Effect of a NH Coadsorbate on the CH3 (or CH2) Adsorption to a

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J. Phys. Chem. C 2009, 113, 19891–19896

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Effect of a NH Coadsorbate on the CH3 (or CH2) Adsorption to a Surface Step on Diamond (100) T. Van Regemorter and K. Larsson* Department of Materials Chemistry, Angstrom Laboratory, Uppsala UniVersity, Box 538, SE-751 21 Uppsala, Sweden ReceiVed: January 29, 2009; ReVised Manuscript ReceiVed: September 15, 2009

This study reports upon the effect of a coadsorbed NH species on the binding of CH3 (or CH2) next to a step edge on the H-terminated (100)-2×1 surface, using density functional theory (DFT). It is a thermodynamic study where the CH3 (or CH2) species is assumed to be either directly chemisorbed to, or surface migrating to, the final position at the edge. Two types of frequently observed monatomic step edges on the (100) surface, have here been considered. For one of these edges, of type SA, the carbon dimer row on the lower terrace is perpendicular to the step. While for step type SB, the lower terrace dimer row is parallel with the step edge. The adsorption energy for CH3 (or CH2), adsorbed next to these steps and in the presence of an NH coadsorbate, were calculated and compared. Three different positions of the NH coadsorbate where chosen, in a neighboring position at the lower or higher terrace. Next to step SA, the CH3 adsorption energy was not found to be significantly affected by the presence of NH in any of the three positions considered. However, the CH2 adsorption reaction was observed to be strongly improved in the presence of NH by the formation of a new interadsorbate C-N bond. The situation was found to be different for step type SB. While the CH3 adsorption reaction was not significantly affected by the presence of NH further away from the chemisorbed CH3 species, the formation of a new C-N bond between the surface radical C and the closest NH coadsorbate, prior to adsorption, was found to seriously hinder the chemisorption. On the other hand, the CH2 adsorption reaction was found to be significantly favored by the presence of NH (for all three positions considered). The same trend in energetic results is expected for the situation with surface migration (instead of a direct adsorption) of CH3 (or CH2) toward to step edge. 1. Introduction A high-quality growth of diamonds using chemical vapor deposition (CVD) is of greatest importance for many applications (e.g., in microelectronics).1 It has experimentally been shown that a smooth surface can be more easily obtained for a (100) diamond surface.2 It is also known that such a surface requires a so-called step-flow growth mechanism, which implies a preferential growth by the extension of steps.3-5 A better understanding of the partial growth reactions occurring at a step is then crucial for the growth of a high quality diamond with a smooth surface. A parameter which has been observed to largely influence the diamond CVD growth is the addition of nitrogen in the reactant gas mixture. For low N concentration, it is well-known experimentally that the growth rate will increase with the N/C ratio, together with a significant change of the final surface morphology.6-8 However, the growth rate has been observed to decrease with a concurrent degradation of surface morphology at high N concentration.9,10 While this effect has been largely described experimentally, the underlying reason for such a strong effect is far from being well understood. Within this topic, only few theoretical studies have been performed which suggest different explanations to the experimental observations. In a first approach, substitutional N was proposed by Frauenheim et al. to act as a catalyst for the modified diamond surface reactivity (through an electron transfer process).11 However, further investigations performed by the present authors have shown that * Corresponding author.

substitutional N might be more related to the negative effect observed at high N concentration.12,13 Substitutional N was observed to generally increase the activation barriers for some key reaction steps and thereby deteriorate the reaction kinetics for growth. In addition, β-scission rearrangements which may generate defects in the diamond lattice was also observed. Another explanation proposed by Butler et al. relates the increase of the diamond (111) growth rate by the presence of adsorbed CN on the surface.14 Within previous studies on the diamond CVD growth mechanism, the same authors proposed the nucleation of a new carbon layer as the rate-limiting step for growth.15 They came to the conclusion that the presence of CN will facilitate the nucleation step, and thereby increase the growth rate. Unfortunately, this mechanism is specific for the (111) growth process and cannot be easily transferred to the growth of the (100) surface. The diamond CVD growth mechanism constitutes a complex and dynamic set of elementary reaction steps on the surface.16 The reaction between gaseous hydrogen radicals (H) and the diamond surface is one of the most important steps. In fact, it is made of several elementary reaction types (i.e., abstraction and adsorption). The H species is especially crucial for the abstraction of an adsorbed H (with the formation of H2 molecules) in order to form a surface carbon radical. The formation of these surface radicals are necessary for the adsorption of gaseous growth species to take place, here considered as the CH3 radical. Further removal of H from the adsorbed methyl species has to take place to form an adsorbed CH2, being an important species in an assumed step-flow growth mecha-

10.1021/jp900853a CCC: $40.75  2009 American Chemical Society Published on Web 10/22/2009

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Regemorter and Larsson

Figure 1. Models used for the SA (a) and SB (b) stepped diamond (100) surface.

nism: (i) adsorption of the growth species on a terrace, (ii) migration on the surface, and (iii) incorporation into the lattice at a step by the formation of a second C-C bond.17-20 However, the possibility for a carbonaceous species to migrate on the diamond surface is still under debate. An alternative mechanism has also been proposed for the observed step-flow growth process. Within that mechanism, CH2 adsorbed on a flat terrace is considered to be more easily etched away when compared to the situation with CH2 adsorbed next to a step edge.21 Even if both mechanisms present different reaction pathways from the level of CH3 adsorption, they agree that the growth finally occurs by the incorporation of CH2 into a step edge on a diamond surface. The purpose of the present study was to carefully study the influence of a coadsorbed nitrogen species (NH) on the adsorption of CH3 (or CH2) species next to step edge SA and SB on the diamond (100)-2×1 surface. The numerical values of adsorption energies, for the various NH positions and steps, were thereby regarded as measures of the thermodynamic driving force for the different adsorption scenarios. Density functional theory (DFT) methods were used to calculate the structural geometries and adsorption energies. In an ordinary chemical vapor deposition setup, nitrogen-based adsorbates with various numbers of H ligands are expected to be found on the growing diamond surface. The very high gas-phase content of hydrogen in the reactor will cause a dynamic set of surface reactions involving both H adsorption and H abstraction from the adsorbates. Hence, the formation of NH adsorbates is considered to be induced by an H abstraction reaction from an adsorbed NH2 species. The NH2 adsorbate has been observed in a recent study by the present authors to induce major sterical repulsions in the process of CH3 (or CH2) adsorption.22 On the other hand, the radical NH species (as a coadsorbate) are known from organic synthesis to play a significant role within radical reactions.23 Hence, the NH species has been chosen to be a plausible coadsorbate in the present study. Moreover, there are two possible types of monatomic steps on a diamond (100)2×1 surface, which both delimits the terraces.4 They are labeled type SA and SB and are both considered in the present study. The dimerization direction on the lower terrace for step type SA is perpendicular to the step edge, and the dimerization direction on the lower terrace for step type SB is parallel with the step edge (see Figure 1).24

functional where the exchange part is generated by B88,26 and the correlation part is generated with the LYP functional27). A mesh of (2×2×1) k-points was generated using the MonkhorstPack scheme,28 and the SCF density convergence was set to 1.00 × 10-6. The numerical basis set of choice included polarization p-functions on all hydrogen atoms, and d-functions on all carbon and nitrogen atoms. Two models have been used to represent the SA and SB steps on the (100)-2×1 H-terminated diamond surface (see Figure 1a and 1b). Only a smaller part of the upper terraces in the steps have here been found adequate to use since it is only the effect of the vertical step edges, in combination with NH coadsorbates, that has been of major interest to study in the present investigation. The unit-cell has a length of 10.06 Å in the x- and y-directions, and 16.65 Å in the z-direction. Due to the infinite repetition of this unit-cell in three directions, the diamond surface is represented by an infinite slab in the x- and y-directions with a thickness of 6.65 Å corresponding to seven atomic carbon layers. The two lowest carbon layers were frozen to simulate the diamond bulk, and all dangling bonds were terminated with H. The vacuum layer was 10 Å which has earlier been found to be adequate to avoid interactions between two repeating slabs in the z-direction.23 The optimized structural geometries for all models used in the present study were obtained using the BFGS algorithm.29 The minima have been localized by starting from different initial structural geometries. The adsorption energies CH3 and CH2 (∆Eads) have been calculated using the following equation:

∆Εads ) Ε(D-CΗΧ) - Ε(D-Rad) - Ε(CHΧ)

(1)

where E(D-CHX) and E(D-Rad) are the energies for the diamond surface with CHX (with X ) 2 or 3) adsorbed to it, or with a single nonterminated (i.e., radical) surface carbon atom. E(CHX) is the energy for a gaseous CHX (with X ) 2 or 3) species. The relative stability of two surfaces is also interesting to investigate since it will complete the information obtained by the calculated adsorption energies. Examples are systems where the only difference is the position of the coadsorbed NH species. It should here be stressed that this energetic difference needs to be calculated between two surface systems which present exactly the same number of atoms. The relative energy for two different surfaces E(D-1) and E(D-2) (∆Erel) have thus been calculated using the following equation:

2. Models and Methods The present investigation was based on a density functional theory (DFT) method using the program package DMol3 from Accelrys, Inc.25 The calculations were performed under periodic boundary conditions with a spin-polarized general gradient approximation (GGA) using the BLYP functional (a hybrid

∆Εrel ) Ε(D-1) - Ε(D-2)

(2)

3. Results A. General. Diamond growth has experimentally been shown to predominantly take place at a SB step edge (when compared

Effect of a NH Coadsorbate

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Figure 2. The NH coadsorbate in positions A1 (a), A2 (b), and A3 (c) on a SA stepped surface, and in position B1 (d), B2 (e), and B3 (f) on a SB stepped surface. The surface radical C onto which the CH2 or CH3 adsorbs is highlighted by a circle.

to a SA step edge).5 The SB step edge presents more irregularities, with also some extension of single row dimers.30 This difference in behavior has been correlated theoretically with a more pronounced reactivity of the SB step. This reactivity is assumed to be induced by the presence of terminating H species at the lower step edge, which is not present for the SA step (see Figure 1). The removal of this specific H species (e.g., by a gas-phase H abstraction reaction) will result in the formation of radical C atoms at the step edge, which thereby facilitates its extension. This radical carbon has been calculated to be more stable compared to a radical C on a diamond terrace, and hence the driving force for the formation of this carbon radical is much larger.31-33 The extension of the dimer row, being another expression for growth, will hence be facilitated by both (i) the possibility for a strong interaction between the C-containing adsorbate and the vertical step edge, and (ii) the strong bond formed by the C-containing species (such as CH2) when adsorbed onto the diamond terrace. It is again worth noticing that this position of, for example, CH2 may either be the result of a surface migration or a direct adsorption. For both SA and SB steps on the diamond (100) surface, the NH coadsorbate has been positioned at three different surface sites (see Figure 2) close to the surface radical carbon, onto which CH3 (or CH2) will become adsorbed. The choice of these positions is based on the possibility for a more pronounced chemical and/or structural interaction between the two resulting coadsorbates, NH and CH3 (or CH2). These NH positions are labeled A1, A2, and A3 for the SA stepped surface (see Figures 2a-c). Correspondingly, the positions for the SB stepped surface are labeled B1, B2, and B3 (see Figures 2d-f). B. Stepped Surface SA. CH3 Adsorption. The CH3 adsorption energies calculated for the SA stepped surfaces are presented in Table 1. For the radical surfaces, prior to the CH3 adsorption reactions, the presence of the radical coadsorbate NH and the radical C adsorption site implies two possible electronic states

TABLE 1: CH3 and CH2 Adsorption Energies Calculated without Any Coadsorbed Dopant and for the Three Different NH Positions (A1, A2, and A3) on the SA Stepped Surface ∆Eads (kJ/mol)

no dopant

A1

A2

A3

CH3 CH2

-329 -396

-304 -638

-325 -568

-324 -583

for the system (a multiplicity of 1 or 3). To calculate the CH3 adsorption energies, only the most stable surface structures are considered as reactant surfaces. The singlet electronic state is considered for NH position A1, and the triplet state is considered for A2 and A3. From Table 1, it can be observed that the CH3 adsorption energy is not affected by the presence of a coadsorbed NH species in position A2 or A3 (-325 vs -324 kJ/mol, to be compared with -329 kJ/mol for the situation without NH). With NH in position A1, the adsorption reaction appears to be slightly disfavored (about 26 kJ/mol) compared to the adsorption on a fully hydrogenated stepped surface. In order to investigate the possible presence of interactions with the coadsorbed dopant, a geometrical and electronic structural analysis of the surface before and after adsorption has been performed. For NH in position A2 and A3, no significant interaction could be observed between the radical dopant and the surface radical carbon, prior to CH3 adsorption, or the adsorbed CH3, after the reaction. This is consistent with the lack of adsorption energy changes in the presence of NH. The situation is different when NH is placed in position A1, for which a small change can be observed in the CH3 adsorption reaction energy. While a geometrical and electronic structural analysis of the surface did not show any interaction between NH and CH3 after the reaction, a significant interaction on the surface between NH and the surface radical C, prior to adsorption, could be detected. For the latter situation, and under the assumption of the most stable

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singlet state, the presence of a favorable interaction has been observed by a shortening of the N-C distance (2.46 Å). In addition, a structural analysis indicates that the interaction between NH* and the surface radical C is causing a significant elongation of the surface C-C dimer bond (1.97 Å). The weak coadsorbate interaction, together with the dimer bond lengthening, will most probably explain the rather limited CH3 adsorption energy loss induced by NH in position A1. For NH in position A2 and A3, a significant surface C-C elongation could also be observed (1.74 and 1.70 Å vs 1.64 for the dimer saturated with two H atoms). These elongations were not that pronounced as was the situation with NH in position A1, and they will therefore only have the capability to cause a minor decrease in CH3 adsorption energy. It is worth noticing that the influence of NH on the CH3 adsorption next to a SA stepped surface is comparable to the situation on a flat terrace, studied by the authors within a previous paper.23 Depending on the relative position of NH on the surface, the adsorption energy of CH3 close to a coadsorbed NH (and in a similar position as described here) was in between 355 and 375 kJ/mol. From this comparison, it can be concluded that the effect of NH next to a SA step on the CH3 adsorption reaction is rather similar to the one observed for a flat terrace. The smaller values reported in the present study is most probably caused by the sterical hindrances induced by the step itself. CH2 Adsorption. As can be seen in Table 1, the CH2 adsorption energy is significantly favored by the presence of a coadsorbed NH species (-638 (A1), -568 (A2), and -583 (A3) kJ/mol, to be compared with -396 kJ/mol for the situation with no NH coadsorbate). A careful structural geometry analysis of the surface can explain this behavior. The analysis of the radical surface prior to CH2 adsorption, as presented in the previous section, showed that a coadsorbed NH is not strongly affecting the surface energetic stability. The observed large energetic changes are instead most probably originating from a surface stabilization that takes place after the adsorption reaction. For all three NH positions on the surface, a rather short distance between N (in NH) and C (in CH2) can be observed (the bond lengths are 1.55, 1.58, and 1.57 Å for A1, A2, and A3, respectively). This rather short distance, being close to the N-C bond length reported for an isolated molecule (around 1.47 Å34), clearly indicates the formation of a new C-N bond between the two adsorbates. This new bond will strongly stabilize the final surface structure and, hence, energetically favor the adsorption reaction. As can be seen in Table 1, there is a strong correlation observed between these bond lengths and CH2 adsorption energies (-638, -567, and -583 kJ/mol, respectively). The significantly larger adsorption energy calculated for NH in position A1 is further supported by studying the relative energies (∆Erel) for the surface structures with an adsorbed CH2 and with NH in three different positions. It is thereby observed that the surfaces with NH in positions A2 and A3 are 73 and 57 kJ/mol less stable compared to the surface with NH in position A1. This finding implies that the N-C bond formation will improve the surface stabilization with NH in position A1, which is to be compared with the A2 and A3 situations. For these latter situations, the lower N-C interaction possibilities is most probably due to the somewhat longer N-C bond lengths: 0.3 (or 0.2 Å) longer for NH in position A2 (or A3) compared to the position A1. C. Stepped Surface SB. CH3 Adsorption. The CH3 adsorption energies (∆Eads) calculated for the SB stepped diamond (100) surfaces are presented in Table 2. As was the situation for the

Regemorter and Larsson TABLE 2: CH3 and CH2 Adsorption Energies Calculated for the Three Different NH Positions (B1, B2, and B3) on the SB Stepped Surface ∆Eads (kJ/mol)

no dopant

B1

B2

B3

CH3 CH2

-289 -379

-265 -610

-291 -570

69 -448

SA stepped surface, two possible electronic states are present for the radical surfaces prior to the CH3 adsorption reactions: a multiplicity of either 1 or 3. Only the electronic state that gives the most stable surface structures will be considered here as reactant surfaces. For the SB stepped surface, the triplet electronic state is thereby considered for NH in position B1 and B2, and the singlet state is considered for B3. From Tables 1 and 2 it can be concluded that, without any coadsorbed NH species, CH3 adsorption is slightly less favored next to a SB step edge than next to a SA step (-289 vs -329 kJ/mol). This difference in adsorption energy can be explained by a larger sterical repulsion between H on the step edge and the CH3 adsorbate for step type SB. This repulsive effect can be visualized by the shorter distance between (C in CH3) and the closest H on the neighboring step edge. This distance is 2.04 Å for the SB step and 2.93 Å for SA. This conclusion is confirmed by studying the angle formed by the adsorbed CH3 and the two surface C’s constituting the dimer (ν(CH3-C-C)), which should be closer to a tetrahedral angel (109.4°) for a situation with no sterical hindrances. For the SA and SB stepped surfaces, this angle is calculated to be 108.4° and 105.9°, respectively. Hence, the smaller value for the SB stepped surfaces is most probably caused by sterical repulsions induced by step SB. The CH3 adsorption energy is not significantly affected by the presence of a coadsorbed NH species in position B1 and B2 (-265 vs -291 kJ/mol, to be compared with -289 kJ/mol for the situation with no NH adsorbates). However, the CH3 adsorption reaction becomes strongly disfavored with NH in position B3 (69 kJ/mol). This behavior can be easily explained by performing a careful structural analysis of the surfaces. For NH in position B1 and B2, the surface geometrical structure did not present any significant stabilization interaction between the radical dopant and the surface radical carbon prior to adsorption. This was also the situation for the radical dopant and the adsorbed CH3 species (i.e., after the adsorption reaction). These results are consistent with the lack of variation in CH3 adsorption energy for the situations with NH binding to either B1 or B2 positions. With NH in position B3, the analysis of the surface structure prior to CH3 adsorption showed a significant structural difference compared to the other NH positions. As observed in Figure 3, a new bond is formed between N (in NH) and the surface radical carbon (N-C2). This bond formation is confirmed by the rather short bond length calculated for N-C2 (1.54 Å), which is to be compared with the length of an N-C bond generally reported in the literature (around 1.47 Å34). The formation of this new bond will, hence, strongly stabilize the surface structure before the adsorption reaction (about 225 kJ/ mol more stable compared to the surface with NH in position B1), which explains the calculated endothermic adsorption energy. The formation of this new bond will also induce structural constraints. Both N-C1 (1.59 Å) and N-C2 (1.54 Å) bonds are both short, but the N-C1 bond is somewhat longer compared to an N-C bond generally reported for an isolated molecule (1.47 Å). The C-C1 bond within the carbon dimer is also observed to be longer (1.82 Å) compared to a neighboring

Effect of a NH Coadsorbate

Figure 3. Representation of the surface structure for a B3 situation on a SB stepped surface.

H-terminated C-C dimer (1.60 Å). For NH in position B1 and B2, a C-C elongation induced by the presence of the radical nitrogen could also be observed (1.65 and 1.74 Å vs 1.60 for the H-terminated dimer). The present observations concerning the effect of a coadsorbed NH on the CH3 adsorption reaction next to a SB step edge can also here be compared with a recent study by the present authors (see section B: Stepped Surface SA).23 From this comparison, it can be concluded that the effect of NH in position B1 and B2 on the CH3 adsorption reaction is rather similar to the one observed for a flat terrace. The minor energetic changes observed can be explained by sterical hindrances at the step. However, the large negative effect that is observed here with NH in position B3, and in the presence of step SB, was not observed for a flat terrace. CH2 Adsorption. As can be seen in Table 2, the CH2 adsorption reaction next to a SB step edge is significantly favored by the presence of a coadsorbed NH species (-610, -570, and -448 kJ/mol for positions B1, B2, and B3, to be compared with -379 kJ/mol for the situations without NH). These large variations in adsorption energies can be explained by performing a structural analysis of the surface after the CH2 adsorption reaction. For NH in position B1, the adsorption reaction of CH2 is strongly favored by the formation of a new bond between N (in NH) and C (in CH2). Similar to the effect observed for the SA stepped surface, this bond formation strongly stabilizes the final surface structure which energetically favors the adsorption reaction. With NH in position B2, the positive effect observed for the CH2 adsorption reaction is explained by the presence of a large degree of surface reconstruction. The large distance (>3.4 Å) between the radical N (in NH) and the radical C (in CH2) hinders the formation of an N-C bond. From the geometry optimization procedure, the surface stabilization is observed to take place through another pathway. As shown in Figure 4, an H atom is transferred from the SB step edge toward the CH2 adsorbate, forming an adsorbed CH3. One C-C bond within the step is thereafter broken, inducing the formation of a new C-C bond, and the C-N bond becomes a double bond. The improvement in CH2 adsorption energy observed for NH in position B3 can be explained by analyzing the surface structure after adsorption. It is shown in Figure 5 how the CH2 adsorption induces the breakage of the C-C dimer bond and becomes incorporated therein. Compared to the fully hydrogenated surface, the formation of these new bonds explains the significant adsorption energy improvement. 4. Summary Within this study, the energetic effect of a coadsorbed NH species on the CH3 (or CH2) adsorption reaction next to a step

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Figure 4. Surface reconstruction observed with NH in position B2 and CH2 adsorbed next to a SB step edge.

Figure 5. Surface structure after the CH2 adsorption with NH in position B3.

edge on the (100)-2×1 surface has been theoretically investigated using density functional theory (DFT). The numerical values of the adsorption energies, for the various NH positions and steps, can thereby be regarded as measures of the thermodynamic driving force for the different adsorption scenarios. The two different types of monatomic step edges (SA and SB) that are frequently found on the diamond (100) surface have been considered here. Next to a step SA type, the CH3 adsorption energy was, compared to the undoped situation, observed to not be significantly affected by the presence of NH in any of the three positions considered. However, an analysis of the surface prior to the adsorption reaction indicates the presence of an interaction between N (in NH) and the surface radical C with NH in position. The CH2 adsorption reaction was observed to be strongly favored by the presence of NH because of the formation of a new bond between N (in NH) and C (in CH2). The observed energetic changes are then generally induced solely by the presence of the NH radical. Next to a step SB type, the CH3 adsorption reaction was, with one exception, observed to not be significantly affected by the presence of NH (compared to the undoped situation). With NH in position B3, a bond was observed to be formed between N (in NH) and the surface radical carbon which made the following CH3 adsorption reaction endothermic. The CH2 adsorption reaction was observed to be always energetically favored by the presence of NH. However, the nature of this effect is dependent on the position of the dopant. In position B1, the reaction was enhanced by the formation of a new bond between N (in NH) and C (in CH2). This bond formation cannot take place with NH in position B2 because of the large distance between NH and CH2. The system was instead observed to relax by large structural rearrangements. After the CH2 adsorption, one H from the step edge was transferred toward the adsorbed CH2 (forming a CH3 adsorbate) and a C-N double bond was

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formed. With NH in position B3, the C-N bond formed prior to the CH2 adsorption was found to induce the structural possibility for the insertion of CH2 within the C-C bond. The effect of NH on the adsorption reactions seems, hence, to be more pronounced next to a SB step edge than next to a SA step edge. Acknowledgment. This work was supported by the European Project RTN DRIVE from the 6th Framework Program (no. MRTN-CT-2004-512224). The results were generated using DMol3 within the program package Material Studio, developed by Accelrys Inc., San Diego. References and Notes (1) Achard, J.; Silva, F.; Tallaire, A.; Bonnin, X.; Lombardi, G.; Hassouni, K.; Gicquel, A. J. Phys. D: Appl. Phys. 2007, 40, 6175–6188. (2) Shiomi, H.; Tanabe, K.; Nishibayashi, Y.; Fujimori, N. Jpn. J. Appl. Phys. 1990, 29, 34–40. (3) van Enckevort, W. J. P.; Janssen, G.; Vollenberg, W.; Schermer, J. J.; Giling, L. J.; Seal, M. Diamond Relat. Mater. 1993, 2, 997–1003. (4) Tsuno, T.; Tomikawa, T.; Shikata, S.; Imai, T.; Fujimori, N. Appl. Phys. Lett. 1994, 64, 572–574. (5) Kawarada, H.; Sasaki, H.; Sato, A. Phys. ReV. B 1995, 52, 11351– 11358. (6) Locher, R.; Wild, C.; Herres, N.; Behr, D.; Koidl, P. Appl. Phys. Lett. 1994, 65, 34–36. (7) Jin, S.; Moustakas, T. D. Appl. Phys. Lett. 1994, 65, 403–405. (8) Achard, J.; Silva, F.; Brinza, O.; Tallaire, A.; Gicquel, A. Diamond Relat. Mater. 2007, 16, 685–689. (9) Silva, F.; Gicquel, A. Electrochem. Soc. 1998, 97, 99–125. (10) Benedic, F.; Belmahi, M.; Elmazria, O.; Assouar, M. B.; Fundenberger, J.-J.; Alnot, P. Surf. Coat. Technol. 2003, 176, 37–49. (11) Frauenheim, Th.; Jungnickel, G.; Sitch, P.; Kaukonen, M.; Weich, F.; Widany, J.; Porezag, D. Diamond Relat. Mater. 1998, 7, 348–355. (12) Van Regemorter, T.; Larsson, K. Chem. Vap. Deposition 2008, 14, 224–231. (13) Van Regemorter, T.; Larsson, K. J. Phys. Chem A 2009, 113, 3274– 3284.

Regemorter and Larsson (14) Butler, J. E.; Oleynik, I. Philos. Trans. R. Soc. 2008, 366, 295– 311. (15) Battaile, C. C.; Srolovitz, D. J.; Butler, J. E. J. Appl. Phys. 1997, 82, 6293–6300. (16) Goodwin, D. G.; Butler, J. E. Theory of diamond chemical vapor deposition. In Handbook of industrial diamonds and diamond films; Prelas G. P. M. A., Bigelow, L. K., Eds.; Marcel Dekker, Inc.: New York, 1997; pp 527-581. (17) Frenklach, M.; Skokov, S. J. Phys. Chem. B 1997, 101, 3025– 3036. (18) Netto, A.; Frenklach, M. Diamond Relat. Mater. 2005, 14, 1630– 1646. (19) Larsson, K.; Carlsson, J.-O. Phys. ReV B 1999, 59, 8315–8322. (20) Larsson, K.; Carlsson, J.-O. Phys. Status Solidi A 2001, 186, 319– 330. (21) Battaile, C. C.; Srolovitz, D.; Oleinik, I. I.; Pettifor, D. G.; Sutton, A. P.; Harris, S. J.; Butler, J. E. J. Chem. Phys. 1999, 111, 4291–4299. (22) Van Regemorter, T.; Larsson, K. J. Phys. Chem. A 2008, 112, 5429– 5435. (23) Miyabe, H.; Ueda, M.; Naito, T. Synlett 2004, 7, 1140–1157. (24) Chadi, D. J. Phys. ReV. Lett. 1987, 59, 1691–1694. (25) (a) Delley, B. J. Chem. Phys. 1990, 92, 508–517. (b) Delley, B. J. Chem. Phys. 2000, 113, 7756–7764. (26) Becke, A. D. Phys. ReV. A 1988, 38, 3098–3100. (27) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B 1988, 37, 785–789. (28) Monkhorst, H. J.; Pack, J. D. Phys. ReV. B 1976, 13, 5188–5192. (29) Pfrommer, B. G.; Coˆte´, M.; Louie, S. G.; Cohen, M. L. J. Comput. Phys. 1997, 131, 233–240. (30) Tsuno, T.; Imai, T.; Nishibayashi, Y.; Hamada, K.; Fujimori, N. Jpn. J. Appl. Phys. 1991, 30, 1063–1066. (31) Tamura, H.; Zhou, H.; Hirano, Y.; Takami, S.; Kubo, M.; Belosludov, R. V.; Miyamoto, A.; Imamura, A.; Gamo, M. N.; Ando, T. Phys. ReV. B 2000, 62, 16995–17003. (32) Zhu, M.; Hauge, R. H.; Margrave, J. L.; D’Evelyn, M. P. Proc. Electrochem. Soc. 1993, 93-17, 138–145. (33) Skokov, S.; Weiner, B.; Frenklach, M.; Frauenheim, T.; Sternberg, M. Phys. ReV. B 1995, 52, 5426–5432. (34) Aylward, G. Findlay, T. SI Chemical Data, 3rd ed.; John Wiley & Sons: Brisbane, New York, Chichester, Toronto and Singapore, 1994.

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