 7‘) is the rate coefficient for the “two-center” process, and v,( T ) is the total collision rate with the surface which is given by uC(7‘) = Ab,2(8rRT/m)’/2 (2) In eq 2, A is Avagadro’s number, m is the mass, and b, is the maximum impact parameter that defines a “collision” of acetylene with the surface radical site. In our study of hydrogen atom abstraction rates,*Oa value of 2.615 A has been estimated forb,. An estimate of the event probability may be obtained by writing k(T) in Arrhenius form with the activation energy taken to be the minimum barrier height
k ( T ) = A exp[-37 400(cal/mol)/RTj (3) Belton and Harris18 have estimated the A factor for acetylene addition to be 10” cm3/(mol.s). Use of this value in eqs 1-3 yields a “two-center” event probability of 1.2 X 10-10 at 1200 K.
Chang et al. The frequency factor could, of course, be larger than that estimated from the gas-phase data.18 An upper limit for the two-center event probability can be obtained by taking the frequency factor to be that for hydrogen abstraction, 1.67 X 1014 cmS/(mol.s). This yields an event probability of 2.0 X le7 a t 1200 K. We are presently in the process of computing the rate coefficients for the important chemisorption processes on diamond-like surfaces. Since the reaction barrier for a concerted, two-center process is much higher than the hydrogen-abstraction barrier (=12.2 kcal!mol), we propose that if such a ring closure process plays an important role in diamond surface growth, it must proceed by a mechanism in which a radical site is created by hydrogen atom abstraction rather than via hydrogen atom migration. The calculated reaction profile for ring closure subsequent to such an abstraction is shown by the dot-dashed line in Figure 7. The reaction barrier is 0.10 eV (2.3 kcal/mol), and the reaction exothermicity is 3.35 eV. Consequently, the rate-controlling step for the total process would be hydrogen abstraction, whose potential barrier is about 1 eV less than that for the migration/ ring closure pathway suggested by HFM.l5 The above mechanism is similar in concept to the growth model suggested by Belton and Harris,18 where C2H2 is added to the diamond surface a t two radical sites formed by successivehydrogen atom abstractions. It is also supported by the molecular dynamics studies of Peploski et al.19 which show that chemisorption of acetylene most frequently involves the formation of two Cs-C single bonds to adjacent radical sites on the C( 111) surface. If growth occurs by addition of a radical species such as C2H instead of C2H2, the radical sites needed to form a second Cs-C bond may already be present. It may, therefore, be unnecessary either to abstract hydrogen or to have hydrogen migration prior to ring closure or other Cs-C bond formation. This increases the probability that addition of radicals such as C2H, CH2, etc. plays an important role in diamond-film growth. In this regard, it should be noted that previously reported flow-field calculations have assumed that chemisorption is accompanied by spontaneous release of all hydrogen in molecular form.lOJI If hydrogen atom abstraction reactions are rate controlling, such an assumption will bias the results toward enhancing the growth contribution of species such as CH3 and C2H2 relative to C2H, CH2, C3H3, etc. D. “Three-Center” Acetylene Addition. Subsequent to ring closure to form structure D in Figure 2, the HFM mechanism’s postulates that a second C2H2 addition occurs to form structure E. This is followed by a hydrogen atom migration combined with a hydrogen atom release into the gas phase to permit two simultaneous ring closures producing structure F in Figure 2. Frenklachl’ has termed the combination of these processes “threecenter” acetylene addition. He has assigned an overall event probability of 0.001 to such additions in his recent Monte Carlo sim~1ations.l~ The reaction profiles for the addition of a second C2H2 molecule to form structure E in Figure 2 and the formation the second, six-membered carbon ring should be similar to those given in Figure 7. According to the H F M model,ls a hydrogen atom is now released into the gas phase to permit a third ring closure leading to structure F in Figure 2. This ring closure completes the “three-center” addition process. The reaction barrier for the hydrogen release is about 3.76 eV (86.7 kcal/mol). The reaction profile is shown in Figure 6. Ring closure subsequent to hydrogen release is a barrierless process with a reaction exothermicity of 2.42 eV. The reaction profile for the closure is given in Figure 9. Thus, the combination of hydrogen release/ring closure has an endothermicity of 1.34 eV (30.9 kcal/mol), which must be a lower limit for the barrier for thecombination of the two processes. The sequence of steps involved in “three-center” acetylene addition is therefore associated with barriers of 1.62 and 1.34 eV. These results indicate that the overall event probability for “three-center”
Low-Pressure Diamond-Film Formation
The Journal of Physical Chemistry, Vol. 97, No. 39, 1993 10117
Formation of the Third Carbon Six-member Ring
I
[
-2.0
f . . l
3.0
.
.
I
.
8
. . . .
2
"
'
)
2.0 3.0 Reaction Coordinate (Angs)
Figure 9. Reaction profile for the third ring closure leading to structure Fin Figure 2 subsequent to the release of the hydrogen atom. The reaction coordinate is the C-C distance at the site of ring closure.
acetyleneadditionat temperaturescharacteristic of diamond CVD experiments is much lower than the 0.001 value assumed by Frenklach." E. ConformationRequirements. All of the above computations have been carried out starting with the chair-chair conformation for structure A. We have also carried out similar calculations starting with the boat-boat, boat-chair, and chair-boat conformations shown in Figure lb, c, and d. It was found that, after C2H2 (or C2H) addition to the surface via single C,-C bond formation, there is a substantial barrier to ring closure if the starting structures are boat-boat or chair-boat. This barrier is due to the energy required to invert the boat-boat and chair-boat conformationsto boat-chair and chair-chair, respectively,which are required to produce the conformationsneeded for ring closure. The same type of barrier is present for the second ring closure; i.e., the boat-chair has to be inverted into a chair-chair conformation prior to closure.
IV. Summary By employing damped classical trajectories on Brenner's empirical hydrocarbon potential:' we have calculated the minimum-energy paths for a number of important elementary reactions, which are involved in previously suggested modelsI2-l8 for the growth mechanism of low-pressure diamond film. The processes investigated include hydrogen atom abstraction, C2H2, CzH, and hydrogen atom additions to surface radical sites, hydrogen atom migration, hydrogen atom release, and three ring closure reactions. The results show that the barrier for addition of both C2H2 and C2H to the surfaceoia C,-C single-bond formation at some radical site is within the range of thermal energies available at temperatures typical of diamond CVD experiments. Although both addition processes are exothermic, the reaction exothermicities are very different. The energy released from C2H2 addition is 0.66 eV compared to 3.5 eV for C2H addition when the end carbon atom of C2Hforms the C A bond. When the C-H carbon is chemisorbed, the exothermicity is reduced to 1.58 eV. These data indicate that C2H addition leads to a more stable product which is much less likely to undergo subsequent desorption than is the case for the corresponding addition of C2H2. Theminimum-energypathshows that the formationof a second C,-C bond between C2H2 and an adjacent carbon radical site is a barrierless (or within the range of thermal energies) and exothermic process. However, the barrier can be as high as 1.62 eV (37.4 kcal/mol) if formation of thesecond Cs-C bond requires hydrogen atom migration from lower to upper layers as assumed in the "two-center" addition process present in the HFM model.15 Such processes are therefore expected to be associated with very small event probabilities (
