J. Phys. Chem. 1994,98, 4375-4381
4375
Theoretical Studies of Elementary Chemisorption Reactions on an Activated Diamond Ledge Surface Martin D. Perry and Lionel M. Raff Department of Chemistry and Diamond Research Group, Oklahoma State University, Stillwater, Oklahoma 74078 Received: December 6, 1993; In Final Form: February 21, 1994'
Rate coefficients, event probabilities, and desorption probabilities at 1250 K for chemisorption reactions of C2H2, C2H, CH3, CH2, C2H4, C2H3, C3H, and C, ( n = 1,2, 3) on an activated diamond ledge structure and for H on sp2 carbon and H on sp3 carbon are computed using classical trajectory methods on the empirical hydrocarbon no 1. potential developed by Brenner. The results show that the chemisorption rates for nonradical species such as C2H2 and C2H4 are 2 or more orders of magnitude smaller than the values obtained for radicals. For ethylene, the chemisorption rate is on the order of lo6 cm3/(mol s), which is too small to permit CzH4 chemisorption to play a role in diamond-film formation. The chemisorption rate for acetylene lies in the range (1-2) X 10" cm3/(mol s) provided acetylene can form two C,-C bonds to the lattice. If only one bond forms, 97% of the acetylene desorbs within four C-C vibrational periods. All of the radical species have chemisorption rates in the range of 1012-1013cm3/(mol s). The least reactive of the radical species investigated is CHs. However, its high concentration in most chemical vapor deposition experiments makes it an important growth species. The chemisorption rates for C, (n = 1, 2, 3) are a monotonically decreasing function of n. The associated desorption probabilities increase as n increases. Atomic carbon has the largest chemisorption rate of all of the species investigated. Consequently, it is likely to be an important growth species in plasma experiments where its concentration is sufficiently high. Hydrogen atom addition to sp2 and sp3 carbon is found to be very fast with rate coefficients of 1.6 X 1013 and 3.7 X 1013cm3/(mol s), respectively. This finding removes the bottleneck that would exist if hydrogen atoms had to be extracted from sp2 carbon to propagate diamond-film growth.
I. Introduction It is now a well established fact that diamond films may be grown at low pressure using a variety of techniques that include microwave and radio-frequency plasma, hot filament or UVassisted chemical vapor deposition (CVD), or combustionmethods with simple hydrocarbon precursors such as methaneor acetylene. Numerous research groups have addressed the question of the mechanism of the process using theoretical and/or experimental methods. The elementary reactions that have been suggested as playing a role in diamond-filmformation include hydrogen atom abstraction from sp, sp2, and sp3 carbon by gas-phase hydrogen, chemisorption of numerous gas-phase species, desorption reactions, and hydrogen atom diffusion. At an even more detailed level in such plasmas, it is likely that electron-transfer processes and excited electronic states will play important roles. Zhu and White' proposed a growth sequence that involves the chemisorption of acetylene followed by several hydrogen atom abstractionreactions. Tsuda et al.2J have suggested a mechanism that assumes that methyl radicals are the primary growth species. Frenklach and Wang4 have reported phenomenological studies in which contributions from numerous gas-phase and surface reactions are included. The results indicate that chemisorption of acetylene is the rate-controlling step. In the mechanism proposed by Huang et U I . , ~surface activation occurs via hydrogen atom abstraction. This is followed by chemisorption of acetylene via the formation of a single C,-C bond (C, denotes a surface carbon atom), a series of hydrogen atom migrations between various chemisorbed moieties, and finally six-membered ring closure to form the diamond structure. Belton and Harris6 have also proposed a mechanism in which the principal growth species is acetylene but suggest that, in order to avoid subsequent desorption, acetylene must chemisorb by the formation of two Abstract published in Aduunce ACS Abstracts, April 1, 1994.
C,-C bonds. One-dimensional flow field calculations reported by Goodwin' and by Goodwin and Gavillets indicate that only CH3, C2H2, and CH4 have sufficient abundance at the surface to be solely responsible for the growth rate measured in filamentassisted CVD experiments. However, other species such as CH2, C2H4, C2H5, C2H6, C3H2, C3H3, C3H5, and C are predicted to have maximum growth rates sufficiently large that some combination of these species could account for the observed diamond growth. Yu et al.9 have recently reported the results of plasma CVD studies that indicate methyl radicals and atomic carbon are the principal growth species. Their results suggest that C2H2 plays only a minor role in the process. Molecular dynamics calculationsby Peploski et al.1° suggest that the ethynyl radical (C2H) may be important. Measurements of the concentration of gas-phase species present in a filament-assisted experiment indicate that the two most likely growth species are methyl radicals and acetylene.11 Quantitative assessment of the above hypotheses has been severely hindered by a lackof quantitativeinformation concerning the rates of the proposed surface reactions. Most of the attempts to quantify the proposed mechanisms have involved arbitrary assumptions for the values of these rates. The flow field calculations reported by Goodwin and Gavilleta assume an arbitrary constantchemisorptionprobability for each hydrocarbon species. Frenklach12 has made analogous assumptions in his Monte Carlo calculations. Yu et ~ 1 assume . ~ a constant chemisorption probability of 0.1 in analyzing the results of their plasma CVD experiments. Other calculations have assumed all hydrogen atom abstraction reactions to be fast relative to the chemisorption processes.*J2 Many studies have assumed that rate coefficients for analogous gas-phase reactions may be used for the corresponding surface reaction^.^.^ Although each of these investigations has led to useful information, it is clear that a
0022-3654/94/2098-4315~04.50~0 0 1994 American Chemical Society
4316
The Journal of Physical Chemistry, Vol. 98, No. 16, 1994
Figurel. DiamondC(1lI)ledgesurface. Thetworadicalsitesavailable for chemisorption are denoted by the asterisks.
definitiveevaluation of the various possible mechanisms requires accurate values for all of the important elementary surface reactions. We have recently reported reaction probabilities,crosssections, rate coefficients, frequency factors, and activation energies for hydrogen atom abstraction from a hydrogen-covered C(111) surface'l using quantum wave packet and classical trajectory methods on the empirical hydrocarbon no. I potential energy hypersurface developed by Brenner.14 Upper bounds for the abstraction rates, activationenergies, and frequency factors were also obtained for six different chemisorbed moieties on a C(11 I ) surface using a classical variational transition-state method.l) The latter studies involved abstraction from sp, sp2, and sp3 carbons. In a separate study.15 we have obtained minimumenergy paths for hydrogen atom migration, C2Ha C2H, and H atom addition to a carbon radical site, and six-membered,carbon ring closure. The results show that the reaction barriers for addition of CzHzorC2Hvia C,-C single-bond formation at some radical surface site is within range of the expected thermal energies. Processes involving hydrogenatom migrationareshown to be associated with potential barriers of at least 31 kcal/mol. Thesecalculations provide many of the rate coefficients required to develop an accurate kinetic Monte Carlo model of the film deposition process. However, the development of such a model still requires accurate values for the rate coefficients and event probabilities of the various chemisorption reactions. Our previously reported molecular dynamics studies10 show that the chemisorption probabilities for C2H2 and C2H are different for an activated diamond terrace and at a radical site on a chemisorbed ledge structure. The thermodynamic Monte Carlo simulations carried out by Xing and Scott16 also yield the same result. These investigators found that the difference in chemisorption rates at terraces and ledges leads to layer-by-layer film growth in which the (n + 1)-layer growth does not start until the n-layer growth is substantially complete. Consequently, chemisorption rates at both ledgesand terracesmust becomputed. In this paper, we report the results of classical trajectory calculations of chemisorption/desorption rates for C2H2,C2H, CH,, CHz, C2Hc CzH,, CIH, and C. (n = 1,2,3) on an activated diamond-ledge structure. We also report results for hydrogen atom addition reactions leading to sp2 and sp3 carbons. 11. Methods and Procedures
A. SurfaceModeland PotenlialSurface. Thediamond-surface model used in the present study is similar to that employed in our previously reported molecular dynamics investigations of elementary processes in diamond-film growth.'0J3 In these studies, a 127-atom model was used to represent the C(11 I ) surface. Figures 3 and 4 of ref 10 show top and side views of this lattice. In the present study, a chemisorbed moiety is added to the lattice to produce the ledge structure represented in Figure 1. This ledge structure has two available radical sites denoted by the asterisks. The total number of lattice atoms is 147.
Perry and Raff
In order to simulate the heat-transfer effects of the crystal bulk, the 147 lattice atoms are partitioned into three subsets comprising Np, NQ.and N Batoms, which are designated as the P-zone, Q-zone, and B-zone, respectively. P-zone atoms have no chemical bonds to 8-zone atoms. Lattice atoms in the Q-zone have at least one bond to a B-zone atom. The motions of the P-zone, atoms are determined solely by the forces produced by the interaction potential and the direct solution of the classical Hamiltonianmotionequations. The motionsoftheQ-zoneatoms calculated fromthe solutionofHamilton'seauationsaremodified by the presence of velocity reset functionsll issociated with each atomin theQ-zone. Theactionof the reset functionsincorporates the heat bath effects of the crystal bulk. The details of the procedure are described in ref 17. The B-zone atoms have fixed positions. These sites serve to reduce edge effects and maintain the proper symmetry of the lattice. In the present calculations, we have taken N p = 12, NQ = 11, and NB = 124. The empirical hydrocarbon potential no. 1 developed by Brenner" is employed in all of the calculations reported in this paper. This potential is based on Tersoffs covalent bonding formalism'* with additional terms that correct for overhinding of radicals and nonlocal environmental effects. Nonlocal effects are included using an analytic function that defines conjugation in termsof thecoordination of carbon atoms that neighbor carboncarbon bonds. Brenner14 has employed this potential to compute atomization energies for 12 alkanes, 13 alkenes, 4 alkynes, 7 aromatics, and 12 radicals. The average absolute deviation of the results from the experimental values are 0.133 (alkanes), 0.546 (alkenes), 0.275 (alkynes), 0.557 (aromatics) and 0.18 eV (radicals). In terms of the average absolute percent error, the resultsare0.30%, 1.31%,0.73%,0.74%,and0.61%,respxtively. Consequently,we havegood reason toexpxt the thermochemistry of the processes involved in chemisorption on diamond surfaces to be well represented. We have also obtained some significant data related to the accuracy of the potential energy harriers predicted hy the Brennerl4surface. Ifthe potential barrier for the H + D2 HD + D exchange reaction is computed on the Brenner surface, the result is in near exact accord with the accurate quantum mechanical results reported by Liu et Our c a l ~ u l a t i o nof s~~ tbeabstractionratefors~-bondedhydrogenatomsfromaC(lll) surface yield a potential barrier on the Brenner" surface of 10.6 kcal/mol. This resultis 3.23 kcal/molgreaterthan themeasured activation energy for the gas-phase hydrogen atom abstraction from the tertiary carbon of isobutane reported by Westbrook et a120 Recent ab initio electronic structure calculations reported hy Brenner et aLZ1indicate that the barrier on a diamond surface should be about 3.00 kcal/mol greater than the harrier for isobutane. Most recently, we have determined the minimumenergy pathway for hydrogenatommigrationonaC(11I ) surface to an adjacent absorption site22 using the Brenner" potential. The result is 75.9 kcal/mol. This barrier has recently been computed by Melnik et aI.23 using a triple-referenced, SDCI/ CASabinitiomethod. Without theinclusionofsurfacerelaxation effects during the migration, the ab initio result is 82.1 kcal/mol. Ourcalculationsindicate that surfacerelaxationlowers the barrier by about 2.0 kcal/mol.15 The barrier obtained with the Brenner" surface is therefore within 4.0 kcal/mol of the quantum mechanical result.') In view of these results, we believe that there is good evidence indicating that the potential barriers for processes involving hydrogen atoms in diamond-film formation are well represented by the Brennerl4 potential. For processes involving C-C bond formation or rupture, the situation is not as clear. Our previous study of minimum-energy paths15indicates that the Bre~~ner~~potential predicts a zero harrier for radical-radical recombination reactions. This is certainly the expected result. However, for gas-phase reactions of small molecules involving insertion of a radical into a neutral molecule,
-
The Journal of Physical Chemistry, Vol, 98, No. 16, 1994 4377
Reactions on a Diamond Ledge Surface
TABLE 1: Velocity Zones for Reaction Rate Calculations on a Diamond-Ledge Surface at T = 1250 I(.
z
Surfaca Radical Site !
I
/
\
/X
'*Ai
Y
Diamond Surface
Figure 2. Definition of the variables for the trajectory calculations.
the results obtained in this investigation suggest that the barriers for this type of C-C formation are too small. For example, the calculated barrier for CHs insertion into ethylene on the Brenner potentiali4is near zero whereas the measured valuez4is 7.3 kcal/ mol. B. Initial Conditions and Numerical Procedures. The thermal rate coefficient for chemisorption on a diamond surface may be written25
where.the total chemisorption cross section, c(Vr), is given byz5
P(b,8,4,r,V1)[0.5sin 8 de] [d4/2r] [C(r)dr] (2) In eq 1, p is the reduced mass of the chemisorbing species plus diamond surface, 6 is (kbT)-' where kb is Boltzmann's constant, and V, is the initial relative velocity vector. In eq 2, b is the surface impact parameter, 8 and 4 are the orientation angles of the incident relative velocity vector, r< and r> are the innner and outer turning points of all of the vibrational modes of the incident gas-phase species, C(r) is the normalized distribution function for the vibrational phases, and P(b,8,4,r,Vr) is the reaction probability for collisions in the range db at b, d8 at 8, d 4 at 4, drat r, and dVr at V,. These variables are defined by the collision diagram given in Figure 2. In order to improve the convergence rate in the Monte Carlo evaluation of eq 1, we divide the velocity range into five zones and evaluate each of the resulting integrals separately. That is, we write
where
c = [2/?r]'/2[p/3]3/2 A Vr) = ~XP[-PB~ , 2 / 2 v,3~( 1 Vr)
(4)
(5)
The velocity zones are given in Table 1. The integrals in eqs 2 and 3 are evaluated using standard Monte
Carlo methods.25 These methods require that the initial variables for the trajectories be selected from the normalized distributions functions. Therefore, in the evaluation of the integral over the range VLI V, I Vu,the initial relative velocity is selected by
where
and 4 is a random number selected from a uniform distribution on the interval [0,1]. The impact parameters are selected from a distribution uniform in b2 over the range 0 Ib I bm, where the upper limit, b,, is chosen such that for impact parameters b > b, the reaction probability is zero. In the case of an infinite lattice model, 8, = u/2. However, the finite size of the lattice requires that an upper limit be chosen to ensure that as the incident molecule approaches the surface radical site, it is over the surface structure when within reaction range. In practice, this yields 8, < r / 2 . In the present calculations, the size of the lattice model described in section 1I.A requires that Bm = 50.19'. Since the probability distribution for the rotation angle is uniform over the interval 0 I 4 I2 r , we select the initial values of 4 from
In all calculations, the initial rotational energy is taken to be OSRT for each mode. This energy and the initial zero-point vibrational energy are partitioned into the appropriate rotational modes and normal vibrational modes of the incident molecule using previously described projection methods.26 The thermal energy of the diamond surface is introduced by placing the lattice in its equilibrium configuration and inserting a kinetic energy of kbT, into each degree of freedom. The signs of the various momentum components are chosen randomly. Thus, the a momentum component of the ith atom is taken to be Pai = f [ 2 mikbT,]'/2, for ct = x, y , or z
(9)
The integrations over the vibrational phases are performed as follows: Subsequent to the introduction of the thermal lattice energy, the equations of motion for the lattice are integrated for a period to sufficiently long to achieve a randomization of the lattice energy. In practice, to is taken to be 10.0 tu [ l tu = 1.019 X lW4SI. The resulting phase-space point describing the lattice is stored and denoted as the initial lattice configuration, b(b). At the start of the trajectory, b(t0)is retrieved, and this initial phase-space point is evolved for an additional period, 71, where ~i is randomly chosen so as to lie in the range 2 tu 5 Ti I10 tu. The new lattice configuration, L(fo+~i), is used as the initial lattice state for the ith trajectory. Vibrational phase averaging over the lattice is achieved by repetition of this procedure for each trajectory so that the initial lattice configuration for thejth trajectory is L Q ( ~ ~ + Z Twhere ~ ) , the summation runs over all trajectories from 1 to j . When the initial state selection is carried out in the manner described above, the statistical uncertainty for each of the integrals
4378
Perry and Raff
The Journal ofPhysical Chemistry, Vol. 98, No. 16, 1994
in eq 3 is given by’s
Q
K
n
where the subscript i specifies the integral in eq 3, N is the total number of trajectories computed, and NR is the number of chemisorption events observed. The overall statistical error in k(TJ is therefore
The Hamiltonian equations are integrated using a variableorder, variable step size, predictor-corrector procedure.” This method produces energy conservation to about four significant digits throughout the integration. The trajectory calculations require approximately 30 CPU minutes per trajectory on a DEC ALPHA 3000/Model 400 workstation. Individual trajectory times vary over the range 0.10-0.87 ps. Chemisorption is assumed to occur when the center-of-mass of the incident molecule or radical experiences more than one inner turning point of vibrational motion. Desorption of the chemisorbed molecule or radical occurs when the center-of-mass doesnot experience four inner turning pointsofvibrational motion. It should be noted that the term “desorpti0n”asusedin the present paper does not describean equilibrium,thermal desorption process but rather a nonequilibrium, dynamical one. The event probabilities requred for a kinetic Monte Carlo simulation of diamond-film formation may be obtained from the calculated chemisorption rate coefficients by using eqs 1 and 2 to compute the total collision frequency. The total collision cross section for collisions in the impact parameter range 0 5 b 5 b. may be obtained from eq 2 by setting P(b,O,@,r,V,)to unity and executing the indicated integrations. The result is u(V,) = nb.2. Combining this result with eq. 1 and integrating over all incident velocities, we obtain the total collision frequency, uc(7‘),
Figore 3.
surface.
Acetylene (CtH3 chemisorption on a diamond C( I 1 I ) ledge
TABLE 2 Total Rate Coefficients, Collision Rates, and Event Probabilities for Chemisorbing Species on a Diamond-Ledge Surface at T = 1250 K for a Maximum Impact Parameter b. = 1 A species k ( n , cml/(mol s) cm3(mols) P(n
+(n,
CiHi CiHf CiH CHI CHI C’H, CiHi CiH C Cl
c3
H(sp3) ~(sp’)
(1.2 i 0.6) X 10” ( 1 . 9 i 1.3) X 10” (2.7 i 0.9) X 10” (1.1i0.4)XlO” (4.3 i 1.4) X 10” (3.4 i 3.4) X 106 (2.0 i 0.9) X 10” (1.7 i 0.7) X 10” (9.7 i 1.7) X IO” ( 7 . 4 i 1.3) X 10” (3.0 0.9) X 10” (3.7 i 0.7) X lo1] (1.6 i 0.5) x 1013
*
1.908 X 1.908 x 1.946 x 2.510 x 2.599 x 1.838 X 1.872 X 1.599 x 2.809 X 1.986 X 1.622 X 9.696 X 9.696 X
IOl3
1013 1013
1013 1013
IO’] IO’] 1013 IOl3 IOl3
IO1]
IO1) IO’]
0.0064 0.0100 0.1389 0.0424 0.1642 0.0000 0.1049 0.1077 0.3438 0.3718 0.1843 0.3821 0.1611
Assuming one chemisorption in velocity zone I .
Acetylene ( C a d . The nature of acetylene chemisorption on the diamond ledge surface has been determined from the results of 1000 collision events. As in our previous molecular dynamics investigation,1° we find that the most probable chemisorption u,(r) = b,,,%3*/~81”~ (12) mode involves theformationofa surface-boundethylenestructure with two C,-C bonds as shown in Figure 3. Of the 1000 collision If M is the number of molecules or radicals per unit volume in events studied, 38 resulted in chemisorption; however, 28 the gas phase, we have subsequently desorbed. Thus, only 10 collisions led to acetylene P,(r) = (reaction rate)/(collision rate) = exhibiting more than four inner turning points of vibrational motion and being incorporated into the diamond film. In 9 of Mk(r)/Mvc(r) = N r ) / v , ( r ) (13) the 10 cases, two C,-C bonds were formed, indicating that desorption is a high probability process unless acetylene is able where P A ( n is the event probability at temperature T. If we to form both bonds. Consequently, if a second, nearby radical write the rate coefficient in Arrhenius form and use eq 12, we surface site is not available, the acetylene molecule will most obtain likely not be able to incorporate itself into the lattice. These PA(r) = e x ~ [ - 8 ~ ~ 1 / [ ~ ~ ~ ~ (14) ~ ~ / ~ 8results ~ ’ ’ support ~ 1 the hypothesis advanced by Belton and Harris6 that, for successful chemisorption to occur, acetylene must form where d is Avagadro’s number which converts v to units of cm3/ an ethylene species bonded to two adjacent lattice sites rather (molecule s). than an ethenyl radical attached uia a single C . 4 bond. Equation 14 gives the event probability for collisions which Thechemisorption rate coefficients,total collision frequencies, occur within a radius of b, of the radical site. If a collision and event probabilities computed from eqs I, 12, and 14, occurs at an impact parameter for which b > b., the event respectively, for all incident molecules and radicals are given in probability is zero. Table 2. The uncertainties in the rate coefficients are obtained fromeq 11. Table3 lists thetotalnumbcroftrajcctoriescomputed 111. Results and Discussion (Ntm1),the number of observed chemisorption events ( N J , the number of desorptions (Nd). the desorption probability (Pd = Classical trajectory methods25 have been utilized to determine Nd/N.), and the average residence time on the surface for thme rate coefficients,collision rates, desorption probabilities, and event molecules and radicals which eventually desorbed. probabilities for chemisorption reactions of C2Hl, CIH, CHI, CH2, ClH4, CIHl, CIH, and C. (n = 1, 2, 3) on the activated No C2H2 chemisorption events were ObServed in the lowest diamond-ledge structureshownin Figure 1. Wealsoreport results relative velocity range (zone I ) after the computation of 200 trajectoriesin spiteof the fact that the potential barrier forC2Hl for hydrogen atom addition reactions to sp2 and sp3 carbon. The surface temperature, T,, is chosen to be 1250 K,which is typical chemisorption on the Brenner potential energy surface is only of most diamond depositionexperiments. In all cases, 6, is 50.19°, 0.48 kcal/mol.” Clearly, the steric factor is very small for this which ensures that the incident molecule or radical will be over process. In addition, in this energy range, the incident acetylene the lattice when within interaction range. molecule does not have sufficient time and energy to rotate and
The Journal of Physical Chemistry, Vol. 98, No. 16, 1994 4319
Reactions on a Diamond Ledge Surface
TABLE 3: Number of Computed Trajectories, Number Of Chemisorptions, Number of Desorptions, Desorption Probabilities, and Average Residence Times for Chemisoibing Species on a Diamond-Ledge Surface at T = 1250 K species NWUI Nca Ndb pd (7). CzHi C2Hf
1om
C2H CHI
250 400 250 350 250 250 250 250 250 250 250
CHz CiHI ClH3 CIH C Cl c3
IO00
38 39 76 46 53
28 28 39 22 5
I
0 11
40 53 116 129 72 114 60
I6
I8 29 22 28 22
0.74 0.72 0.51 0.48 0.10 0.00 0.28 0.30 0.16 0.22 0.31
7.0 X 7.0 X 9.6X 9.8 X 3.1 X
IO-"
1.0x
1v13
9.0 X 6.9 X 8.3 X 9.5 X
IO-"
1V" IO-" IO-" lV"
IVI' lV1'
IV"
Figure 5. Methyl (CHI) chemisorption on a diamond C(111) ledge surface.
0.25 2.8 X IO-]' H(sp1) 0.37 2.5 X IVl4 H(sd) a Exhibited more thanoneinner turningpoint ofvibration. Exhibited less than four inner turning points of vibration. Assuming one chemisorption in velocity zone I.
Figwe 6. Methylene (CHl) chemisorption on a diamond C(I 11) ledge surface. The new radical site is denoted by the asterisk.
F i p 4. Ethynyl (ClH) chemisorption on a diamond C(1II) ledge
surface. form the second C,-C bond. The result is a chemisorption rate coefficient equal to (1.2 f 0.6) X 1011 cm3/(mol s), which is one of the smallest values obtained for any of the carbon-containing species investigated. The corresponding event probability is 0.0064. The failuretoobserveanychemisorptioneventsin energy zone 1 means that the statistical error in this zone is infinite. To obtain an estimated upper limit of the actual error introduced by the lack of chemisorption in zone 1, we have computed a rate coefficient assuming that the correct value corresponds to one reactive event in the 200 trajectories computed. This rate and associated event probability are listed as the second ClH2 entry in Tables 2 and 3. Comparison of the two entries shows that we expect the maximum error to correspond to about 50%. The phenomenological model studies reported by Frenklach and Wang' and by Belton and Harris6 suggest that the ratedetermining step in diamond-film formation is acetylene chemisorption. The very small chemisorption rates obtained for CzHi support their conclusions. The fact that these rates will be near zero if there is only one surface radical site available (thus preventingthe formation of the second C,-C bond) lends additional support. Ethynyl Radial ( C a ) . Unlike acetylene, the ethynyl radical readily chemisorbs to the diamond-ledge radical site. We have investigated this process by thecalculationof250 collisionevents. The total rate coefficient for CzH chemisorption is (2.7 0.9) x 1012 cm?/(mol s), which is a full order of magnitude greater than that for acetylene. In addition, the ethynyl radical is less likely to desorb. Its desorption probability is 0.51 compared to 0.74 for CIHl. When the ethynyl radical incorporates into the lattice, it does so via the formation of only one C,-C bond as shown in Figure 4. Of the 37 events which resulted in chemisorption, only one rotated to form the second C,C bond. The remaining 36
*
chemisorptionsoccurred via C,-C bond formation from the bare carbon end of the ethynyl radical. Thus, for the second bond to form, the C = C triple bond must open. This requirement significantly reduces the probability of occurrence. Methyl Radical (a3). Since the feed gas in most diamond CVD experiments is methane, methyl radicals are usually the most abundant of the gas-phase radical species. As a result, most ofthe mechanismswhich have been suggested for diamondfilm growth assume that deposition and incorporation of CH3 radicals into the film is a major component of the process. We have obtained rate coefficients, event probabilities, and desorption probabilities for methyl radical chemisorption from theinvestigationof 400suchcollisionevents. Themethyl radical is found to behave much like the ethynyl radical incorporating intothelatticeviasingleC,-C bond formationasshown in Figure 5 . The CHI chemisorption rate coefficient is (1.1 0.4) X IOI2 cml/(mol s) at 1250 K,which is a factor of 2.4 less than that for the CzH radical but an order of magnitude greater than the corresponding ratecoefficient for acetylene. The probability that theCH3radical willdesorh within four vibrational periods (0.48) is almost identical to that for C2H (0.51). The relatively large value for the CHI chemisorption rate coefficient combined with its high gas-phase concentration obviously means that it will be an important growth species in CVD experiments. Methylene Radical ( a d . The molecular dynamics of methylene chemisorption and its subsequent dynamics on a reconstructed C(OOl)-(2Xl) surface have been investigated in detail by Garrison et Our results show that CH2 is an ideal growth species for diamond-film formation. Its chemisorption rate coefficient at 1250 K is nearly 4 times that of the methyl radical while i t s desorption probability of 0.10 is only 21% that for CHI. In addition to the favorable chemisorption and desorption rates, the methylene radical also provides a new radical site for subsequent bond formation by another chemisorbing species as illustrated in Figure 6. Therefore,one hydrogen atom abstraction step is circumvented when CHl rather than CH3 is incorporated into the lattice. Only the relatively low gas-phase concentration ofCH2preventsitfrombeingamajorgrowthspecies indiamondfilm formation
4380
The Journal of Physical Chemistry, Vol. 98, No. 16. 1994
Figurel. Vinyl(C~H3)chemisorptianonadiamondC(11I)ledgesurface. The new radical site is denoted by the asterisk.
Ethylene (C,H,). The flow field calculations reported by Goodwin and Cavillets show that in some CVD experiments the gas-phase concentration of ethylene is sufficiently large for this species to account for the entire diamond growth rate provided its chemisorption rate is comparable to that for acetylene. However, our results show that this is not the case. After the investigation of 350 collision events, we observed only one chemisorption of the ethylene molecule. This result yields an estimated rate coefficient of (3.4 f 3.4) X IO6 cm3/(mol s). This is 5 orders of magnitude smaller than the corresponding rate coefficient for acetylene. Although the statistical error in the ethylene rate coefficient is large (.- lOO%), the upper limit is still too small to make C2H, a viable growth species. The above result is not surprising. The steric hindrance produced by the four ethylene hydrogens and planar structure of ethylenewould beexpected toexceed that expectedforacetylene. For ethylene to incorporate into the lattice, the double bond between carbon atoms must open. This is chemically similar to the process that acetylene must undergo. However, in the case of acetylene, it is a triple bond which must open. Our previously reportedcalcuIationsisshow that thepotential harrier foracetylene incorporation into the diamond lattice is only 0.48 kcal/mol. Similar calculations for ethylene yield a barrier of 1.94 kcal/ mol. The fact that our results for CHI insertion into ethylene suggest that thebarrier for ethyleneinwrporation into thelattice may betoosmall furthersupportsourconclusion that theethylene chemisorption rate is too small to make C2H1 a viable growth species. Vinyl Radical (CzH3). Unlike ethylene, the vinyl radical is capableofinitial incorporationinto thelattice without thenecessity of breaking a bond. Just as the ethynyl radical bonds to the surface uia the bare end of the radical, C2H3 undergoes the same typeofchemisorption. Computationof250collisionevents results in40chemisorptions, 11 ofwhich subsequentlydesorbed. Ofthe 29 events that led to bond formation, all hut two formed a single C,-Cbond with theradicalend. Theothertwo formed thesurface bond with the nonradical end, which means that the double bond in the vinyl radical broke during C,-C bond formation. One of these two events also resulted in a second C,-C bond forming via rotationofthe radical toenableit to bond with thesecond surface radicalsiteshown in Figure 1. Theresultingstructureisdepicted in Figure 7. Such an event is highly conducive to diamond-film growthsinceit naturallyproducesansplcarbonalongwithanew radical site for subsequent chemisorption events. However, the overall probability of this sequence of events is low. C&I [C=C=C-HI Radical. The flow field calculations reported by Goodwin and Cavillets indicate that the gas-phase concentration of the linear C=C=C-H radical is very small. However, since these investigators have examined its possible contribution to diamond-film formation, we have included it in the present study. Althoughthis radical is probably not important in diamond growth, the results of the calculations are interesting from a chemical point of view.
Perry and Raff The computation of 250 C3H collision events resulted in chemisorption in 53 cases of which subsequent desorption was observed in 16cases. Thecalculatedchemisorptionratecoefficient and desorption probability are (1.7 f 0.7) X IO1’ cm]/(mol s) and 0.30, respectively. Thus, in spite of the fact that the C3H radical has more possible sites for bond formation than either C’H, CH2, or C2H3 and would appear to be a more reactive chemical species, the C3H chemisorption rate is smaller than any of these other radical species, and its desorption probability is larger than those for CH2 and C2H3. Carbon AtomsandCluster?, C.(n= 1,2,3). Thechemisorption hehaviorofeachoftheC. (n= 1,2,3) specieshas been investigated by the computation of 250 collision events. Qualitatively, we find that the chemisorption rate coefficients decrease monotonically with increasing n while theassociateddesorption probabilities increase with n. C3 is about twice as likely to undergo chemisorption as C3H, but once chemisorbed, the desorption probabilities of the two speciesare nearly identical. Both C2and C have chemisorption rate coefficients that are larger than those for any of the other carbon-containing species investigated. The mostreactivespeciesisatomiccarbonwhich hasaratecoefficient equalto(9.7f 1.7)X 1012cm3/(mols)at1250K. Itsdesorption probability (0.16) is also smaller than that of any of the other carbon-containing species. Consequently, it is a highly reactive species. Since all hydrogen atoms have already been removed, it isan idealspecies for diamond-filmgrowth. However,if atomic carbon is the only growth species present, sp3 diamond growth may not be achieved. Yu et aL9have recently reported the results of plasma CVD experiments in which they show that both atomic carbon and CHI radicals can account for their observed growth rates, but not acetylene. In their analysis, they assumed a chemisorption probability of 0.1 for atomiccarbon. Our calculations show that when atomic carbon undergoes collision within a radius of 1 A of the radical site, the probability of chemisorption is actually 0.34. When desorption is taken into account, the probability of lattice incorporation is about 0.29. Thus, atomic carbon is even more favorable as a growth species than Yu et a1.9 suggest. It seemsvery likely that its deposition will be the principal pathway for diamond-film formation in plasma CVD experiments. Atomic Hydrogen (H). We have investigated the rates for hydrogen atom chemisorption on sp3 and sp2 carbon atoms. Chemisorption studies on sp3 carbon were carried out using the diamond-ledge structure shown in Figure 1. For sp2chemisorption, the resulting diamond structure once acetylene has incorporated into the lattice (see Figure 3) was used. Addition of a hydrogen atom to an sp2carbon is likely to be a critical component of diamond growth when acetylene chemisorption plays a major role. As we have shown, acetylene chemisorption almost always requires the formation of two C,-C bonds soas to avoid nearly immediatedesorption. Consequently, the chemisorbed moiety will be an ethylene structure containing two sp2 carbon atoms, each bonded to a single hydrogen atom. In order to continue the growth process from such a structure, one of two things must occur: either hydrogen atom abstraction from the spzcarbon must take place, or atomic hydrogen or some other radical species must add across the double bond to the sp2 carbon to form an sp3 carbon and a radical site at the second carbon. Frenklach and Wang‘ have previously referred to the latter process at sp’ sp3 conversion. Our previous studies of hydrogen atom abstraction processes” have shown that abstraction fromansp’carbon isassociated with an activation barrierof 23.8 kcal/mol. Therefore, if this is the path that must be followed to continuefilmgrowth,suchhydrogenatomabstractionwill become the rate-determining step in filament-assisted or combustion experiments. If, on the other hand, the sp’ sp3 process is facile, then the abstraction bottleneck can be avoided and
-
-
Reactions on a Diamond Ledge Surface mechanisms such as the one suggested by Belton and Harris6 become feasible. The results of our calculations are unequivocal. Hydrogen atom addition to both sp2 and sp3carbon atoms is very fast with rate coefficients of (1.6 f 0.5) X 1013 and (3.7 f 0.7) X 1013 cm3/(mol s), respectively. The corresponding desorption probabilities, 0.37 and 0.25, respectively, are sufficiently small that sp2 sp3 conversion is viable. We therefore conclude that our previous conjecture that hydrogen atom abstraction might be the rate-determining step in diamond-film growthls is incorrect. The slow process involving abstraction from sp2carbons can be easily avoided by the sp2 sp3 conversion pathway suggested by Frenklach and Wang.4
-
-
IV. Summary We have computed rate coefficients, event probabilities, and desorption probabilities for several elementary chemisorption reactions on a diamond-ledgestructure at 1250K. All calculations were performed using classicaltrajectory methods on the empirical hydrocarbonno. 1 potential hypersurface developed by Brenner.14 The chemisorbing molecules and radicals that have been investigated include C2H2, C2H, CH3, CH2, C2H4r CzH3, C, C2, CS,CSH,and H on sp2carbon and H on sp3carbon. A summary of all results can be found in Tables 2 and 3. We find that the chemisorption rates for nonradical species such as C2H2 and C2H4 are orders of magnitude smaller than the values obtained for radicals. For ethylene, the chemisorption rate is too small to permit C2H4 chemisorption to play a role in diamond-film formation in spite of the high gas-phase concentration of ethylenepresent in some experiments. Acetylene, however, has a chemisorption rate between 1 X 10" and 2 X 10" cm3/ (mol s) provided sufficient surface radical sites are available to permit two C,-C bonds to form. If, however, only one CrC bond forms, 97% of the chemisorbed acetylene desorbs within four C,-C vibrational periods. All of the radical species have chemisorption rates in the range of 10*2-1013cm3/(mols).Theleast reactiveoftheradicalspecies investigated is CH3. However, its high concentration in most CVD experiments makes it an important growth species. The chemisorption rate for C, (n = 1, 2, 3) is a monotonically decreasing function of n. The associated desorption probabilities increase as n increases. Atomic carbon has the largest chemisorption rate of all of the species investigated. Consequently, it is likely to be an important growth species in plasma experiments where its concentration is sufficiently high. Hydrogen atom addition to sp2 and sp3 carbons is found to be very fast with rate coefficients of 1.6 X 1013and 3.7 X 1013cm3/ (mol s), respectively. This finding removes the bottleneck that would exist if hydrogen atoms had to be extracted from sp2 carbon to propagate diamond-film growth. Xing and Scott*6 have recently reported a thermodynamictype Monte Carlo simulationof diamond-filmgrowth on a C( 111) substrate from acetylene,ethynyl, and hydrogen vapor deposition. In their calculation, Monte Carlo steps are accepted or rejected based on a Kawasaki29 algorithm computed using Brenner's14 potential. This is the first reported simulation that examines atom-by-atom growth of diamond films using acceptance/ rejection criteria based on an accurate potential energy surface. Their results show chemisorption to a C( 111) terrace is thermodynamically favored over bonding to a ledge structure. Consequently, ( n + 1)-layergrowth does not start until the n-layer growth is substantially advanced. While these Monte Carlo studies yield significant information related to the microscopic
The Journal of Physical Chemistry, Vol. 98, No. 16, 1994 4381 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. If, however, such calculations are carried out using acceptance/rejection criteria based on the rate coefficients reported here and in our previous studies,it will be possible to obtain an accurate temporal simulation of diamond-film formation.
Acknowledgment. We are pleased to acknowledge financial support from the National Science Foundation (Grant CHE921 1925),fromtheAir ForceOfficeofScientificResearch(Grant F49620-92-5-001 l), and from the Oklahoma State University Center for Energy Research. Many helpful discussions and cogent comments from Professor H. L. Scott and Dr. J. Xing are deeply appreciated and gratefully acknowledged. The authors also thank Mr. Dhandapani Subramanian for his assistance with the methylene radical calculations. References and Notes (1) Zhu, X. Y.; White, J. M. Surf. Sci. 1989, 214, 240. (2) Tsuda, M.; Nakajima, M.; Oikawa, S. J. Am. Chem. Soc. 1986,108, 5780. (3) Tsuda, M.; Nakajima, M.; Oikawa, S.Jpn. J. Appl. Phys. 1987,26, L527. (4) Frenklach, M.; Wang, H. Phys. Rev. B 1991,43 (2), 1520. (5) Huang, D.; Frenklach, M.; Maroncelli, M. J . Phys. Chem. 1988,92, 6379. (6) Belton, D. N.; Harris, S.J. J. Chem. Phys. 1992, 96, 2371. (7) Goodwin, D. G. Appl. Phys. Lett. 1991,59 (3), 277. (8) Goodwin, D. G.; Gavillet, G. G. J . Appl. Phys. 1990,68 (12), 6393. (9) (a) Yu, B. W.; Han, H.; Girshick, S. L. Proceedings 4th Annual Diamond Technology Workshop, Madison, Wisconsin, March 2425,1993. (b) Yu, B. W.; Han, H.; Girshick, S. L. Proceedings 11th International Symposium on Plasma Chemistry,Loughborough,England, Aug 22-27,1993, (10) Peploski, J.; Thompson, D. L.; Raff, L. M. J. Phys. Chem. 1992,96, 8539. (11) Harris, S. J.; Weiner, A. M.; Perry, T. A. Appl. Phys. Lett. 1988, 53, 1605. (12) Frenklach, M. J . Chem. Phys. 1992, 97, 5794. (13) Chang, X. Y.; Perry, M.; Peploski, J.; Thompson, D. L.; Raff, L. M. J . Chem. Phys. 1993,99,4748. (14) Brenner, D. W. Phys. Rev. B 1990, 42, 9458. (15) Chang, X. Y.; Thompson, D. L.; Raff, L. M. J . Phys. Chem. 1993, 97, 10112. (16) Xing, J.; Scott, H. L. Phys. Rev. B 1993, 48 (7), 4806. (17) Riley, M. E.; Coltrin, M. E.; Diestler, D. J. J. Chem. Phys. 1988,88, 5934. (18) Tersoff, J. Phys. Rev. Lett. 1986, 56, 632; Phys. Rev. B 1988, 37, 6991. (19) Liu, B.; Siegbahn, P. J. Chem. Phys. 1978,68. 2457. (20) Westbrook, C. K.; Warnatz, J.; Ptiz, W. J. Proceedings of the 22nd Symposium on Combustion; Combustion Institute: Seattle, 1988; p 893. (21) Brenner, D. W.; Tupper, K. J.; Harrison, J. A.; Dunlap, B. I. Hyperconjugation Subsurface Bonds, and the Energeticsof Radical Formation on Diamond Surfaces. (22) Chang, X. Y.; Thompson, D. L.; Raff, L. M. J. Chem. Phys. 1994, 100, 1765. (23) Melnik, S.California Instituteof Technology,private communication and unpublished results. (24) (a) Lide, D. R. CRC Handbook of Chemistry and Physics, 72nd ed.; CRC Press: Boca, Raton, FL, 1991. (bl Kerr, J. A.: Parsonage. M. J. Evaluated Kinetic Data on Gas Phase Reactions of Atoms and RadTcals with Alkanes,Alkynes, and Aromatic Compounds;Buttenvorths: London, England, 1972. (25) Raff, L. M.; Thompson, D. L. The Classical Trajectory Approach to Reactive Scattering. In Theory of Chemical Reaction Dynamics; Baer, M., Ed.;CRC Press: Boca Raton, FL, 1985; Vol. 111, p 1. (26) Raff, L. M. J. Chem. Phys. 1990, 93, 3160. (27) Shampine, L. F.; Gordon, M. K. Computer Solutions of ordinary Differential Equations, The Initial Value Problem; W. H. Freeman: San Francisco, 1975. (28) Garrison, B. J.; Dawnkaski, E. J.; Srivastava, D.; Brenner, D. W. Science 1992, 255, 835. (29) Kawa5aki.K. Phys.Rev. 1966,145,224. 1966,148,375. 1966,150, 285.
