J. Phys. Chem. 1992,96,9369-9376 The time evolution of the photoreflectance presented in Figure 5 demonstrates the longest limit of the lifetime of the hole is 2 ns. As the major reaction path is the corrosion which contains the atomic rearrangement of the surface, the rate-determining step is probably the surface movement of atoms. The estimated limit of the lifetime is strikingly short. The reaction rate of the photocorrosion is probably accelerated by the heat generation through the recombination process. Rcfwry No. CdS, 1306-23-6; Na$304, 7757-82-6; Na2S03,775783-7; CdO, 1306-19-0.
Re!fereacea and Notes (1) Lincot, D.; Vedel, J. J. Phys. Chem. 1988,92, 4103. (2) Prybyla, S.;Struvc, W. S.;Parkinson, B. A. J. Electrochem. Soc. 1984, 13i,isa7. (3) Freee Jr., K. W. J. Electrochem. Soc. 1983, 130, 28. (4) Mc Evoy, A. J.; Etman,M.;Memming, R. J. Elecrroanal. Chem. 19W, 190,225.
9369
(5) Etman, M. J. Phys. Chem. 1986,90, 1844. (6) Allongue, P.; Blonkowski, S.;Lincot, D. J. Electroanal. Chem. 1991, 300,261. (7) Nakabayashi, S.; Amemiya, T.; Kira, A. J . Phys. Chem. 1992, 96, 2272. ( 8 ) Nakabayashi, S.; Era, A. J. Phys. Chem. 1991, 95, 9961. (9) Shay, J. L. Phys. Rev. B 1970, 2, 803. (10) Kanata, T.; Sugawa, H.; Matunaga, M.;Takahra, H.; Hamakawa, Y.; Kato, H.; Nishino, T. Phys. Rev.B 1990,41,2936. (1 1) Pankove, J. 1. Optical Processes in Semiconductors; Dover Publications: New York, 1971; Chapter 3. (12) Aspens, D. E. Phys. Rev.Lett. 1972, 28,913. (13) Cardona, M.Modulation Spectroscopy; Solid States Physics S u p plement 11; Seitz, M., Turnbull, D., Ehrcnreich, H.,Eds.; Academic Press: New York, 1969. (14) Reeves, H. M.; Cocivera, M. J . Elecfrochem. Soc. 1984,131,2042. (15) Ferrer, I. J.; Salvador, P. Ber. Bunsen-Ges. Phys. Chem. 1987, 91, 374. (16) Inoue, T.; Watanabe, T.; Fujishima, A.; Honda, K.; Kobayakawa, K. J. Electrochem. Soc. 1977, 124, 719. (17) Ancdda, A,; Fortin, E. Phys. Status. Solidi A 1976, 36, 385.
A Theoretical Study of Growth Mechanisms of the (110) Surface of Diamond from Acetylene and Hydrogen Mixtures Brent H.Besler, William L. Haw,* Department of Chemistry, Wayne State University, Detroit, Michigan 48202
and Kenneth C. Hass Research Staff. Ford Motor Company, Dearborn, Michigan 48121-2053 (Received: January IO, 1992)
Possible mechanisms for the growth of the (110)surface of diamond by chemical vapor deposition (CVD) from an acetylene carbon source are examined by MNDO and PM3 semiempiricalquantum mechanical calculations. A large model compound is shown to be necessary to obtain reasonable convergence. Growth is assumed to proceed via addition of neutral acetylene molecules to radical sites on the surface which are made available by H atom abstraction by gas-phase hydrogen atoms. A multistep reaction pathway is investigated whereby the added C2H2 forms either an ethylene-like or an ethyl radical-like species attached to the diamond surface by two single carbon-carbon bonds. The various ways in which any two of these species, adjacent to one another, may d t e to produce net s$ growth are also examined. The amciation of a third t w w h species in this manner makes the growth essentially irreversible. The relationship of the present study to previously proposed mechanisms for CVD growth of (1 10)diamond by acetylene addition is diricussed. AU such mechanisms are shown to produe locally oriented growth which implies much higher defect densities in the resulting films than are observed exprimentalty. This inconsistency may be reconciled if some one-carbon species are also incorporated during growth and/or if any of the twwarbon species have a high surface mobility. A critical evaluation of the semiempirical methods is made by comparing theoretical and experimental energetics for a number of known carbon-based radical reactions.
I. Iatroduction Diamond films grown by low-pressurechemical vapor deposition (CVD) have potential for use in a wide variety of commercial applications such as machine tool and optical coatings and high-temperature electronics.'-4 The films exhibit many of the same characteristics as single-crystal bulk diamonds including extreme hardness and high thermal amductivity. One of the most attractive featurea of the CVD process is its ability to deposit f h on a variety of dissimilar substrates. Such films are generally polycrystalline. Efforts are also currently underway to grow large-area, single-crystal diamond films by CVD? although, to date, this has only been possible on preexisting diamonds.' Diamond is a cubic crystal with three low-index faces: (1 lo), (1 1 l), and (100)(see Figure 1). Upon examination by scanning electron microscopy, only the (100)and (1 11) faces are found to occur commonly in polycrystalline diamond films.'-" Which of these two f a a s predominates depends upon the experimental ~ ~ n d i tThe i ~ slowest ~ . growing face will be the predominant one. Since the (1 10)face is seldom found, except in the case of growth on a preexisting (1 10)diamond substrate, it is the most rapidly
0022-365419212096-9369SO3 .OO/O
growing. Although experimental measurements of the relative growth rates of the different surfaces are difficult, the relative growth rates of the three surfaces were found to be (l~):(lll):(llO) = 1.01.4:5.2byGeis6and 1.01.3:3.3by Chu et ala8 The Geis study involved boron-doped films in which the dopant may alter the relative growth rates of the different faas. It is likely that different mechanisms are responsible for growth on the three different faces due to differing growth rates and geometries at the molecular level. Of the three, the (1 10) surface will likely have the lowest potential energy barriers to growth, although other factors such as the rates of etching of newly deposited diamond on the different surfaces may play a role. Using an isotopically labeled hydrocarbon feed gas, Chu et aI.8 concluded
thatthemethylradicalistheprincipalgrowthspeciesforthe(ll1) and (100) surfaces. However, they were unable to draw any conclusions concerning the growth species for the (1 10) surface. The growth species (carbon source) responsible for film deposition is the subject of much recent experimental work.*I2 Experimental evidence suggests that CH,' and/or C2Hz are the important growth species. It has not been conclusively shown that Q 1992 American Chemical Society
Besler et al.
9370 The Journal of Physical Chemistry, Vol. 96, No. 23, 1992
TABLE I: Comparison of Semiempirical and Experimental Bond Dissociation Enthalpies“ MNDO PM3 bond UHF CIb UHF CIb exptC H CH3 88.7 90.6 93.1 94.8 105 H + t-C,H, 68.7 71.3 72.3 68.1 93 70.5 74.1 76.8 90 CH3 + CH3 69.0 CH3 C2H5 60.1 62.7 66.1 70.1 88 CH3 + t-CdH, 38.3 41.9 54.2 58.7 84
+
+
“All enthalpies in all tables are given in kcal/mol. bThis is a 3 X 3 CI calculation as discussed in section 11. cThe experimental bond dissociation energies are from ref 35.
Figure 1. Cutaway of bulk diamond showing hydrogens on the surface. Relative positions of the (Til), (loo), and (1 10) faces are shown. The view is along a (1TO) direction.
either species alone is responsible for film growth on any of the three surfaces. Both species may be involved in the growth mechanism of a particular surface.12 Knowledge of the fundamental growth mechanism of diamond films at the molecular level may provide insight into ways to improve growth. In conjunction with macroscopic kinetics/ transport simulations such as that of Frenklach and Wang,13 modifications to deposition techniques and gas mixtures may be suggested and tested via computer simulation. A number of research groups have examined possible diamond growth mechanisms at the molecular level using quantum mechanical techniques. Tsuda et al.14 published the first semiempirical study of a possible growth mechanism using Dewar’s MIND0/315 technique. In this study a mechanism based on the addition of CH3+ to the (1 11) surface was considered. Huang and Frenklach have published a number of studies using the MNDO method16-18to investigate mechanisms based upon addition of CH3 or C2Hzto the (1 11) or (100) surfaces. Valone et al.9 examined a CH3 mechanism for the (1 11) surface with the AM1 method20 of Dewar. Deak, Giber, and Oechsner21 performed an MINDO/3 study of another CH3addition mechanism for the (1 11) surface. Using the ASED-MO semiempirical technique, Mehandru and Anderson22studied the absorption and migration of H, CH3,CH2, and C2H2on a diamond (1 11) surface. Mintmire et al.23and Pederson, Jackson, and P i ~ k e tinvestigated t~~ the binding of various one- and two-carbon species to the (1 11) surface using density functional techniques. Page and Brenner25 used a multiconfiguration ab initio self-consistent-field (MCSCF) calculation to study the abstraction of an H atom from isobutane as a model for H atom abstraction from a diamond surface. Very recently, Belton and Harris26have proposed growth mechanisms for all three surfaces of diamond. They examined the free energies of their proposed mechanisms using a group additivity technique, along with corrections for strain. In this work we investigate C2H2reactions on the (110) surface using semiempirical quantum mechanical calculations. In section I1 of this paper the computational method is described. Calculations of different C2H2-basedreactions participating in (1 10) surface growth are presented and discussed in section 111. Different mechanisms for C2H2growth of the (1 10) surface are surveyed in section IV. The paper concludes with a summary in section V.
II. Computational Method Due to the size of the system necessary to provide a realistic model of a diamond crystal, the MND027 and PM328 semiempirical quantum mechanical methods of Dewar and Stewart were used, rather than an ab initio or density functional treatment. The PM3 method uses the same Hamiltonian as MNDO but uses a much larger database of compounds in the parametrization, in addition to a better fitting algorithm for the parameters.28 The
TABLE Ik Comparison of Semiempirical and Experimental Radical Enthalpies of Formation (in kcal/mol) radicalb MNDO“ PM3“ exptc 24.6, 25.8 28.0, 29.8 34.8 CH3 14.5, 17.3 28.0 C2H5 10.6, 12.8 9.2, 12.0 22.8 C3H7 5.2, 7.6 t-C,H, -10.2, -7.0 -9.4, -6.0 9.0 “The first number is a UHF calculation; the second is a half-electron calculation (see section 11). bBoth PM3 and MNDO have a parametrization such that the calculated AHf for the H atom equals the experimental value of 52.10 kcal/mol. Experimental heats for formation are from ref 35.
PM3 method was used for most of the calculations in this study as it is found to have a much lower average deviation from experimental values in the calculated heats of formation of molecules containing only hydrogen and carbon than the MNDO method.29 PM3 molecular geometries are also in better agreement with experiment than those determined with MND0.29 The Mopac 6.0 code of Stewart30was used for all calculations. All geometry and transition-state optimizations were carried out using the eigenvector following algorithm of Baker3’as implemented in Mopac 6.0. However, as in the case of the studies of Huang and Frenklach,16*17we sometimes encountered difficulty in the optimization of transition-state (TS) structures. In these cases, we fmed the distance between two atoms which are forming a bond or breaking a bond and optimized the position of the rest of the atoms, except those in the fixed “backbone”. The energy was then plotted as a function of this fixed distance and the TS energy determined from that plot. Transition states determined in this manner are clearly identified in the following presentation. Open-shell systems with a single unpaired electron were treated using both the unrestricted Hartree-Fock (UHF)32and halfelectron33methods. The UHF method frequently encountered problems with spin ~ontamination,~~ and thus the half-electron method was used for all calculations reported in this study. Biradicals and systems with biradical character were treated with small configuration interaction (CI) calculations which involved only those configurations which include HOMO-LUMO excitations. The MNDO and PM3 methods calculate heats of formation of compounds at 298 K, rather than 0 K total energies as is the case for ab initio and density functional methods. Also, reaction barriers calculated at 298 K are enthalpy barriers instead of potential energy barriers. To assess the accuracy of the semiempirical methods, barriers and heats of reaction were calculated for several known carbonbased radical to complement previous semiempirical work for such reactions.m2 Theoretical and experimental C-H and C-C bond dissociation energies are listed in Table I. Overall, the PM3 enthalpies are in better agreement with experiment than are the MNDO enthalpies and, for both theoretical methods, including CI tends to improve ‘theagreement. However, the overall agreement between theory and experiment is at best modest. The PM3/CI bond dissociation enthalpies for H + t-C4H9and CH3 + t-C4H9are each too low by 25 kcal/mol. As shown in Table 11, the semiempirical methods give inaccurate radical heats of formation, which may contribute to the errors in the calculated bond dissociation enthalpies. At a more fundamental level the
Growth Mechanisms of the (1 10) Diamond Surface
TABLE IIk
The Journal of Physical Chemistry, Vol. 96, No. 23, 1992 9371
Compdsoa of !Semiempirid lad TlworLticrl Ac~vatkmEnergies and Heats of Reaction for Radical Addition Reactiolll,
(io kc8l/mol)
heats of reaction" reactionb
MNDO -51.0, -51.0, -33.1, -34.8, -24.6, -25.3, -3.1, -2.3,
-46.2 -54.1 -29.9 -33.6 -21.6 -25.1 -10.8 -3.1
PM3 -45.0, -39.5 -54.2, -51.4 -29.3, -25.6 -35.4, -34.3 -21.2, -18.3 -26.3, -26.2 -7.8, -4.6 -13.0, -13.5
expt -40.3 -36.5 -30.5 -24.4 -24.0 -22.1 -18.1 -18.1
MNDO 3.0, 1.7 2.4, 1.2 16.5, 22.6 13.1, 22.9 20.8, 26.1 11.1, 26.0 32.6, 31.3 30.1, 31.9
activation energies" PM3 exut 0.0, 0.0 0.0, 0.0 8.0, 25.8 4.0, 10.3 11.8, 15.5 1.0, 12.8 19.3, 22.9 14.4, 19.1
2.1 2.2 1.7 7.3 4.1 1.3 5.3 1.1
rep 39 39 31 31 36 36 36 36
"The first number listed under MNDO and PM3 is a UHF calculation; the second a half-electron calculation (see section 11). The PM3 heats of reaction were determined by treating the bimolecular reactants semrately. bThe experimental heats of reaction were taken from refs 35 and 36. 'These are the references td the experimental activation energies. errors in the UHF bond energies can be attributed to serious spin contamination as bond rupture occurs. Initially, the UHF dissociation takes place on a singlet potential surface, but the total wave function for the dissociated products is a triplet. Though the CI calculation corrects the spin problem, it does not significantly affect the bond enthalpies. Semiempiricaland experimentalheats of reaction and activation energies for H, CH3, C2HS,and t-C4H9addition to C2H2and C2& are listed in Table 111. The first step in finding the activation energy was to calculate the potential energy as a function of the length of the forming bond with all other coordinates optimized. If the potential was not purely attractive and had a maximum, a true transition state and activation energy were found by starting at the maximum energy point and using the eigenvector following algorithm of Baker.31 It is of interest to note that the potential energy of this maximum was less than 1 kcal/mol higher than the true transition-state energy for all radical addition reactions in Table 111. Except for H C2H4 and t-C,Hg C2H2,the agreement between the PM3 and experimental heats of reaction is respectable. However, the activation energies are another matter. There is no consistency in the PM3/UHF activation energies. Some are zero, while others are large. For the reactions other than H + C2H2and H C2H4, the PM3/half-electron method overestimates all the activation energies with the error particularly severe for the radical additions to C2H2. In summarizing the results in Tables 1-111, one sees that PM3 gives better agreement with experiment than does MNDO. However, overall the agreement is only qualitative. The PM3 bond dissociation enthalpies in Table I differ from experiment by as much as 25 kcal/mol. The agreement between theory and experiment is better for the radical addition heats of reaction in Table 111. However, the substantial difference between the theoretical and experimental activation energies for these reactions is disappointing. Finally, the difference between the MNDO and PM3 energies in Tables 1-111 is a result of different parametrizations involving simple molecules. For example, the MNDO and PM3 heats of formation for H2 are 0.7 and -13.4 kcal/mol, respectively. Consequently, PM3 overestimates the bond strength of H2as 117.6 kcal/ mol. An appropriate model compound for a diamond surface must have the same basic structure as the surface and include a sufficient amount of the bulk lattice to avoid "edge" effects, Le., effects of the finite size of the model on computational results. Bulk diamond consists of carbon atoms arranged in six-membered rings similar in structure to the 'chair" form of cyclohexane. Models used in this and other published studies may be classified by the number of such rings incorporated into the model. All published studies so far have terminated "dangling" bonds with hydrogens. In the case of models for CVD diamond film growth, covering the surface of the model with hydrogen atoms is particularly relevant to experimental deposition conditions, namely, the high impact rate of atomic hydrogen with the film surface. For this study, we chose models for the (1 10) surface consisting 2, 3, 5, 7, and 11 rings with "dangling" bonds terminated by hydrogens (Figure 2). The molecular formulas for the models are CIOHIE,C13H22r C d h C25H38, and C37H9, respectively. The
+
h
2 Ring Model 3 Ring Model
+
5 Ring Model
7 Ring Model
+
Figure 2. Model compounds used for the computational studies.
geometries of the model systems were completely optimized to remove any strain. For all other calculations involving the given model, the ring "backbone" structure was constrained at the optimized geometry to simulate the rigid nature of a bulk diamond crystal. The resulting geometries are very similar to that of bulk diamond. Some test calculations were done in which complete optimization of the ring "backbone" was allowed for reactions between C2H2and the ring models. The "backbone" structures were found to buckle into structures which no longer resembled the structure of the (1 10) surface. To avoid such buckling, very large models are required. If complete geometry optimization were to be performed for a reaction between a gaseous species and a proper model for the surface, one would find so"relaxation of the model's geometry in the vicinity of its reactive site but no relaxation at the model's periphery. This is the behavior expected for bulk diamond. For all the models considered here, including the eleven-ring C3,H9 model, all the atoms relaxed when amplete optimization was performed for reaction on the model's surface. Thus, constraining the positions of some atoms, while optimizing the positions of others, would only introduce ambiguities into the calculations. Therefore, for all calculations involving reactions between the ring models and other species, the ring "backbone" structure was constrained at its optimized geometry to simulate the rigid nature of a bulk diamond crystal.
9372 The Journal of Physical Chemistry, Vol. 96, No. 23, 1992
Besler et al.
TABLE rV: PM3 EntMpka of RmcctiOa v e m a Modd Sizd
TABLE V: PM3 d MNDO He& of R e s c t h for the SercbRhg
(la kul/mol)
Model (bkal/md) reaction4 C2H2addition (4) surf. radical recombination (5) surf. H abstraction (6) surf. radical insertion (7) C-H homolysis (8) H abstraction (9)
no. of rings 2 3 5 7 11
reaction 2 -15.4 -16.4 -17.4 -14.3 -18.8
reaction 1 -21.9 -24.3 -24.5 -24.5 -25.2
reaction 3 -39.3 -33.9 -26.1 -25.5 -31.2
“The calculations for reaction 1 used the half-electron method.
Semitivity ofR& lheqetics to the Sizeof the Rhg Madel To determine how the size of the ring model affects the heat of reaction, PM3 calculations were performed for the following three overall reactions:
I
Cd
I + I
2 d:(
:d)
+
+ H*
X2H2
-
-
H2 + Cd*
2H2 + 2
H,
,c=c,
Cd
+4.8 -59.1 -16.8 -11.6 +51.3 -52.2
AH(PM3) -1 -63.5 -11.7 -18.9 +52.1
w
-65.5
#Reactions are given in the text. All radical calculations used the half-electron method.
III. Computationrl Results and Discussion
H
AH(MND0)
(1)
for the (1 11) surface and performed high-level MCSCF ab initio calculatiw for abstmtion of the isobutane tertiary hydrogen atom by an H atom. They found a barrier of 9.0 kcal/mol and an exothermicity of 3.0 kcal/mol. When all of the isobutane atoms were allowed to fully relax, the barrier lowered to 7.3 kcal/mol and the exothermicity increased to 8.4 kcal/mol. The initial step in an acetylenebaed growth mechanism is the addition of a single CzHzmolecule to a radical site on the diamond surface, i.e.
H , (3) cd
In these reactions, Cd represents a carbon in the ring model and Cd’ represents such a carbon with a hydrogen atom removed. Reaction 1 is the abstraction of an H atom in the ChaMel of the (1 10) surface (see Figures 1 and 2). Reaction 2 is the addition of an acetylene molecule across this channel. Reaction 3 is the same as reaction 2, except two acetylene molecules are added adjacently and in parallel. The calculated heats of reaction as a function of the number of rings in the model are listed in Table IV. In all cases, the reactive sites were taken to be as far away from the ends of the channel as possible. The heats of reaction are in approximate agreement for the seven- and eleven-ring models, and thus, unless otherwise stated, the seven-ring model is used in the following calculations. The origin of the dependence of the heat of reaction on model size is not clear. For reaction 1, the H atom abstracted is a secondary hydrogen for the two-ring model, but a tertiary hydrogen for the three- to eleven-ring model. For reaction 2 acetylene adds to two secondary carbons for the two-ring model, a secondary and a tertiary carbon for the three-ring model, and two tertiary carbons for the five- to eleven-ring models. For reaction 3, all four carbon atoms are secondary for the two-ring model and tertiary for the seven- and eleven-ring models. The carbon atoms are both secondary and tertiary for the three- and five-ring models. The calculated dependence of the heats of reaction on model size does not appear to be related to the secondary or tertiary character of the carbon atoms. This is also illustrated by considering theoocumnce of reaction 2 at both mndaryand tertiary sites on the seven-ring model. The resulting heats of reaction are -23.0,-13.1, and -14.3,if the two Cd-H bonds are secondary, secondary and tertiary, and tertiary,qmtively. There is no clear trend between the heat of reaction and whether the Cd-H bonds are secondary or tertiary. We suspect that the strain in the reaction products partially explains the heats of reaction versus model size. However, as discussed in section 11, determining whether this is indeed thecase will require the use of larger models so that complete geometry optimization of the products will relax the geometry in the vicinity of the reaction site but not affect the geometry of the periphery of the model. Reactions for Adding a C2H2Molecule to the (1 10) Surface. All growth mechanisms p r o p o d to date agree that the creation of radical sites on the diamond surface via the abstraction of surface H atoms by gas-phase H atoms is necessary to activate the surface for addition of carbon-containing species. To obtain a reliable theoretical estimate of the potential energy barrier for such a process, Page and BrennerZsused a rigid isobutane model
If a gas-phase H atom abstracts an H atom from a carbon on the oppusite side of the channel on the (1 10) surface, the vinyl-like radical in reaction 4 can associate with the surface to give a bridged twocarbon (ethylenalike) species attached to the surface by two carbon-rbon single bonds; i.e.
There are alternative reactions for forming this ethylene-like species. The vinyl radical in reaction 4 may abstract a nearby H atom on the opposite side of the (1 10) face:
H
I Cd
The resulting surface radical may then undergo an addition reaction to the double bond of the dangling ethylene, leading to a radical held to the surface by two carbon-carbon single bonds: (7)
Ed
There are two possible pathways for conversion of the product radical of reaction 7 into the ethylene-like species which is held to the surface by two bonds. One is the homolysis of a C-H bond
The other is the abstraction of an H atom by a gas-phase atomic H:
An alternative pathway for formation of the product radical in reaction 7 is the addition of an atomic H to an ethylene-like species doubly bonded to the surface, i.e., the reverse of reaction 8. Under normal depaeition conditions, the flux of H atoms incident upon the diamond film surface will be much greater than that of carbon-containing sya. Using a thermodynamic model, Sommer, Mui, and Smith‘ estimated the H atom flux rate to be 5.22 X lezatoms cnr2 s-’ and the flux of carbon-containing species to be 2.64 X 1020 C atoms s-l. The temperature and
Growth Mechanisms of the (1 10) Diamond Surface partial pressures of the deposition gases for which these rates are calculated are not specified. The high H atom flux and the low activation barrier for addition of H atoms species with carbon multiple bond^^^.^ (e.g., 2.2 kcal/m\31 for ethylene and 2.7 kcal/mol for acetylene) will also likely result in H atom addition to the *-bonds of C-C multiply bonded species on the surface. In Table V, the 298 K heats of reaction calculated with the MNDO and PM3 methods are compared for reactions 4-9 on the seven-ring model. The most substantial difference between the PM3 and MNDO AH'Sis for reaction 4. The reliability of the calculated LWS for reactions 4-9 can be assessed by comparing experimental and theoretical AH'S in Tables I and I11 for similar reactions. Reaction 8 is similar to the conversion of ethyl radical into ethylene by C-H bond homolysis, which has an experimental potential energy barrier of 36.5 kcal/mol at 300 K.35+45 As shown in Table 111, C-H bond homolysis in the ethyl radical is found to have an endothermicity in the range 51-57 kcal/mol with MNDO and PM3. Reaction 9 will likely have a lower bamer than that of an H atom abstraction from a neutral alkane (approximately 13 kcal/mol).* To illustrate, the reaction H f CzHs Hz C2H4 is experimentally found to be barrierle~s.4~ This reaction is barrierless with both half-electron MNDO and PM3 methods, while the exothermicities are 48.9 and 66.2, respectively. The 298 K enthalpy barrier for reaction 4, addition of acetylene to a radical site on the (1 10) surface, was calculated to be 67.8 kcal/mol with MNDO for the seven-ring model. A frequency calculation was performed on the TS geometry to verify that it had only one imaginary frequency whose normal model corresponds to formation of the surfaceacetylene carbon-bon bond. The calculation of the TS was repeated, allowing the five surface H atoms nearest the radical site to relax their positions. This only lowered the barrier by 2 kcal/mol. Huang, Frenklach, and MaroncelliI6report a barrierless addition mechanism for acetylene to a radical site using MNDO. However, this process was not straightforward addition of acetylene to form a vinyl radical by a single step but rather a multistep process leading directly to formation of the sp3ethyl-like radical in reaction 7. Bond lengths and angles were optimized at various stages of the reaction, and the absence of a barrier was attributed to the lack of rigidity of the part of the surface where the reaction takes place. In their later study of the growth on the (100) surface using MNDO, Huang and FrenklachI8report high addition barriers to a number of tertiary radical sites, depending on radical site geometry. Their lowest bamer for addition of acetylene to any single radical site was approximately 40 kcal/mol. The substantial barriers found in this latter study were attributed to increased rigidity of the suface in the vicinity of the reaction site. Addition of C2Hzto a tertiary radical site on the seven-ring model has a true PM3/half-electron transition state with a potential bamer of 13.6 kcal/mol. The results in Table I11 indicate that PM3 consistently overestimates radical addition barrier heights. The experimental bamers are 7.7 and 5.3 kcal/mol for and rerr-butyl radical3*addition to acetylene, mpectively. There is no reason to expect the experimental barrier for acetylene addition to a tertiary carbon site on the (1 10) surface to be smaller than the experimental barrier for acetylene addition to the rertbutyl radical. Association of Adjacent Ethylemlike Species on the (110) sllrhce. A set of calculations was performed to determine whether a series of C2H2molecules, deposited adjacently across the channel of the (1 10) surface, transform spontaneously from a sp2 to sp3 configuration. Consideration of this problem was stimulated by analogous sp2 sp3 conversion from bulk H-6 carbon to diamond." For two adjacent ethylene-likespecies,the transformation forms a singlet biradical:
-
+
-
PM3 and MNDO calculations for reaction 10 on the three, seven-,
The Journal of Physical Chemistry, Vol. 96, No.23, 1992 9373 TABLE VI. Heab of Ructioa and Earthrlpr Men (IrerVmOl) for A s ~ ~ c h t i oofa Adjacent E t h y b l i k e spcdcr (Rcrctiolr 10) ~~
method and model 3-ring (PM3)' 7-ring (PM3) 1 1-ring (PM3) 7-ring (MNDO)
heat of reaction +14.0 -8.6 -9.0 -16.1
bamer 20.5 4.7 4.2 8.2
'A 3 X 3 CI is used for all calculations in this table. TABLE W: Energies (kul/mOl) for the c.S-Phrse Ethylene E t h v b S i t Tetrrmethylene Reaction theory heat of reaction bamer MCSCF/STO-3G 26.2 36.7 MCSCFj4-3 lG* 51.3 51.7 MCSCF/6-31G* 46.4 46.4 PM3' 17.8 30.7 MNDW 12.2 37.6
+
+
~~~~~~
~
"A 3
X
3 CI is used for this calculation.
and eleven-ring models were performed using a 3 X 3 CI calculation.@ This is necessary to describe properly the electronic staalong the curves. All coordinates of the two ethylene species were optimized versus C 4 distance in the calculations. The transition state was assumed to be the highest potential energy point on the curve. Based on calculations reviewed in section 11, the resulting bamers are expected to be too high by less than 1 kcal/mol. (It was not possible to converge to the true transition state with the eigenvector following algorithm,31presumably because of the flatness of the potential in the vicinity of the transition state and the dimensionality of the coordinate space.) The reaction was simulated on the centermost sites of the three-, seven-, and eleven-ring models. All the Cd atoms directly involved in the reaction are tertiary sites for the seven- and eleven-ring models. Listed in Table VI are the enthalpy barriers and heats of reaction calculated for reaction 10. There is a large difference between the energies for the three-ring model and those for the seven- and eleven-ring models. The apparent convergence of these enerBies for the seven- and eleven-ring models is similar to that observed for reactions 1-3, see Table IV. As the ring "backbonemis enlarged, the enthalpy barrier decreases from 20.5 to 4.2 kcal/mol with the PM3 method. The conversion also goes from being endothermic to slightly exothermic. The MNDO result for a seven-ring model has a slightly higher enthalpy barrier and is slightly more exothermic. The gas-phase association of two ethylenes to form singlet tetramethylene has been studied using ab initio MCSCF techNques." The results of these calculations are listed in Table VII. The agreement between the results for the 431G and 6-31G* basis sets is indicative of convergence with an endothermicity of 46.4 kcal/mol and no barrier for tetramethylene dissociation. As shown in Table VII, when the same reaction is studied using the PM3 semiempiricaltechnique with 3 X 3 CI, it is found that there is a 30.7 kcal/mol enthalpy barrier and an endothermicityof 17.8 kcal/mol. MNDO with 3 X 3 CI finds an enthalpy barrier of 37.6 kcal/mol and an endothermicity of 12.2 kcal/mol. (True transition states were found in these PM3 and MNDO calculations.) Comparison of the ab initio and semiempirical barriers in Table VI1 for the gas-phase analog of reaction 10 indicata that the PM3 semiempirical method underestimates AH by 30-35 kcal/mol and the barrier height by 10-15 kcal/mol. If these erron carry over to the calculation of ethylene-like species association on the (110) surface, the actual heat of reaction is not exothermic as indicated in Table VI, but slightly endothermic. A large amount of strain energy is associated with ethylenalike species bound to the diamond surface, as for the reactants in reaction 10. The Cd-C-C and torsion angles for the ethylene-like species are 123.5" and 20.3", respectively (as determined from the eleven-ring model with a single ethylenelike species at the optimized geometry). In contrast, for cis-2-butene theae angles are 124.0" and 0.0°.50 Conversion to the biradical relieves such
9374 The Journal of Physical Chemistry, Vol. 96, No. 23, 1992 TABLE VIIk Huts of R u c t h rad Eathrlpy Barriers (kd/mol) for Association of Adjacent TwoCuboll Species method and model heat of reaction barrier Reaction 11 3-ring (PM3) -23.7 5.4 7-ring (PM3) -33.9 0.0 Reaction 12
7-ring (PM3)O
-65.7
0.0
'A 3 X 3 CI is used for this calculation.
strain. This is most likely the origin of the less endothermic heat of reaction for reaction 10 on the surface than in the gas phase. For three adjacent ethylene-like species converting in a concerted reaction to a singlet biradical on a five-ring 'backbone", the conversion is barrierless and exothermic by approximately 70 kcal/mol with PM3. Due to the computational expense, calculations were carried out near the TS C-C bond length of 2.2 A (for the five-ring model) with the eleven-ring 'backbone". (As described above for the two ethylenelike species, the TS was taken as the maximum in the potential energy curve versus C-C bond length.) The resulting enthalpy barrier is approximately 8 kcal/mol, and the exothermicity is approximately 50 kcal/mol. The association of three ethylenelike species is energetically more favorable than the association of only two (Table VI). This can be interpreted by considering the association of the three ethylene-like species in two steps: (1) the association of two adjacent ethylenelike species to form the tetramethylene biradical and (2) addition of this biradical to the C = C double bond of the third ethylene-like species. Since this last step is exothermic, the association of three ethylene-like species will be more exothermic than two. The strain energy associated with the third ethylenelike species will further enhance the exothermicity of the three species' association. For the same reasons, association of four or more of the ethylene-like species will be even more exothermic but need not be considered since three readily associate. Benson's method" was used to calculate L1s for the association of two adjacent ethylene-like species on the (1 10) surface. These calculations show that at 1000 K entropy favors the singlet biradical by 9 kcal/mol for two ethylene-like species and 18 kcal/mol for three ethylene-like species. To illustrate this effect, consider reaction 10 in an equilibrium environment and endothermic by either 10 or -20 kcal/mol. If the entropy effect is included at 1000 K, 50% and 1% of adjacent ethylene-like species will convert to the singlet biradical, respectively, for these two endothermicities. Ilrdicrl Rerctioa4 for the AssociPtioa of Adjacent Two-Carbon Species on the (110) Surface. In reaction 10, the association of two ethylenelike species results in sp3 growth on the diamond surface. There are also radical reactions of adjacent two-carbon species which yield sp3 growth. The radical formed in reaction 7 can add to an adjacent ethylene-like species:
-
H
Besler et al.
A PM3 3 X 3 CI calculation shows this reaction to be bamerless and have an exothermicity of 65.7 kcal/mol (Table VIII). For comparison, the experimental C-C bond enthalpy for a secondary-secondary carbon-carbon bond is approximately 86 kcal/ mo1.35-53The comparisons in Table I show that PM3 underestimates C-C bond enthalpies.
IV. Survey of C2H2 Growth MeebPnisms of the (110) Surface The discussion in the previous sections considers multiple mechanisms for attaching CzHzto the (110) surface, Le., reactions 4-9. The resulting two-carbon species held to the surface via two carbon-carbon single bonds can be either an ethylene or an ethyl radical-like species. If two of these species are adjacent, they can associate to form a sp3 structure. This association can be (i) concerted for two ethylenelike species, reaction 10; (ii) an addition for ethylene and ethyl radical-like species, reaction 11; and (iii) a recombination for two ethyl radical-like species, reaction 12. Since gas-phase hydrogen atoms are continually bombarding the surface, adding to double bonds, abstracting H atoms, and closing off radical sites, interconversion between the ethylene and ethyl radical-like species is expected when these species are either isolated on the surface or if only two are adjacent. However, once a third two-carbon species participates in the association, the sp2 sp3 conversion becomes nearly irreversible. Harris and Belton26bhave proposed a mechanism for (1 10) surface growth which is a subset of the reactions considered in the previous section. Adjacent ethylene-like species are assumed to be formed by two Occurrences of reactions 4 and 5 at four adjacent radical sites. A gas-phase H atom then adds to one of the C-C double bonds and growth Occurs by reaction 11. This mechanism requires five gas-phase hydrogen atoms: four to abstract H atoms from the surface to form radical sites and one to add to the C-C double bond. For comparison, sp3growth by the addition of an ethyl radical-like species (formed by reactions 4, 6, and 7) to the ethylene-like species (formed by reactions 4,6, 7, and 9) requires only three gas-phase hydrogen atoms. Frenklach and Spear54 and Huang, Frenklach, and Maroncelli16 have proposed a sp3 growth mechanism at a step on an infinite (1 11) plane of diamond. However, since the carbon atoms at this step have an orientation like those on the (1 10) surface, their mechanism is also relevant for growth of the (1 10) surface. The first step of the mechanism is the formation of an ethyl radical-like species as given by reactions 4,6, and 7. A gas-phase acetylene molecule then adds to this radical site. The resulting radical then abstracts an H atom from the surface as in reaction 6, and the resulting two-carbon species adds to the radical site on the surface as in reaction 7 to give the structure
-
.
I Cd
PM3/half-electron calculations for this reaction (Table VIII) show it to be bamerless and highly exothermic (-33.9 kcal/mol for the seven-ring model). For reaction 11, the heat of reaction is less exothermic with the three-ring model than with the seven-ring model (Table VIII). Table VI shows a similar result for reaction 10. The analogous addition reaction of ethyl radical to cis-2butene has an experimental barrier of 8.5 kcal/mol and is exothermic by 23.7 k c a l / m ~ l . ~ ~ If two adjacent ethyl-like radicals have the proper configuration, the radicals will recombine:
By analogy with experimental work by Tabayshi and BauerSsin the gas phase, the Cd-H bond is assumed to break and a C-Cd bond formed in a concerted manner to give the final structure U
This mechanism has been criticized by Harris and BeltorPb for its large entropy reduction. However, there is some uncertainty in using equilibrium thermodynamic arguments to analyze a
Growth Mechanisms of the (1 10) Diamond Surface
The Journal of Physical Chemistry, Vol. 96, No. 23, 1992 9375 is expected to involve a TS with less strain, which should lower the barrier. Conversely, the 1,3 carbon-carbon distance will be greater than a 1,2 carbon-carbon bond. This will tend to increase the barrier to migration. Though we have not performed calculations of the mobility of various species on the (1 10) surface, there is still considerable interest in speculating on their mobility. The vinyl-type radical (product of reaction 4) and the "dangling" ethylene-like species (product of reaction 6) are expected to rotate on the surface and translate between two radical sites with no barrier (or a negligible one at the given surface temperature). The barrier for the migration of the ethyl radical-like species (product of reaction 7) should be substantially less than a C-C bond energy, since a partial carbon-carbon double bond C-C should be formed at the TS:
Ld
I
I Cd
Cd
c,.
5d
d;
x Figure 3. Representation of diamond (1 10) face showing a one-carbon gap caused when two areas of Propagating growth of opposite directionality meet. A methyl radical has added to the gap. Speckled atoms represent carbons which are part of the backbone.
nonequilibrium growth process. The mechanisms proposed here in section 111, that of Harris and Belton,26band that of Frenklach and Spear54use C2H2as the sole source of carbon. Growth of new diamond will initiate and propagate from many sites along the (1 10) surface. As shown in Figure 3, there are two possible orientations of the new growth. If two areas of propagating growth meet as in Figure 3, a single-carbon gap will be left in the new layer of diamond. Such gaps would result in a very high defect density in the growing film. Such high defect densities are not found experimentally at the atomic particularly on films grown on single-crystal diamond substrates. If C2H2is assumed to be the dominant growth species, two possible explanations for the absence of the gaps are (1) that a single-carbon species fills the gap when the relevant surface site is a radical and (2) that one or more of the intermediate growth species have a high surface "mobility". A single-carbon species such as CH3 or triplet CH2 may add to the gap sites. In Figure 3, a CH3has added to the gap. A series of further hydrogen atom abstractions at the gap site would allow the gap to be closed (e.g., two H atoms must be abstracted from the CH3 in Figure 3). Steric hindrance near the gap, when H atoms terminate the edges of the new growth, may hinder this addition. Though we tend to feel the inclusion of single-carbon species into the growth mechanism is the likely explanation for the absence of gaps, migration of intermediate growth species on the diamond surface cannot be ruled out. Such migrations resemble 1,3-shifts in neutral organic radicals. Transfers of a group between carbon atoms connected by a C-C bond, a 1,2-shift, are much more common and well-studied compared to 1,3-shifts. It is found that for transferable R groups containing only carbon and hydrogen, only phenyl, and vinyl groups migrate with low barriers in 1,2shifts.57 These migrations are thought to proceed via a threemembered ring TS. A 1,3-migration in the diamond structure
The ethylene-like species (product of reaction 5 ) may also migrate between two radical sites on the (1 10) surface. The other important factor affecting the mobility of surface species is the probability of two surface radical sites being adjacent. Frenklach and Wang13suggest that the fraction of surface radical sites is simply given by the ratio of the rate constant for the surface H atom abstraction reaction (Cd-H 4-H* Cd*- H2) over the recombination reaction (cd*-4- H' Cd-H). Using their values for the rate constants, the fractional radical coverage is given as &ad = 4.4 exp(-3520/T (K)), which at 1000 K gives a coverage of 13%. The kinetic model of Harris and Belton26bpredicts a of approximately 20% with about 20% of these having a neighboring radical site. The Frenklach and Wang13prediction depends on the ratio of Arrhenius A factors for the reactions. Arrhenius A factors estimated using equilibrium thermodynamics may be in error by as much as a factor of 3.51 Thus, they may be high or low by as much as a factor of 3. The Harris and BeltonXbvalue for the coverage enhances the probability of the surface mobility and thus allows for the possibility of an acetylene-only growth mechanism.
- -
+
V. Summary Possible reactions participating in the growth of the (1 10) surface of diamond have been presented which utilize acetylene as the sole carbon source. A mechanism with a number of possible branch points (see reactions 4-12) is considered for sp3 growth on the (1 10) surface. While the semiempirical calculations presented here are not quantitative when compared with model reactions, it is possible to state quantitatively that all of the reactions for addition of a two-carbon species to the surface, with the exception of the C-H bond homolysis (reaction 6) and the association of three ethylene-like species (reaction lo), are exothermic and have barriers below 20 kcal/mol. Any adjacent sp2 species will rapidly be incorporated into the diamond lattice, which is kinetically stable. Additionally, any two-carbon species which deposit adjacent to one of the chains of growth on the (1 10) surface will be rapidly incorporated into that new growth area. We have also shown that all proposed acetylene-based growth mechanisms, including those presented here, have a directionality. This will result in onecarbon gaps in the new growth. To reconcile these models with the lack of such defects in experimental films, it is necessary that either one-carbon species fill these gaps or at least some of the two-carbon species are mobile along the channels on the (110) surface. Our results, those of Huang and Frenklach," and those of Liu et al.58show that it is necessary to use fairly large models to avoid "edge" effects. Huang and Frenklach18use a C28H48model in their most recent study, which is approximately the size of the seven-ring model of this study. In their two earlier ~ t u d i e s , ' ~ ~ ' ~ they used a C1&8 model, which using our ring nomenclature is a two-ring system. Liu et al.58and Almlof and L ~ t hshowed i~~ that as the cluster size was increased, calculated properties ap-
9376 The Journal of Physical Chemistry, Vol. 96, No. 23, 1992
Baler et al.
proached those of bulk diamond. The need to use large models to represent the diamond surface does not bode well for ab initio calculations of diamond film growth since the computational effort required for these calculations increases rapidly with the number of atoms. Finally, a comparison between theoretical and experimental energetics for known carbon-based radical reactions indicates that PM3 and MNDO semiempirical calculations only provide qualitative support to proposed mechanisms for diamond film growth. More quantitative quantum chemical calculations are sorely needed. However, as discussed above, the apparent need to use large models for the diamond surface severely limits a p plication of ab initio and p i b l y density functional m e t h ~ d s . ~ J ~ In future work, it would be interesting to test the accuracy of a semiempirical method for diamond growth reactions if the method was only parametrized to known energetics and structures for diamond and related hydrocarbon systems.
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Acknowledgment. This research was supported by the Ford Motor Co. Scientific Research Laboratories, the Institute of Manufacturing Research of Wayne State University, and the donors of the Petroleum Research Fund, administered by the American Chemical Society. We thank Drs. M.A. Tamor and C. H. Wu of Ford for valuable discussions. We also gratefully acknowledge Dr. Patrick M. Woster of the Department of Pharmacy at Wayne State for the use of graphics facilities. Registry No. Diamond, 7782-40-3. References and Notes (1) Angus, J. C.; Hayman, C. C. Science 1988, 241, 9 13. (2) Spear, K. E. J. Am. Ceram. Soc. 1989, 72, 171. (3) Yarbrough, W. A.; Messier, R. Science 1990, 247, 688. (4) Angus, J. C.; Wang, Y.; Sunkara, M. Annu. Rev. Mater. Sci. 1991, 21, 221. (5) b a n , R. Physical Properties of Diamond; Oxford University Press: London, 1965. (6) ais,M. W.; Smith, H. I.; Argoitia, J.; Angus,J.; Ma, G.-H. M.; Glass, J. T.; Butler, J.; Robinson, C. J.; Pryor, R. Appl. Phys. Lett. 1991, 58, 2485 and references therein. (7) &is, M. W. In Materials Research Society Proceedings of Diamond, Silicon Carbide, and Related Wide Bandgap Semiconductors; Glass, J. T., Messier, R., Fujknori, N., Eds.;Materials Research Society: Pittsburgh, 1990, Vol. 62, p IS. (8) Chu, C. J.; DEvelyn, M.P.; Hauge, R. H.; Margrave, J. L. J . Appl. Phys. 1991, 70, 1695. (9) Harris, S. J.; Weiner, A. M.; Perry, T. A. Appl. Phys. Lett. 1988, 52, 2043. (10) Wu, C.; Tamor, M.; Potter, T. J.; Kaiser, E.W. J . App. Phys. 1990, 9,4825. (11) Harris, S. J.; Martin, L. R. J. Mater. Res. 1990, 5, 2313. (12) Chu, C. J.; Bai, B.J.; Hauge, R. H.;DEvelyn, M. P.; Margrave, J. ..I In Materials Research Society Proceedings of Diamond, Silicon Carbide, and Related Wide Bandgap Semiconductors; Glass, J. T., Messier, R., Fujimori, N., Eds.; Materials Research Society: Pittsburgh, 1990, Vol. 62, p 85. (13) Frenklach, M.; Wang, H. Phys. Rev. B 1991, 43, 1520. (14) Tsuda, M.; Nakajima, M.; Oikawa, S. J. Am. Chem. Soc. 1986,108, 5780; Jpn. J . Appl. Phys. 1987, 26, L527. (15) Bingham, R. C.; Dewar, M. J. S.; Lo, D. H. J. Am. Chem. Soc. 1975, 97, 1285. (16) Huang, D.; Frenklach, M.; Maroncelli, M. J . Phys. Chem. 1988,92, 6379. (17) Huang, D.; Frenklach, M. J. Phys. Chem. 1991, 95, 3692. (18) Huang, D.; Frenklach, M. J. Phys. Chem. 1992, 96, 1868. (19) Valone, S. M.; Trkula, M.; Laia, J. R. J . Mater. Res. 1990,52296. (20) Dewar, M. J. S.; Zoebiwh, E. G.;Healy, E. F.; Stewart, J. P. P. J. Am. Chem. Soc. 1905, 107, 3902.
