Chemisorption of Fluorine, Chlorine, HF, and HCl on the Diamond

Mar 1, 1995 - Chemisorption of Fluorine, Chlorine, HF, and HCl on the Diamond ... CCl Radicals As a Carbon Source for Diamond Thin Film Deposition...
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4710

J. Phys. Chem. 1995, 99, 4710-4719

Chemisorption of Fluorine, Chlorine, HF, and HCl on the Diamond (100)2xl Surface: An ab Initio Study Terttu I. Hukka* and Tapani A. Pakkanen University of Joensuu, Department of Chemistry, P.O. Box I 11, SF-80101 Joensuu, Finland

Mark P. D'Evelyn" General Electric Corporate Research and Development, P.O. Box 8, Schenectady, New York 12301, and Departments of Chemistry and Materials Engineering, Rensselaer Polytechnic Institute, Troy, New York 121 80 Received: October 26, 1994; In Final Form: January 13, 1995@

This work addresses mechanistic issues in halogen-assisted diamond growth via ab initio molecular orbital calculations on halogenated and hydrohalogenated carbon clusters ( C ~ H I ~ CXY~H, I ~ X X, = F or C1; i = 0, 1, or 2) as models of the dimer-reconstructed diamond (100)2x 1 surface. The bond lengths (XC-CX, XCCH, XC-C', C=C, C-X, XCC-H) and the C-X and XCC-H bond energies have been determined along with the effects of lattice constraints. The dimer bonds are highly strained and are longer in clusters where only the topmost carbon layer is allowed to relax and the remaining carbon atoms are constrained to lie at diamond lattice positions than in fully relaxed clusters. The first C-F and C-Cl bond energies in monohalide structures are calculated to be 502 and 366 kJ/mol, respectively, and are approximately the same in constrained and fully relaxed clusters. The second C-X bond is distinctly weaker due to JC bond formation, particularly in fully relaxed clusters. The pairing energies for F F, C1 C1, H -I- F, and H C1 were each found to be very nearly equal to that for H H, calculated as 64 and 117 kJ/mol for constrained and relaxed clusters, respectively, affirming the identification of the pairing energy with the n bond strength. The optimized structures of the transition states (TS) and the activation energies for adsorption and desorption of HF and HC1 on diamond (100)2x 1 have also been determined. The TS calculations suggest that HF adsorbs and desorbs on diamond (100)2x 1 via an asymmetric four-centered transition state, whereas HC1 prefers a twocentered (C1- *EC ) electrophilic addition. Both transition states are reactant-like ( C ~ H I ~HX), Le., occur early in the reaction coordinate. Desorption of HX from diamond (100)2 x 1 is predicted to be approximately as endothermic as that of Hz, ca. 360 and 3 10 kJ/mol for constrained and relaxed clusters, respectively, and therefore should be unimportant during halogen-assisted chemical vapor deposition (CVD) and atomic layer epitaxy (ALE) growth of diamond. Adsorbed F and C1 are predicted to be stable at substantially higher temperatures than observed experimentally. The discrepancy is attributed to electronic repulsion effects at near-monolayer coverage that cannot be accounted for properly in small cluster models.

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Introduction Gas-surface interactions enable the chemical vapor deposition (CVD) of good quality diamond films under metastable conditions,' but the specific reactions responsible for growth are only beginning to be understood. The (100) crystal face is prevalent in growth and typically has the lowest defect density; thus it is particularly important for epitaxy. Diamond (100) surfaces analyzed after growth typically show a 2 x 1 dimer reconstruction, which strongly suggests that this phase dominates on the surface under conventional hydrogen-rich CVD growth conditions.2 Therefore, this face appears to be the most promising orientation for electronic applications of epitaxial diamond and is likely to be the most suitable for atomic layer epitaxy (ALE)3 growth of diamond as welL4 Reduction of the substrate temperature necessary to achieve growth of high-quality diamond at substantial rates is the focus of much ongoing research. Reduced growth temperatures, which mitigate the stress resulting from the mismatch in thermal expansion coefficients between the diamond film and typical substrate materials, may yield improved heteroepitaxial nucleation and growth and would reduce diffusion in microelectronic structures. Halogenated-carbon precursors or hydrogen@

Abstract published in Advance ACS Abstracrs, March 1, 1995.

0022-365419512099-47 10$09.00/0

halogen-carbon mixtures have been shown to lower diamond growth temperatures by as much as 400-750 K from those needed with conventional methane/hydrogen feedstock^.^-'^ Halocarbon radicals may also provide a means for lowtemperature diamond growth by novel ALE methods, wherein hydrogen and halogen atoms are used to cap surface dangling bonds during alternating growth cyclesG4 Diamond growth using CFq as a precursor instead of C€& has been found to yield enhanced nucleation d e n s i t i e ~ ' ~and .'~ lower defect level^'^-'^ under suitable conditions. The mechanisms for these effects, the detailed mechanisms of halogenassisted growth generally, and the chemisorption and desorption'*.Iyof fluorine and chlorine on diamond (100) are not yet adequately understood. The only experimental data available to date about the reactivity and behavior of fluorine and chlorine on the diamond (100) surface are the recent studies by Freedman.I8 He has investigated the adsorption and desorption of fluorine and chlorine on diamond (100) by X-ray photoelectron spectroscopy (XPS), low-energy electron diffraction (LEED), and temperature-programmed desorption (TPD) techniques. Adsorption of neither F2 nor C4 could be detected, but atomic F and C1 were found to adsorb up to a saturation coverage of approximately three-quarters of a monolayer and less than half a monolayer, 0 1995 American Chemical Society

Chemisorption of F, C1, HF, and HCl on Diamond respectively, at 300 K. Fluorine adsorption and formation of a carbon monofluoride species and dangling bonds were observed in F(1s) and C(1s) XPS spectra taken from the fluorinated surface. Thermal desorption of surface fluorine was observed between 300 and 1200 K, an unusually wide temperature range, with most of the desorption occurring between 700 and 950 K. The only desorption product detected by mass spectrometry was atomic fluorine; no evidence for desorption of F2, HF, or CF, etch products was observed. Chlorine adsorption produced a Cl(2p) XPS peak, but the C(1s) chemical shift associated with C-Cl bond formation was too weak to be observed. Chlorine desorption took place at even lower temperatures, 223-600 K, with most of the desorption occurring between 223 and 423 K. The wide temperature range for the thermal desorption of fluorine has been interpreted as an indication of binding sites with a range of energies, perhaps generated by coexisting phases of 1x 1 and 2x 1 fluorinated regions.ls In related work, FreedmanI8and Yamada et a1.20investigated the surface chemistry of fluorine on diamond (111) using similar techniques. In the latter study fluorine adsorption was produced by exposures to XeF2 rather than to F atoms. Freedman found the thermal stability of F on diamond (1 11) to be similar to that on the (100) face, with desorption occurring over the range 300-1200 K.I8 Yamada et al. observed qualitatively similar behavior, but desorption occurred in a higher temperature range, 300-1600 K, and ca. 10% of the surface fluorine remained after heating above 1500 K. The origin of the discrepancy in maximum temperature necessary to desorb F is not yet known, but may be related to the difficulty in making accurate temperature measurements on single-crystal diamond.21 Only one theoretical study of the adsorption of fluorine on diamond (100) has been reported to date. Pederson and PickettI9 optimized the structures of 10-layer-thick diamond slabs with a fluorinated (100) surface using the local spin density approximation and found that a slightly dimerized 2 x 1 reconstructed surface is energetically more favorable than an unreconstructed 1 x 1 surface with fluorine ions located directly above the pseudo-4-fold hollows. They have also determined the FC-CF dimer bond length to be between 1.69 and 1.96 8, in an isolated cluster (CZIF~HZO), which they used as a model of the fluorinated dimer-reconstructed (100)2x 1 surface. Adsorption and desorption of HF and/or HC1 have been studied previously on the s i l i ~ o n ~ and ~ -germanium26 ~~ (100) surfaces but have not been investigated on diamond surfaces before. However, with the development of halogen-assisted diamond growth methods it has become important to understand the basic surface chemistry of these molecules on diamond as well. In the proposed diamond ALE method? each growth cycle would be completed by regeneration of a hydrogenated surface from a halogen-terminated surface by abstraction and recombination reactions with atomic hydrogen. During this cycle it is possible to have hydrogen and halogen atoms coadsorbed on same dimer units on diamond (100)2xl, and therefore understanding the energetics of HF and HC1 desorption is essential. Moreover, HX species are present in the gas phase in most of the halogen-assisted CVD growth systems demonstrated to date5-8.13-17 and, if the energetics are favorable, would be expected to adsorb on the growing diamond surface. In addition to finding answers to the practical questions, understanding of the desorption energetics of HX relative to that of hydrogen on diamond (100)2x 1 is important from a fundamental chemical and mechanistic point of view. In this paper the first ab initio results for chemisorption of fluorine, chlorine, hydrogen fluoride, and hydrogen chloride on diamond (100)2x 1 are presented. We have used methods and

J. Phys. Chem., Vol. 99, No. 13, 1995 4711 models analogous to those in our previous study of hydrogen on diamond (100)2x l.27 However, experimental bond-energy corrections were omitted here, as thermochemical data of sufficient accuracy are not available for alkyl halides. The bond lengths (XC-CX, XC-CH, XC-C', C=C, C-X, XCC-H) and the C-X and XCC-H bond energies have been determined along with the effects of lattice constraints. In addition, optimized transition state structures for adsorption and desorption of HF and HCl on diamond (100)2x 1 and the corresponding activation energies are determined.

Computational Methods Ab initio self-consistent field (SCF) molecular orbital calculations were performed with the Gaussian 92 and Gaussian 90 programsz8on Stardent 2040, SGI Personal Irid3.5, SGI Indigo R4400, Convex C3840, and Cray X-MP EN432 computers. The spin-unrestricted Hartree-Fock method (UHF)was used for radicals and the spin-restrictedHartree-Fock (RHF) method for closed shell species.29 The geometry optimizations were carried out with the 3-21G(*) and 6-31G* split-valence basis sets.30 In addition, all the equilibrium geometries and corresponding total energies obtained from the Hartree-Fock calculations were corrected for correlation between the motion of electrons of opposite spin by Moller-Plesset perturbation theory terminated at second order (UMP2 and RMP2, frozen

ore).^'-^^ The most reliable results of this work are considered to be the ones obtained at the MP2/6-31G* level of theory,27because it can usually reproduce the experimentally observed geometries of small hydrocarbons and alkyl halides a ~ c u r a t e l y . ~It~is. ~ ~ known that inclusion of d-type polarization functions on carbon in the basis set brings the structures (and, accordingly, the energies) of strained, cyclic hydrocarbon compounds to closer agreement with experimental r e s ~ l t s . ~In~ addition, -~~ DeFrees et al.39have noted that d-type polarization functions are required in the atomic basis set in order to properly describe the equilibrium geometries at the level of second-order MollerPlesset theory. Inclusion of electron correlation at the MP2 level of theory usually produces longer bonds, especially in small molecules comprising strongly electronegative atoms, and in most cases improves the HF/6-31G* geometries with respect to the experimental s t r u c t ~ r e s .The ~ ~ ~mean ~ ~ absolute errors between the MP2/6-3 lG* and experimental single- and multiplebond lengths between heavy atoms in two-heavy-atom molecules have been reported as 0.019 For example, for ethylene the MP2/6-3 lG* carbon-carbon double-bond length is 1.335 A, to be compared with the experimental value of 1.339 A,39 The effects of electron correlation on the equilibrium geometries of molecules comprising second-row elements, especially chlorine atoms, are not widely studied and therefore not well under~tood.~~ Evidently, as single bonds in molecules involving chlorine atoms are already well described using the HF/6-3 lG* level, electron correlation effects are less significant in influencing the structures34and, accordingly, as one would expect, the energetics of these systems. In radicals comprising heavy atoms the deviation between calculated and experimental single-bond lengths is typically ca. 0.024 A.34 The MP2/6-3 lG* bond angles in small molecules typically deviate approximately up to 1-2" from the experimental values.34 Basis set and correlation effects typically cause larger changes in the total energies than in the geometries. However, possible insufficiencies in describing electron correlation are expected to be minimized when the differences in total energies between the products and reactants are c a l ~ u l a t e d .At ~ ~the ~ ~MP2/6~ 31G* level of theory the bond dissociation energies usually

Hukka et al.

4712 J. Phys. Chem., Vol. 99, No. 13, 1995

Figure 1. Stick model of the reconstructed diamond (100)2x 1 surface showing the CScluster colored with the dark balls.

deviate from the experimental values by ca. 20-40 kJ/mol. In general, insufficient treatment of correlation will result in a greater relative error for a bonded system, which has higher correlation energy, than for separated molecular fragments, and therefore calculated dissociation energies will be typically too We calculated C-X bond dissociation (X = F, C1) energies of small alkyl halides and halocarbons within 40 kJ/ mol of the experimental values using the MP2/6-31G* level of theory, as discussed below. It is also well-known that large basis sets and extended correlation treatments are needed to describe the homolytic bond dissociation processes of F2, Cl2, HF, and HCl a c ~ u r a t e l y . We ~ ~ found that the bond enthalpies of both HF and HCI are underestimated at the MP2/6-31G* and MP2/6-3 1G*//6-3 1G* levels of theory by 77-78 kJ/mol, respectively. The correlation energy corrections are expected to be smaller in molecules involving chlorine atoms than in those comprising only first-row elements, as pointed out above. The more extensive MP4 calculations would not be expected to alter the MP2/6-3 1G* energies significantly and have not been used in this phase of the work because the systems investigated are relatively large. In the Gaussian 92 program the unrestricted MP2 energies are corrected for spin contamination using the Lowdin spin projection operator. Pure doublets were obtained for the radicals studied here after annihilation of the first spin contaminant.'" Harmonic vibrational frequencies, associated zero-point energies, and thermal energies at 298 K were calculated at the SCF/321G(*) level. The vibrational frequencies were scaled by a factor of 0.89 in making the zero-point energy and thermal energy calculations within the Gaussian 92 program.28 Transition state geometries were optimized at the HF/3-21G(*) and HF/6-31G* levels of theory and in addition at the MP2/ 3-21G(*) level of theory for the adsorptiotddesorption of HF on the fully relaxed cluster model. The transition state optimizations reached stationary points, i.e., first-order saddle points, with one and only one negative eigenvalue corresponding to the direction in which the energy is at the maximum. Vibrational frequency calculations were carried out at the same levels of theory, and they confirmed that the transition state structures possessed only one imaginary frequency, demonstrating authentic first-order saddle points. An imaginary frequency corresponds to a geometric distortion for which the energy of the system is lower than that at the current structure (indicating the existence of a more stable The intrinsic reaction coordinate (IRC) path following procedure was too timeconsuming computationally for the systems studied in this work

and was omitted. Therefore, it is only assumed that the optimized saddle points correspond to the transition state structures which connect the equilibrium structures of the related reactants and products. However, the geometries which correspond to the vibrations along the reaction coordinates (the imaginary frequencies) have been checked and can be interpreted as the ones between the reactants and the forming products. The correlation corrected energies for the transition states were calculated at the MP2/6-31G*//6-31G* level of theory. C9 clusters (C9H12Xj9 C ~ H I ~ X X= , F or C1; i = 0, 1, or 2), representing one surface unit cell of the diamond lattice, were used as models of the dimer-reconstructed (100)2x 1 surfaces. A C9H12 cluster model is presented in Figure 1. The capped sticks on the (100)2x1 surface represent the dangling bonds saturated by chemisorbed H, F, or C1. Similar cluster models have been previously used by Verwoerd4' and Tsuda et ~1.'"' In order to determine upper and lower bounds for the surface structures and energetics, the lattice constraints were treated in two different ways. The first set of calculations was performed with clusters in which all the structural parameters were fully optimized. These calculations give results which are underconstrained with respect to the structures and energetics on the real diamond surface. In the second set of calculations only the parameters of the surface carbon atoms and the halogen (and top-layer hydrogen) atoms chemisorbed on them were fully optimized. The remaining carbon atoms were constrained (in Cartesian coordinates) to lie at bulk lattice positions (see Figure l), using the diamond lattice constant of 3.5670 A!5 This set of calculations overconstrains the cluster model relative to the real diamond surface. In all cases, the subsurface dangling bonds were terminated with hydrogen atoms located at a distance of 1.100 A along the broken bond directions. The real surface structures and energetics on diamond (100)2x 1 are predicted to lie in between the under- and overconstrained results, because the full relaxation allows unrealistic distortions of the cluster and the constrained cluster is too rigid to accurately describe the effects of the real lattice. Results and Discussion

Geometries. The optimized surface dimer, C-H and C-X bond lengths, and the angles between the chemisorbed surface atoms and the surface dimer carbon atoms of the fully relaxed and the constrained clusters are summarized in Tables 1 and 2. In general, the HF/6-31G* model predicts shorter bonds than either the HF/3-21 G(*) or MW6-3 1G* models. Increasing the

Chemisorption of F, C1, HF, and HCl on Diamond

J. Phys. Chem., Vol. 99, No. 13, 1995 4713

TABLE 1: Surface Dimer, Surface C-H, and C-X Bond Lengths (A) Calculated at Different Levels of Theory" bond 3-21G(*) MP2/3-21G(*) 6-31G* MP2/6-31G* Constrained Clusters C-Cb HC-CHb FC-C' FC-CH FC-CF ClC-C' ClC-CH ClC-CCI HCC-Hb F-CC' F-CCH FCC-H FCC-F Cl-CC' Cl-CCH CICC-H ClCC-c1

1.387 1.727 1.706 1.724 1.733 1.700 1.728 1.765 1.080 1.391 1.395 1.078 1.386 1.799 1.808 1.077 1.787

C=Cb HC-CHb FC-C' FC-CH FC-CF ClC-C' ClC-CH ClC-cc1 HCC-Hb F-CC' F-CCH FCC-H FCC-F Cl-CC' Cl-CCH CICC-H CICC-Cl

1.338 1.594 1.568 1.584 1.590 1.564 1.589 1.606 1.087 1.397 1.399 1.079 1.391 1.802 1.807 1.077 1.788

a

1.448 ~. 1.739 1.723 1.743 1.758 1.712 1.742 1.786 1.094 1.414 1.418 1.093 1.411 1.808 1.814 1.092 1.795

1.384 . 1.713 1.677 1.705 1.712 1.680 1.717 1.762 1.083 1.363 1.367 1.082 1.357 1.799 1.804 1.080 1.785

1.43s .. 1.708 1.673 1.706 1.721 1.673 1.716 1.773 1.096 1.392 1.388 1.095 1.386 1.792 1.795 1.094 1.778

Fully Relaxed Cluste:rs 1.388 1.336 1.608 1.583 1.584 1.552 1.602 1.573 1.613 1.579 1.576 1.552 1.604 1.580 1.623 1.601 1.094 1.083 1.422 1.368 1.423 1.371 1.093 1.082 1.417 1.361 1.812 1.800 1.8 14 1.802 1.092 1.080 1.797 1.786

1.378 1.581 1.550 1.574 1.584 1.547 1.579 1.602 1.095 1.398 1.399 1.094 1.390 1.792 1.792 1.093 1.779

Coordinates are available on request. From ref 27a.

TABLE 2: Bond Angles (deg) between Chemisorbed Atoms and Surface Dimers Calculated at Different Levels of Theory 3-21G(*)

MP2/3-21G(*) 6-31G* MP2/6-31G*

Constrained Clusters LH-C-CH" LH-C-C'" LF-C-C' LF-C-CH LFC -C -H LF-C-CF LCl-C-C' LCl-C-CH LClC-C-H LC1-C-CCl

110.5 111.8 112.5 110.4 108.3 109.4 111.8 110.9 109.3 113.7

110.5 111.8 111.9 110.2 108.7 109.6 111.9 111.1 109.5 114.3

110.2 111.7 111.8 109.2 108.2 109.0 111.7 110.8 109.0 113.5

LH-C-CH" LH-C-C' a LF-C-C' LF-C-CH LFC-C-H LF-C-CF LC1-C-C' LC1-C-CH LCIC-C-H LCl-C-CCl

Fully Relaxed Clusters 113.6 113.4 113.8 103.1 114.7 114.9 115.2 115.3 114.7 113.2 113.2 113.2 111.5 111.0 112.0 112.3 111.9 112.5 114.3 114.2 114.6 113.8 113.5 114.0 112.8 112.4 113.2 116.7 115.9 117.2

113.7 115.0 114.8 113.0 111.5 112.0 114.6 114.0 112.8 116.7

a

110.7 112.1 112.9 110.8 108.3 109.4 112.0 111.0 109.3 113.2

From ref 27a.

basis set size from 3-21G(*) to 6-31G* does not significantly affect the calculated C-H and C-Cl bond lengths in the clusters. Inclusion of electron correlation increases the C=C and C-F bond lengths (in the constrained and fully relaxed clusters) and the XC-CX bond lengths (in the constrained

clusters) most significantly as compared to the uncorrelated HF/ 6-31G* values. At the MP2/6-31G* level the C-F bond in monofluoromethane is reported to be 0.009 8, longer than the experimental value of 1.383 Therefore, the C-F bonds predicted in this work might be somewhat longer than the real C-F bonds. However, tie longest calculated-C-F bonds are comparable to the experimental bond length of 1.398 8, in fl~oroethane.~~ The MP2/6-31G* C-H bonds are slightly longer than the HF/6-31G* bonds and within 0.003 8, of the experimental C-H bond lengths reported for ethane (1.096 The correlation correction decreases the lengths of the C-C1 bonds by ca. 0.010 A from the HF/6-31G* values and brings them within 0.014 8, of the experimental value of 1.781 8, observed in ~hloromethane.~~ On the clean dimer a highly strained double bond is predicted, with a bond length of 1.38 or 1.44 A for the fully relaxed or constrained C9H12 cluster, re~pectively.~~ These are longer than normal C=C (1.34 8,) double bonds and are significantly affected by electron correlation. Clean and symmetrically adsorbed dimers are symmetric with respect to the plane containing the dimer carbon atoms and the chemisorbed species. No buckling was observed even when the starting geometries were asymmetrically distorted before the optimizations. In the CgH12X. clusters with only one surface adsorbate a slight asymmetry is induced by contraction of the radical carbon toward the bulk, closer to a planar sp2-hybridizedconfiguration. In the fully relaxed clusters with adsorbates the calculated C-C dimer bond lengths are close to the normal C-C singlebond lengths of 1.54 A, whereas in the constrained clusters the bonds are distinctly (0.13-0.18 8,) longer. When fluorine, HF, or HCl is chemisorbed on the surface dimer, the XC-CX and XC-CH dimer bond lengths are practically the same as the corresponding bond on the hydrogen-terminated surface as calculated in our recent (see Table 1). However. with two chemisorbed chlorine atoms the dimer bond is lengthened by ca. 0.23 8, (in the constrained cluster) and 0.06 (in the 'luster) from the c-c single-bond length due to electronic repulsion between the chlorine atoms. In addition, the Cl-C-CCl surface bond angle (113.5", Table 2) in the constrained cluster model is predicred to be 3.3" greater than the H-C-CH bond angle (1 10.2", Table 2) on the hydrogen-terminated surface.27a On the basis of the present cluster calculations the electron clouds (van der Waals radius 0.97 8,) of two chlorine atoms on adjacent dimer rows would overlap each other by about 0.1 A. Therefore, electronic repulsion should inhibit adsorption of two chlorine atoms on adjacent carbon atoms in neighboring dimer rows on the real diamond (100) surface. If the second chlorine atom is replaced by a hydrogen atom, the dimer bond length becomes comparable to those predicted for the fluorinated surfaces (see Table 1). These results are in qualitative agreement with the experimental observations that the saturation coverages of fluorine and chlorine on diamond (100) are about three-quarters of a monolayer and less than half a monolayer, respectively.l 8 Pederson and Pickett have calculated two different FC-CF dimer bond lengths in a cluster model which consists of three adjacent dimers on a same dimer row, 1.96 8, for the central dimer and 1.69 8, for the two outer dimers. Thev allowed the two top carbon layers to relax during the geometry optimization. The latter value for the outer dimers is close to the bond length of 1.72 8, we predict for our constrained cluster model. A more comprehensive determination of the effect of chemisorbed fluorine atoms on the FC-CF bond length on adjacent dimers would require a model with fluorinated dimers on neighboring dimer rows in addition to adjacent dimers in the same row.

Hukka et al.

4714 J. Phys. Chem., Vol. 99, No. 13, 1995

TABLE 3: Optimized Structural Parameters (Bond Lengths in Angstroms, An es in Degrees) and Imaginary Frequencies (cm- ) for the Transition States of Fully Relaxed Clusters parameters 3-21G(*) 6-31G* MP2/3-21G(*)

P

c-c H-F C-H C-F LF*C-C LH-C-C Y

c-c H-Cl C-H LCI. .H-C 1H.C-C V

CsH12 1.442 1.058 1.630 1.932 90.1 74.0 9791'

1.439 1.134 1.436 2.069 83.8 78.5 1850i C9Hi2

1.398 1.574 1.361 174.7 116.2 13741'

+ HF 1.439 1.100 1.650 1.894 93.6 72.1 1320i

+ HC1 1.393 1.545 1.404 175.1 114.5 15521'

Moreover, it would be important to determine how the number of the relaxed layers affects the FC-CF bond length on the central dimer. Unfortunately, such a large model would be too bulky for high-level ab initio calculations. Transition State Geometries. Some optimized structural parameters and the imaginary vibrational frequencies of the transition states (singlet states) for adsorptioddesorption of HF and HC1 on the surface dimer in the fully relaxed C9Hl2 clusters are presented in Table 3. Transition state structures for the constrained clusters were qualitatively the same as for the fully relaxed clusters; however, in reality lattice vibrations have more degrees of freedom in transition states than allowed by our constrained model, and therefore these results are omitted. The HF/6-31G*-optimized transition states are drawn in Figure 2. Hydrogen atoms saturating the subsurface dangling bonds are omitted for clarity. The arrows illustrate the displacement vectors of the reaction coordinate, indicating the direction of the imaginary vibration at the transition state, and lie in the symmetry plane which contains the dimer carbon atoms. In separate TS calculations with constrained clusters (not shown), the TS for HF adsorption looks similar to that shown in Figure 2a, but the vectors are oriented asymmetrically away from the symmetry plane. Charges obtained from Mulliken population analysis with MP2/6-3 1G*//6-3lG* densities are indicated in parentheses for H, X, and the surface carbon atoms but have been omitted elsewhere. The calculations suggest that HF chemisorbs dissociatively onto diamond (100)2x 1 via an asymmetric four-centered transition state (cf: Figure 2a) in which the hydrogen is closer to the surface carbon atom, whereas HCl prefers a two-centered (Cl. *HaC ) nonconcerted electrophilic addition which is led by the positively charged hydrogen atom approaching the negatively charged Cl atom of the polarized double bond (cf: Figure 2b). The vibrational structure along the reaction coordinate for a dissociative chemisorption (cf:Figure 2b) shows that the hydrogen end of HCl vibrates almost parallel to the surface dimer atoms CI and Cz and would be expected to chemisorb onto atom C2, whereas the chlorine atom could adsorb onto the atom Cl. Both saddle point geometries more closely resemble free HX plus the C9H12 "surface" than the chemisorbed species (hydrohalogenated dimers) and are therefore considered as early transition states on the reaction coordinate for adsorption. The calculated H-F and H-Cl bond lengths are slightly greater in the transition states than in the isolated HX molecules, for which the calculated (HF/6-3lG*)/experimental bond lengths are 0.91 1/ 0.917 A and 1.266/1.275 A, respectively. In addition, the C-C bond lengths in the transition states are closer to the C=C than

to the XC-CH bond lengths. The calculations predict that at the point of the TS for HF addition the H-F bond is breaking and the C-H bond is forming, but the interaction between fluorine and the second surface carbon atom is still relatively weak. The reactant-like nature of this TS is more pronounced than that calculated recently for HF ethylene, for which a longer H-F bond and shorter C-F and C-H bonds were This is most probably due to the increased reactivity of the double bonds in the strained C9H12 clusters so that a closer interaction between the reactants would already lead to chemisorption. Conversely, it is more difficult to eliminate HF from the C ~ H I clusters ~F than from ethyl fluoride because the double bonds being formed are less stable in the clusters, and therefore a later TS is expected. The transition state structures obtained with the Hartree-Fock models for HF addition were established also at the MP2/3-21G level of theory (Table 3). Searches for a two-centered TS for HC1 adsorption at the MP2/3-21G* level ended at structures with zero or two negative eigenvalues. The predicted transition state geometry for chemisorption of HC1 is similar to the TS geometry for hydrogen atom addition from HC1 to a C9H13' cluster (doublet state) calculated recently in our lab~ratory.~' A transition state for chemisorption of HC1 analogous to that shown in Figure 2b has been previously calculated with a Hartree-Fock model for addition of HC1 to silene (H2S~=CHZ).~* In these calculations an electrophilic attack is predicted on the negatively charged carbon atom of silene. However, the displacement vectors of the reaction coordinate given in the latter work4* strongly suggest that the predicted transition state for addition of HC1 on silene is rather a TS for chemisorption of hydrogen from HC1 wherein the chlorine atom will adsorb neither on the carbon nor the silicon atom. On the other hand, however, elimination of HC1 from both ethyl ~ h l o r i d e ~ and ~ , ~d*i ~* i~l e~n e has ~ * ~been predicted to occur in a concerted manner via an asymmetric TS, which is more strongly distorted from the four-centered TS in the case of ethyl chloride. Attempts to locate an analogous TS for desorption of HC1 from C9H13C1 consistently produced two negative eigenvalues. Chemisorption of HX molecules has been previously observed to be dissociative on other group IV semiconductors as well, including HFZ2 and HClZ4 on Si(100)2x1 and HC1 on Ge(100)2 x l ,26 but to the authors' knowledge has not been studied experimentally on diamond (100)2 x 1. Bond Dissociation Energies and Heats of Dehydrohalogenation and Dehalogenation. Bond dissociation energies (BDEs) of the first and second C-X bonds (X = F or C1) and the energies of dehydrohalogenatioddehalogenation of the hydrohalogenated and monohalogenated surface dimers are obtained from the calculated energies of the following reactions:

+

C,Hl,X, C,H,,X'

-

-

+

C9H12X' X'

BDE (C-X,,,)

(1)

+

C9HI2 X' (3)

Bond dissociation energies of the first C-H bonds of the hydrohalogenated surface dimers are obtained from reaction 1 by replacing the second X with H. The driving force for ordering of surface halogen and hydrogen atoms is described by the pairing energy,50given by reaction 1 minus reaction 2: C,H,,XY

+ C9H12 - C9HI2X' + C,H,,Y*

E(XY)

(4)

where Y = H or X. The pairing energy is seen to be the

Chemisorption of F, C1, HF, and HC1 on Diamond

J. Phys. Chem., Vol. 99, No. 13, 1995 4715 (-0.351)

(-0.486)

c1

1.545

F (0.134)

(0.423)

; 2.069

/ 1.404

Figure 2. (a) 6-3 lG*/SCF-optimizedtransition state geometry for HF + fully relaxed C9 cluster. (b) 6-3 lG*/SCF-optimizedtransition state geometry for HCl + fully relaxed C9 cluster. The atomic charges are given in electrons (in parentheses), bond lengths in angstroms, and angles in degrees. The arrows indicate the directions of the atomic displacements along the reaction coordinate for an adsorption reaction. TABLE 4: Calculated Total Energies, Zero-Point Energies (hartree),”and Thermal Corrections (kJ/mol) for the CS Clusters cluster 3-2 lG(*) MP2/3-2 lG(*) 6-31G* MP2/6-31G*//6-31G* MP2/6-31G* 3-21G(*) ZPE E(298) - E(0) Constrained Clusters -345.704 25 -346.319 99 -444.705 00 -445.343 02 -543.666 17 -803.206 14 -803.844 25 - 1260.665 74

-346.538 -347.176 -445.611 -446.275 -544.713 -804.138 -804.798 -1261.758

-345.769 -346.418 -444.743 -445.382 -543.704 -803.245 -803.884 -1260.705

-346.592 -347.201 -445.645 -446.306 -544.742 -804.169 -804.829 -1261.788

67 17 59 52 90 35 19

-347.624 -348.295 -447.151 -447.181 -546.642 -801.200 -801.836 -1266.735

33 31 03 33 46 44 88 80

-341.687 47 -348.333 89 -441.189 30 -441.827 46 -546.680 56 -807.239 70 -807.871 07 - 1266.775 74

00

17 16 03 13 34 38 97 62

-348.818 65 -449.136 87

-348.820 -349.453 -448.476 -449.137 -548.159 -808.491 -809.152 -1268.186

31 72 56 54 16 49 34 97

0.200 10 0.212 07 0.203 10 0.216 63 0.207 14 0.201 77 0.215 47 0.205 01

14.0 14.6 16.8 16.9 19.1 17.7 17.7 20.7

-348.811 -349.486 -448.508 -449.170 -548.190 -808.524 -809.186 -1268.220

72 60 20 88 69 45 31 04

0.202 71 0.215 50 0.206 1 2 0.220 68 0.211 91 0.205 36 0.219 50 0.209 28

14.7 14.9 17.1 17.1 19.3 18.0 18.0 21.0

Fully Relaxed Clusters 61 39 03 42 29 98

08 80

-348.868 98 -449.169 25 -809.185 12

1 hartree = 2625.5 kJ/mol.

energetic driving force for pairing of chemisorbed atoms (and are corrected for the change in enthalpy on going from 0 to dangling bonds) on surface dimers, since it costs this amount 298 K.42 Calculated total energies, zero-point vibrational of energy to unpair two halogen atoms or a hydrogen atom and energies, and thermal energies of the partially and fully relaxed a halogen atom (and dangling bonds) by transfer of a halogen C ~ H I ZC, ~ H I ~C’ ,~ H I ~ Xand . , C ~ H I ~ Xclusters Y are listed in atom from a doubly occupied dimer to an unoccupied dimer, Table 4. The total energies, which were used to calculate the producing two singly occupied dimers. The pairing energy for activation energies for adsorption and desorption of HX (see surface hydrogen provides a measure of the n bond ~trength.”.~~.~’ the transition state energies below) at the MP2/6-3 1G*//6-3lG* The identification of the n bond strength with the driving force level of theory, are also given in Table 4. The heats of reactions for pairing suggests that the pairing energy for adsorbed halogen 1-4, which correspond to the calculated first and second C-X atoms and for coadsorbed hydrogen and halogen atoms should bond energies, the “first” C-H bond energy, Xz and HX be approximately the same as for hydrogen, as indicated desorption energies, and pairing energies c(XY) are presented below.26b in Tables 5 and 6 for the fluorinated and chlorinated clusters, The heats of the reactions at 0 K are obtained when the respectively. The energies of F,HF, CP, HC1, F2, and C12 were appropriate zero-point vibrational energy corrections are added. calculated at the corresponding levels of theory. In order to get the enthalpies at 298 K, the calculated results The first C-F and C-Cl bond energies are slightly larger

4716 J. Phys. Chem., Vol. 99, No. 13, 1995 TABLE 5: Calculated Bond Strengths, Heats of Reaction, and Pairing Energies (kJ/mol) of Fluorinated Surface Dimers at 298 K

Hukka et al.

energies with the 6-31G* basis set, as expected (cJ: the Computational Methods section). The C-X bond strengths calculated here predict that adsorbed MP2/ MP21 F and C1 should be stable against atomic desorption up to quite reaction 3-21G 3-21G 6-31G* 6-31G* high temperatures, in contrast with experiment. For purposes of comparison let us assume that the activation energy for 504 323 desorption of X is equal to the calculated first C-X bond energy 327 506 (Le., atomic adsorption has no barrier, and the desorption rate 42 1 437 is limited by the first, strong C-X bond), desorption follows 334 398 885 79 1 first-order kinetics with a pre-exponential factor of Y = l O I 4 34 1 409 s-l, and the surface is annealed at various temperatures for a 97 67 period of 5 min.18a One then predicts that desorption of 10-94 69 90% of surface F and C1 should occur over the temperature ranges of 1500-1630 and 1100-1 190 K, respectively, much higher than the corresponding ranges of 450-1000 and 250322 500 525 K observed by Freedman.Is The magnitude of the dis328 505 crepancy is reduced if one focuses on the low coverage limit, 353 383 337 40 1 where the importance of steric and electrostatic repulsion and 816 734 charge transfer effects not included in the calculations are 343 29 1 minimized. The annealing temperatures reported by Freedman 118 -31 to reduce the surface fluorine coverage on diamond (100) and 123 -25 (111) below 5% of the initial value were 1100 and 1200 K, respectively.I8 In contrast, Yamada et aL20 reported that TABLE 6: Calculated Bond Strengths, Heats of Reaction, approximately 5% of the initial fluorine coverage remained on and Pairing Energies (kJ/mol) of Chlorinated Surface diamond (1 11) even after heating to nearly 1600 K.*O Further Dimers at 298 K work will be necessary to resolve the temperature discrepancy, MP2/ MP2/ but the latter experiment is consistent in the low coverage limit reaction 3-21G* 3-21G* 6-31G* 6-31G* with the C-F bond energies calculated here. We attribute the Constrained Clusters anomalously low desorption temperatures at higher coverages C9Hi2C12 C9HizCl' + CY 225 366 224 367 observed by Freedman (on diamond (100) and (1 11))18and by C ~ H I ~ C ~ - C ~ HCl' I~'+ 239 371 24 1 375 Yamada et al. (on diamond (1 11))20to electronic and steric C9Hi2Cl' C9Hi2 Cl' 343 315 335 307 repulsion effects that are not included in the small cluster models C9Hi3Cl- CgHizCl' + H' 341 401 334 397 515 C9H12C12 C9Hiz + Cl2 526 507 506 employed in this work. These electronic effects will include C9Hi3Cl- C9H12 + HCl 400 358 385 350 direct steric repulsion due to overlap of electron density on -111 C9HizC12+ C9Hi2-2 C9Hi2C1' -118 51 60 neighboring X atoms. Our cluster calculations showed steric C9Hi3Cl+ C9Hi2 -104 56 -94 68 repulsion to be important in the case of C1, as discussed above. C9Hi3' + C9Hi2Cl' In addition, the substantial charge transfer from the diamond Fully Relaxed Clusters carbon atoms to adsorbed halogen atoms associated with C-X C9Hi2Clz C9HizCl' + C1' 226 362 224 366 bond will give rise to long-ranged, repulsive 376 243 C9Hi3C14 C9Hi3. CP 241 370 256 270 C9Hi2Cl' C9Hi2 Cl' 272 254 dipole-dipole interactions between the C-X groups. Finally, C ~ H I ~ C ~ - C ~ H I+ ZH C'P 342 400 334 399 additional weakening of the C-X bonds may result from the CsHizC12 C9Hi2 + Cl2 456 443 454 450 decreasing ability of the surface to donate charge to the adsorbed C9Hi3Cl C9Hiz + HC1 330 297 321 30 1 halogen atoms as the coverage increases. Properly accounting C9H12C12 + C9Hi2- 2 C9H12Cl. -46 108 1 IO -45 for these effects in the calculations would of course require much CgHi3Cl+ C9H12 -31 116 -27 120 CsHi3' + C9Hi2Cl' larger models. The first C-X bond strengths are approximately the same in and the second bond energies slightly smaller than in tert-butyl fully relaxed and constrained clusters, but the second C-X bond halides (F-t-C4H9 485 kJ/mol, Cl-t-C4H9 345 kJ/m01).~~Our is distinctly weaker in the fully relaxed clusters. These results MP2/6-3 lG* test calculations predict a 35 kJ/mol smaller indicate that the surface ~t bond, while energetically significant, dissociation energy for a CH3-F bond with respect to the is weakened by the constraints imposed by the underlying lattice. experimental value of 477 kJ/m01.~~ However, in the case of The dependence of the ~t bond strength on the lattice constraints the CdH9-F bond we calculate an energy of 485 kJ/mol, is also responsible for HX desorption being about 50 kT/mol virtually the same as the value estimated by Luo and B e n s ~ n . ~ ~ more favorable from the fully relaxed clusters than from the For the CH3-Cl and C4H9-Cl bonds we calculate energies of constrained clusters. If instead of having two bulky chlorine 324 and 343 kJ/mol, which are about 27 and 2 kJ/mol smaller atoms on the same surface dimer, one chlorine atom is replaced than the experimental values,52 respectively. Therefore, it is by a smaller hydrogen atom, a 8-10 kJ/mol stronger C-C1 expected that the C-X bond energies are predicted with a bond results, whereas only a small (2-5 kJ/mol) increase is reasonable accuracy (error < 40 kJ/mol) in this work. The observed in the C-F bond strength on the hydrofluorinated calculated C-F bond energies on the monofluorinated dimers surface dimer. This is due to the reduced electronic and steric are about 104- 111 kJ/mol stronger than the corresponding C-H repulsion between the chemisorbed species. The C-H bond bonds (393-396 kJ/mol) on the monohydrogenated dimers strengths on the hydrohalogenated dimers are typical for tertiary calculated in our recent and the C-Cl bonds are weaker carbon atoms (H-t-C4H9401.2 k.l/m01).~~,~~ They are also the by only about 22-30 kJ/mol relative to the C-H bond same within 5 kJ/mol as on the hydrogenated varying energies.27a It is worth noting that the correlation energy by only ca. 2 kJ/mol with the type of halogen (F or C1) correction has a greater effect on the C-F than C-C1 bond chemisorbed on the neighboring surface carbon atom.

-

-

-

+

-

-

--

+ +

-

J. Phys. Chem., Vol. 99, No. 13, 1995 4117

Chemisorption of F, C1, HF, and HCl on Diamond

TABLE 7: Calculated Total Energies, Zero-Point Energies (hartree): and Thermal Corrections (kJ/mol) for the Transition States of AdsorptiodDesorption Reactions of HF and HCl on Surface Dimers cluster 3-2 1G(*) MP2/3-2 lG( *) 6-31G* MP2/6-31G*//6-31G* 3-21G(*) ZPE E(298) - E(0) Fully Relaxed Clusters CsHizHF

-445.210 05

-446.154 07

-447.652 71 -807.735 56

C9HnHCl -803.741 48 a 1 hartree = 2625.5 Id/mol.

TABLE 8: Activation Energies and Internal Energies (kJ/mol) for Adsorption and Desorption of HF and HCI on Surface Dimers at 298 K MP2/ 3-21G(*) 3-21G

reaction

MP2/6-3 1G* 6-31G* //6-31G*

Fully Relaxed Clusters C9H13F4 TS C9H12 + HF TS C ~ H I ~ F - C ~+HHF I~

432 51 381 350 22 328

+

C9Hi3Cl- TS C9H12 HC1- TS

+

C9H13Cl-

C9H12

+ HCl

380 52 328

439 98 341 347 29 318

317 85 292 315 12 303

The calculationspredict that desorption of F2 and C12 is highly endothermic, 734-791 and 454-506 kJ/mol, respectively. The activation energies for desorption of X2 are greater than or equal to the overall endothermicities and are consequently higher than the activation energies for desorption of atomic F and C1 (ca. 502 and 366 kJ/mol, respectively). Atomic desorption of F and C1 would therefore be expected to dominate over molecular desorption of F2 or Cl2, as was observed experimentally in the case of F on diamond (1O0).l8 Qualitatively similar behavior occurs on the Si( 100)2x 1 surface, from which no Cl2 desorption has been detected at any Clz exposure.56 Desorption of HF is calculated to be about 20 kJ/mol more favorable energetically than that of H2 (359 and 31 1 kJ/m01),~'~ while the energetics of desorption of HC1 are less endothermic by only about 9-10 kJ/mol from those of H2. However, as noted above, the bond enthalpies of HF and HCl are underestimated by 77 kJ/mol at the MP2/6-31G* level of theory. Consequently, the energetics of desorption of HF and HCl are likely to be significantly (perhaps as much as 80 kJ/mol) more favorable than the values given in Tables 5 and 6. The calculated pairing energies for F F, C1 C1, H F, and H C1 (cfi Tables 5 and 6) are essentially the same (within 10 kJ/mol) and differ at the most by 7 kJ/mol from the pairing energy for H H determined in our recent work (64 and 117 kJ/mol at the MP2/6-31G* level for constrained and fully relaxed clusters, re~pectively).~~" This affirms that the pairing energy can be identified with the n bond strength. An analogous correspondence has been previously observed on the hydrohalogenated Ge( 100)2x 1 surface, where the pairing energies of H H, H X, and X X inferred from the desorption kinetics were all found to be within 4 kJ/mol of 11.5 kJ/mo1.26b Transition State Energies. The calculated transition state energies for C9H12 HX (X = F, C1) are presented in Table 7 and the corresponding activation energies for dissociative chemisorption and recombinative desorption in Table 8. The correlation corrected energies at the MP2/6-31G* level were calculated using the HF/6-3 1G*-optimized geometries. For adsorption of HF on the fully relaxed cluster the TS total energy has been computed also at the MP2/3-21G//MP2/3-21G level (cJ: Table 7). Activation energies for chemisorption (Ea,c)and desorption (&d) of HX at 298 K have been calculated at the MP2/6-3 1G*//6-3 lG* level of theory and are presented schematically in Figure 3. Straight lines are used to connect the transition states to the reactants and products because the intrinsic reaction coordinate (IRC) path following procedure was too time-consuming computationally and was omitted. Internal

+

+

+

+

+

+

+

+

+

-449.017 81 -809.055 62

1 3 @

450

T

AM

i

.""

Transition State C9HnfHX

300 250 200

p

150

2

18.2 20.4

350

5

s

0.212 50 0.209 10

100 50

0

Reaction Coordinate (Arbit. units) Figure 3. Relative energies (MP2/6-3 1G*//6-31G*) and activation energies for chemisorption (Ea,c)and desorption (Ea,d)reactions corresponding to the transition states in Figure 2a,b: (-M-) (1) fully relaxed C9H12 cluster 4-HF, Ea.c= 85 kJ/mol, and Ea,d = 377 Idlmol; (-A-) fully relaxed C9H12 cluster + HCl, Ea,c= 12 M/mol, and Ea,d = 315 kJ/mol. energies, AU298~,presented in Figure 3, are given as differences between the activation energies for chemisorption and desorption, E,,c - Ea,d, and differ slightly from the corresponding heats of reaction given in Tables 5 and 6 according to the equation AU298~= AH - AnRT. The calculations predict a relatively high activation energy of 85 kJ/mol for chemisorption of HF in the fully relaxed cluster. Because the H-F bond energy is underestimated at this level of theory by 78 kJ/mol, the actual activation energy for adsorption is probably larger than we calculate. This high activation energy suggests that the sticking coefficient for HF on diamond (100)2x1 will be rather low, and therefore adsorption of HF may not be important under diamond growth conditions. Taking exp(-Ea,c/RT)as a rough estimate for the reactive sticking coefficient on clean dimer sites, one predicts a value of 2 x at 1200 K, using the calculated activation energy for chemisorption. Since most dimer sites will contain chemisorbed species under diamond growth conditions and therefore be unavailable for adsorption, HF adsorption is unlikely to be important. In contrast, for adsorption of HCl the calculations predict a low activation barrier of 12 kJ/mol, even though the calculated heat of adsorption is essentially the same as for HF. Again, the actual activation energy for adsorption is probably larger than we calculate because the H-Cl bond energy is underestimated at this level of theory. Using the same rough estimates for the reactive sticking coefficient described above, one predicts a value of 0.3 for HC1 adsorption at 1200 K. Therefore, HCl adsorption may be important in C1-containing diamond growth environments, but a more refined estimate of the activation energy for adsorption would be desirable. Dissociative chemisorption of HCl has been previously observed also on Si(100)2x 124and Ge(100)2x 126with relatively high initial sticking probabilities. Due to the high observed sticking probability for HC1, a negligible activation energy for adsorption and an asymmetric four-centered transition state similar to that found here for HF has been proposed for adsorption of HC1 on Ge (100)2x 1.26 Even though we predict the heat of HC1 adsorption to be approximately 140-190 kJ/ mol more favorable on diamond than the value estimated on

Hukka et al.

4718 J. Phys. Chem., Vol. 99, No. 13, 1995

germanium,26bit seems reasonable that the activation energy for adsorption of HCl on diamond (100) would nonetheless be slightly higher than that on Ge(100). That is because the surface n bond is stronger on diamond (44-82 kJ/m01)~’~ than on Ge (21 kJ/mo1).26b Similar results have been obtained by ab initio calculations on addition of HC1 on ethylene and d i ~ i l e n e . ~ The *~ calculated barrier for HC1 addition to ethylene is ca. 127 kJ/ mol higher than that with disilene (68 kJ/mol), which has a weaker and, accordingly, more reactive n bond than ethylene. Both reactions are predicted to occur via asymmetric four-centerlike transition states, but the TS for disilene is more symmetric due to the longer Si=Si bond and is therefore likely to lead to a lower activation barrier. The activation energy for elimination of HF from the fully relaxed cluster is calculated to be 377 Wlmol. Since the HF bond energy is underestimated at this level of theory, the actual value is probably smaller. This activation energy is significantly higher than the calculated value of 249 kJ/mol for elimination of HF from ethylene46 and can be accounted for by the less stable 7~ bonds in the C9 clusters. This value is slightly higher than the experimentally estimated activation energies of 30457c and 335 kJ/mol2Iafor desorption of H2 from diamond (100)2x 1. Assuming first-order desorption and a pre-exponential factor of v = l O I 4 s-l, a TPD experiment with a heating rate of 5 K s-’ would yield a peak temperature of 1325 K for HF desorption, which lies at the upper end of the temperature ranges reported for H2 desorption on diamond (100).21a*57 The present results suggest that thermal desorption of HF is negligible under typical fluorine-containing CVD or ALE conditions, as long as steric and/or electronic repulsion effects at high coverages are small. The kinetic parameters discussed above for HF desorption would predict a rate constant of only 0.004 s-I at 1200 K. Under typical diamond growth conditions an atomic hydrogen flux of more than lo4 monolayers SKI is present.58 The activation energy for abstraction of surface F by atomic hydrogen is predicted to be sufficiently that abstraction of surface F predominates over thermal desorption of HF under typical halogen-containing growth conditions. For diamond ALE, where atomic hydrogen may not be present during the halocarbon adsorption cycle, a lower temperature range may be preferable if HF desorption (and F desorption’*) is undesirable. At 900 K, for example, the aforementioned kinetic parameters would predict a rate constant of lo-* s-], which would be negligible even for relatively slow ALE cycles. For the recombinative desorption of HC1 our calculations predict an activation energy of 315 kJ/mol. The actual value is probably smaller, since the H-C1 bond energy is underestimated at this level of theory. This value is similar to or somewhat less than the activation energy for H2 desorption. Assuming a pre-exponential factor of l O I 4 s-l with this activation energy, one estimates a TPD peak temperature of 1111 K for HCI desorption at a heating rate of 5 K s-I. This peak temperature is somewhat lower than those observed experimentally for HI desorption on diamond (100)2x 1 (117357c and 1250 K2Ia). The kinetics of desorption of H2 and HCl therefore appear not to be quite as similar to one another on diamond (100)2x 1 as they are on Si(100)2x 124159and Ge(100)2 x 1.26360 The somewhat more favorable kinetics for HCl desorption relative to HF indicates that coadsorbed H and C1 will be less stable than H and F under CVD and ALE conditions. At 1200 K, the aforementioned kinetic parameters for HC1 desorption predict a rate constant of 2 s-I, and desorption may be competitive with abstraction of C1 by incident hydrogen atoms under CVD conditions. At 900 K the predicted desorption rate

constant reduces to 5 x s-l. Based on Freedman’s results,’*however, the low stability of surface C1 (against atomic desorption, presumably) renders it unsuitable for termination of the diamond surface under ALE conditions above 400-500 K. The effect of steric andor electronic repulsion in coadsorbed H and F or C1 upon the desorption kinetics of HX will require further attention. Conclusion Our calculations predict surface C-F and C-C1 bonds that are similar to those in typical small molecules, both in terms of bond lengths and bond energies. The present results indicate that adsorbed F and C1 should be rather strongly bound to diamond surfaces, at least in the low coverage limit. The calculated second C-X bond is weaker than the first by ca. 60- 120 kJ/mol, due to formation of a weak n bond on the clean surface. This n bond energy provides a driving force for preferential pairing of surface halogens and dangling bonds, so that under typical diamond CVD conditions many or most dangling bonds are likely to be paired on dimers. The calculated pairing energies for F 4- F, C1 C1, H F, and H C1 are very nearly equal to that for H f H, affirming the identification of the pairing energy with the n bond strength. Lattice constraints strain the dimer bond and reduce the n bond strength considerably, but have little effect on the first C-X bonds. A comparison of the calculated C-X bond energies with experimental measurements of the stability of adsorbed F and C1 leads to the conclusion that the surface C-X bond strength is greatly reduced at monolayer coverage, due to steric and/or electronic repulsion effects that cannot be adequately included in small cluster models. The transition state calculations suggest that HX species can chemisorb dissociatively on vacant surface dimers on diamond (100)2x 1, HF via a synchronous four-centered transition state, and HCl via a two-centered (Cl.*H C ) nonconcerted electrophilic addition. HF adsorption is likely to be negligible under halogen-containing CVD conditions, due to a high activation energy, whereas HC1 adsorption is predicted to be more favorable and might be important. The activation energy for desorption of HF is similar to that for desorption of H2 and is high enough that thermal desorption of HF is unlikely to be important under fluorine-containing CVD or ALE growth conditions. Desorption of HC1 is somewhat more facile and may be competitive with abstraction by atomic hydrogen or atomic desorption. Careful treatment of electron correlation and of lattice constraints is necessary to obtain reliable results. The present work yields upper and lower bounds on the dimer bond lengths and C-X bond energies, but larger clusters or slabs will be needed for fully converged results and also to take account of steric and electronic repulsion effects that appear to be very important at halogen coverages approaching a monolayer.

+

+

+

Acknowledgment. The authors want to acknowledge Dr. W. J. Hehre for his helpful comments. M.P.D. acknowledges financial support from the National Science Foundation (Grant CHE-9214328) and the Office of Naval Research. References and Notes (1) (a) Angus, J. C.; Wang, Y.; Sunkara, M. Annu. Rev. Mater. Sci. 1991,21,221. (b) Butler, J. E.; Woodin, R. L. Philos. Trans. R. Soc. London, A 1993,342, 209. (2) (a) Tsuno, T.; Imai, T.; Nishibayashi, Y.; Hamada, K.; Fujimori, N. Jpn. J . Appl. Phys. 1991,30, 1063.(b) Busmann, H.-G.; ZimmermannEdling, W.; Sprang, H.; Gtintherodt, H.-J.; Hertel, I. V. Diamond Relar. Mater. 1992,1, 979.( c ) Maguire, H.G.; Kamo, M.; Lang, H. P.; Meyer,

Chemisorption of F, C1, HF, and HCl on Diamond E.; Weissendanger, K.; Guntherodt, H.-P. Diamond Relat. Mater. 1992, 1, 634. (d) Sutcu, L. F.; Chu, C. J.; Thompson, M. S . ; Hauge, R. H.; Margrave, J. L.; D’Evelvn. M. P. J. Auul. Phvs. 1992. 71. 5930. (3) Suntola, T. Mater. yci. Rei. 1989, 4, 265. (4) (a) Hukka, T. I.; Rawles, R. E.; D’Evelyn, M. P. Thin Solid Films 1993, 225, 212. (b) Hukka, T. I.; Rawles, R. E.; D’Evelyn, M. P. Mater. Res. Soc. Symp. Proc. 1993, 282, 671. (5) (a) Patterson, D. E.; Chu, C. J.; Bai, B. J.; Xiao, Z. L.; Komplin, N. J.; Hauge, R. H.; Margrave, J. L. Diamond Relat. Mater. 1992, 1, 768. (b) Patterson, D. E.; Bai, B. J.; Chu, C. J.; Hauge, R. H.; Margrave, J. L. In New Diamond Science and Technology, Proceedings of the 2nd International Conference on New Diamond Science and Technology, Materials Research Society Symposium Proceedings; Messier, R., Glass, J. T., Butler, J., Roy, R., Eds.; Materials Research Society: Pittsburgh, PA, 1991; p 433. 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