- Email: [email protected]
Surface properties of diamond-like amorphous carbon
Journal of Non-Crystalline Solids 227–230 Ž1998. 597–601
Surface properties of diamond-like amorphous carbon P.C. Kelires
)
Physics Department, UniÕersity of Crete, P.O. Box 2208, 710 03 Heraklion, Crete, Greece Foundation for Research and Technology-Hellas ŽFORTH., P.O. Box 1527, 711 10 Heraklion, Crete, Greece
Abstract Monte Carlo simulations show that the surface in tetrahedral amorphous carbon networks reconstructs in a graphite-like manner. The top surface layer is found to be largely composed of distorted sixfold-ring patterns of sp 2 sites. Stresses at the surface are tensile, while they vary with depth in a complex oscillatory way. Defect formation energies close to the surface are much less than in the crystal. q 1998 Elsevier Science B.V. All rights reserved. Keywords: Amorphous carbon; Monte Carlo simulation; sp 2 sites
1. Introduction An effort has been devoted in recent years to understand the properties of tetrahedral diamond-like amorphous carbon Žta-C., both at the fundamental and practical level. Despite the interest, theoretical studies have been restricted to the bulk system. Although this information is useful, our comprehension of the physical processes related to this material will be incomplete if we do not address the surface properties as well. The growth mechanisms, for example, are basically determined by the near-surface structure. Since the overall bulk phase of the system, which on the average determines the electronic properties, results from the freezing of sequentially deposited material, the knowledge of the exact surface microstructure is important. In this paper, we investigate the role of the surface topology in affecting the properties of ta-C. We )
Corresponding author. Fax: q30-811 394 201; e-mail: [email protected]
are mostly interested in two issues, both related to the growth mechanism. The first concerns the distribution of atomic leÕel stresses in the growing surface region. It was proposed earlier w1x that these stresses, which are indicative of the local rigidity of the network, determine the hybridization of a site in amorphous carbon. Local tensile conditions favor the formation of sp 2 sites, while compressive conditions lead, most probably, to sp 3 sites. The cause and effect of this relationship is still a matter of debate. The second issue is related to subplantation processes believed to produce densification and compressive stress generation and to promote sp 3 bonding as well. One is interested to know how the amorphous network responds to the incorporation of incoming C atoms during deposition. Subplantation models have been proposed by Robertson w2x and Davis w3x. In the following, we outline the method used in our calculations, we give the results regarding the surface microstructure, atomic stresses and defect energies, and discuss the implications of these results with respect to possible growth models.
0022-3093r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 Ž 9 8 . 0 0 1 4 3 - 4
598
P.C. Keliresr Journal of Non-Crystalline Solids 227–230 (1998) 597–601
2. Theoretical methods The investigations are based on Monte Carlo ŽMC. simulations within the empirical potential approach. Two types of cells are used. One is a standing free slab geometry with 480 atoms periodically repeated in two dimensions Žsix cells generated.. The other type of cell has 550 atoms with the lateral dimensions constrained to be those of the diamond lattice, while the vertical dimension is allowed to vary Žfour cells generated.. Results from these two types of cells give a full account of the surface properties. The amorphous networks are MC generated by quenching the liquid under pressure within the constant pressure–temperature Ž N, P, T . ensemble, as done previously w1,4x. The liquid is equilibrated at ; 9000 K and then cooled to 300 K under various pressures up to 300 GPa and cooling rates up to ; 25 ŽMC steps.ratom-K. After removing the pressure, the cell density is equilibrated and the atomic positions are thoroughly relaxed to avoid local energy minima due to artificial surface geometries. The empirical potential of Tersoff w5x is used to model the interactions. It is tested extensively and found to describe reasonably well the properties of ta-C. Though in principle less accurate than ab initio methods, this approach is appealing because it permits extraction of atomic leÕel properties, otherwise inaccessible. This kind of analysis already gave valuable information, generally confirmed by experiment, regarding the metastability w4x and elastic properties w1x of ta-C networks. The potential also describes strain conditions quite well, as recent work by Kelires and Kaxiras w6x shows.
3. Results 3.1. Surface microstructure The resulting microstructure Žaverage atomic positions. in a typical 550-atom cell constrained on a diamond lattice is shown in Fig. 1. Atoms are indicated according to their coordination. The average coordination, z, of this cell is 3.6, so the bulk regions of the film, especially close to the interface with the substrate, are sp 3 rich. Note the increased
Fig. 1. Atomic positions in a 550-atom cell, constrained on a diamond substrate, projected on a vertical plane along the nonperiodic direction of the cell. Filled and open circles denote sp 2 and sp 3 atoms, respectively.
ordering Žreduced degree of amorphicity. as we approach the interface, which is attributed to the lattice match of the film with the substrate. ŽThis ordering does not occur when there is a lattice mismatch, as in the case of a-C on Si substrates.. The sp 2 sites in the film are largely clustered Žpairs and small chains.. Only few sp 2 sites are isolated. The degree of clustering increases as we approach the surface region, which at the top is enhanced with threefold coordinated atoms. Such inhomogeneous distribution of sp 2 atoms as a function of depth from the surface Žor the interface. is observed in every cell studied, so we may conclude that this is a generic behavior of ta-C networks. Further details are given in a top view of the surface structure, illustrated in Fig. 2 Žonly top atoms are shown., for two characteristic cases: Ža. a cell with z , 3.5 and Žb. a cell with z , 3.75. The enrichment of the top layer with sp 2 atoms is profound, especially for the more diamond-like film in panel Žb., in which the bulk content of sp 2 sites is only ; 25%. Perhaps, the most interesting finding is the specific reconstruction of the amorphous surface in the form of distorted sixfold-ring patterns of sp 2 sites. ‘Defects’ in this structure are odd-membered rings and sp 3 atoms. The graphite-like, in a large extent, nature of the surface in ta-C is in contrast to its bulk topology, for which researchers w4,6x have reached a consensus about the clustering of sp 2 sites: they are found in pairs, chains and small clusters rather than in aromatic rings. Experimental work w7x has observed sp 2 rich ta-C surfaces, but did not infer the atomic structure at the top.
P.C. Keliresr Journal of Non-Crystalline Solids 227–230 (1998) 597–601
Fig. 2. Top view of the surface layer in two typical slab cells. Filled and open circles denote sp 2 and sp 3 atoms, respectively. Ža. ˚ Žb. z , 3.75; cell width,10.2 A. ˚ z , 3.5; cell width,12.9 A, Lines are guide to the eye.
599
w1x.. The majority of atoms are under compression, but the two surfaces are under tensile stress. To show more quantitatively how the atomic stresses vary as a function of depth, we cut the slabs into amorphous layers Žslices. either of equal width Žs aamorp r4, 0 typically ; 0.1 nm. and varying number of atoms, or with fixed number of atoms Žequal to that in the respective crystalline layer. and varying layer width. The average of the atomic stresses within each layer is then calculated. A characteristic case is depicted in Fig. 4a. I find large tensile stresses in the surface layer Ždenoted as layer 1.. In the layer below the stresses become compressive, and subsequently they vary in a complex oscillatory way. These oscillations are larger near the surface and tend to diminish deep in the bulk, where stresses approach the average stress of the film Ž; 8 GPa in this case.. This complex behavior is present in every cell studied. We suggest that these anomalous oscillations are induced by the reconstructed amorphous surface, an effect which is reminiscent of stress oscillations near
3.2. Atomic leÕel stresses The graphite-like nature of ta-C surfaces has an effect on the local atomic stresses nearby. ŽThese were previously defined w1x.. We show in Fig. 3 a slab cell Ž z , 3.7. with atoms identified as being under compressive or tensile stress. The inhomogeneous distribution of stresses is clear Žsee also Ref.
Fig. 3. Atomic positions in a slab cell Ž z , 3.7., projected on a vertical plane as in Fig. 1, with atoms distinguished according to their local atomic stress. Filled and open circles denote atoms under tensile and compressive local stress, respectively.
Fig. 4. Depth profile of local atomic stresses in a slab cell with z , 3.7. Values shown are averages over the respective layers in the two halves of the slab. Layer 1 is the surface layer. Compressive stresses are positive. Lines are guide to the eye. Ža. Total average local stress. Žb. Decomposition into contributions from sp 2 atoms Žtriangles. and sp 3 atoms Žsquares..
600
P.C. Keliresr Journal of Non-Crystalline Solids 227–230 (1998) 597–601
crystalline reconstructed surfaces w8x. So, the layers just below the surface tend to compensate for the stress conditions above, because in the overall structure the total strain is minimized and the effect propagates deeper. The separate contributions from threefold and fourfold atoms to the variation of stresses are given in Fig. 4b. We see that both contributions exhibit the same kind of oscillation, while compensating each other in some layers. Note that in most layers fourfold geometries are on the average under compression, while threefold ones are under tension. 3.3. Defect energetics Information about defect formation energies in amorphous materials is either rare or lacking. This lack of information arises because reliable amorphous geometries of adequate size, and the statistical accuracy needed, are difficult to achieve. Owing to the simplicity and statistical accuracy of our approach, we have been able to extract for the first time defect formation energies in ta-C, especially in the near-surface region. These are very useful for understanding the incorporation processes of energetic atoms Žions. impinging on the surface. The relevant defects to our investigations are vacancies, interstitials, and Frenkel pairs. The significant outcome of our calculations is that all formation energies Žaverages over about twenty configurations for each cell and over four cells of varying z . are considerably less than in the crystal Žeither diamond or graphite.. For example, the vacancy in the graphite-like top layer has a formation energy of ; 4 eV, compared to ; 7 eV in the graphite plane. The interstitial costs ; 7 eV, compared to the tetrahedral interstitial in diamond or the in plane hexagonal interstitial in graphite which both cost more than 20 eV. Subsequently, Frenkel pairs Ža surface vacancy–deep interstitial pair. also cost much less than in the crystal. A careful analysis of the insertion process reveals that this difference is a result of significant rebonding in the region around the incorporated atom, which partly compensates for the energy expense. We also find that insertion and rebonding do not always lead to the formation of sp 3 geometries, but to sp 2 sites as well, depending on the local stress conditions.
4. Discussion The above results lead to a number of interesting observations regarding the structure and growth of thick ta-C films, which I discuss below. Ži. Surface topology; intrinsic or not: It has been argued w7x that the sp 2-rich surface layer is intrinsic to the growth process and that it does not form by a surface relaxation after deposition. The energetic ions with high kinetic energies and thus large subplantation depth are incorporated deep into the film, and so they do not densify the surface layer. Our simulations, on the other hand, show that the sp 2 layer always forms because the surface environment relaxes the compression. Samples generated ultrahigh larger pressure conditions, with all atoms artificially overcoordinated before allowing relaxation, always end up with sp 2 surfaces and sp 3-like bulk after relaxation. I should take into account, however, that the thickness of the sp 2 layer seen experimentally is ; 1.3 nm Žlarger than it is possible at present to simulate with our cells.. This indicates that probably the inner regions of this layer are indeed formed due to deep subplantation, rather than surface relaxation. There is another issue related to the above: Do the incoming energetic ions penetrate the surface Žsubplantation model., or do they just stick on the growing surface, as suggested recently w9x, distorting locally the surface and producing compressively stressed geometries, which are ‘locked-in’ as growth proceeds? Based on our finding of spontaneous relaxation of compressive stress and the dominance of tensile conditions in the surface region, we conclude that the latter mechanism has much less chance to operate, at least for deposition methods with energetic ions. We can not exclude it, however, in other than energetic ion methods such as magnetron sputtering with intense argon bombardment, which do not allow for sufficient surface relaxation. Žii. Low defect formation energies: This result not only suggests that subplantation events are possible, but that they have a smaller penetration threshold than previously estimated using defect energies appropriate for the crystal. In the subplantation models w2x, the penetration threshold, Ep , depends on the displacement threshold, Ed , the energy needed to create a permanent Frenkel pair by displacement.
P.C. Keliresr Journal of Non-Crystalline Solids 227–230 (1998) 597–601
This energy equals the Frenkel formation energy plus the migration energy for sufficient separation of the vacancy and the interstitial to prevent recombination. According to our calculations for the Frenkel energies, we suggest that the values for Ed and Ep should be reduced by ; 12 eV from the crystal-based values, and so model predictions should be reexamined. A reasonable value for Ep would be ; 16 eV. Žiii. Subplantation Õs. compressiÕe stress model: From our work, present and previous w1x, it has become clear that compressive stress generation is a local process extending over few atomic volumes for every ion impact event. Densification is also a local process, and from this point of view the two concepts, and thus the two models, are interrelated and equivalent: The incorporation of an atom which densifies a small region produces most likely compressive conditions over the region. Thinking the other way around, an atom entering into a compressively stressed area will rather become an sp 3 site and increase the density. In the incorporation process, however, tensile conditions may also arise and sp 2 sites may be formed w1x. This rather complicated procedure gives rise to an inhomogeneous stress distribution, such as the one shown in Fig. 3. Whether the film is finally under compression or tension is determined by summing up the individual local atomic contributions. So, the final metastable state of the film is produced by quenching continuously during growth the non-equilibrium local structures, resulting from densification and compressive stress generation. The initial interpretation of the compressive stress model as proposed by McKenzie et al. w10x, which supports the idea of a transition from sp 2 ™ sp 3 phase at a critical average intrinsic stress of the film, being a theory at pure thermodynamic equilibrium, seems not to be valid. Finally, the finding of extensive rebonding around interstitials suggests that accumulation of incorpo-
601
rated atoms in small regions makes the above mechanisms more effective, because it prevents relaxation of density and stress. Shallow subplantation near the surface is rather ineffective because of the tensile conditions and the driving force for surface relaxation. Deeper subplantation is more effective because the amorphous network is more constrained.
5. Conclusion Monte Carlo simulations revealed the graphite-like nature of the surface in ta-C networks. Characteristic ingredient of the surface structure are distorted sixfold-ring patterns of sp 2 sites. The profile of local stresses varies with depth in a complex oscillatory way, driven by the tensile stresses found on the surface. The defect formation energies in the nearsurface region are considerably less than either diamond or graphite, supporting the likelihood of subplantation events. Rebonding occurs in the region of interstitial insertions, not always leading to sp 3 bonding, pointing out the importance of accumulation processes.
References w1x w2x w3x w4x w5x w6x w7x
P.C. Kelires, Phys. Rev. Lett. 73 Ž1994. 2460. J. Robertson, Diam. Relat. Mater. 2 Ž1993. 984. C.A. Davis, Thin Solid Films 226 Ž1993. 30. P.C. Kelires, Phys. Rev. Lett. 68 Ž1992. 1854. J. Tersoff, Phys. Rev. Lett. 61 Ž1988. 2879. P.C. Kelires, E. Kaxiras, Phys. Rev. Lett. 78 Ž1997. 3479. C.A. Davis, K.M. Knowles, G.A.J. Amaratunga, Surf. Coat. Technol. 76–77 Ž1995. 316. w8x P.C. Kelires, J. Tersoff, Phys. Rev. Lett. 63 Ž1989. 1164. w9x N.A. Marks, D.R. McKenzie, B.A. Pailthorpe, Phys. Rev. B 53 Ž1996. 4117. w10x D.R. McKenzie, D. Muller, B.A. Pailthorpe, Phys. Rev. Lett. 67 Ž1991. 773.
Surface properties of diamond-like amorphous carbon P.C. Kelires
)
Physics Department, UniÕersity of Crete, P.O. Box 2208, 710 03 Heraklion, Crete, Greece Foundation for Research and Technology-Hellas ŽFORTH., P.O. Box 1527, 711 10 Heraklion, Crete, Greece
Abstract Monte Carlo simulations show that the surface in tetrahedral amorphous carbon networks reconstructs in a graphite-like manner. The top surface layer is found to be largely composed of distorted sixfold-ring patterns of sp 2 sites. Stresses at the surface are tensile, while they vary with depth in a complex oscillatory way. Defect formation energies close to the surface are much less than in the crystal. q 1998 Elsevier Science B.V. All rights reserved. Keywords: Amorphous carbon; Monte Carlo simulation; sp 2 sites
1. Introduction An effort has been devoted in recent years to understand the properties of tetrahedral diamond-like amorphous carbon Žta-C., both at the fundamental and practical level. Despite the interest, theoretical studies have been restricted to the bulk system. Although this information is useful, our comprehension of the physical processes related to this material will be incomplete if we do not address the surface properties as well. The growth mechanisms, for example, are basically determined by the near-surface structure. Since the overall bulk phase of the system, which on the average determines the electronic properties, results from the freezing of sequentially deposited material, the knowledge of the exact surface microstructure is important. In this paper, we investigate the role of the surface topology in affecting the properties of ta-C. We )
Corresponding author. Fax: q30-811 394 201; e-mail: [email protected]
are mostly interested in two issues, both related to the growth mechanism. The first concerns the distribution of atomic leÕel stresses in the growing surface region. It was proposed earlier w1x that these stresses, which are indicative of the local rigidity of the network, determine the hybridization of a site in amorphous carbon. Local tensile conditions favor the formation of sp 2 sites, while compressive conditions lead, most probably, to sp 3 sites. The cause and effect of this relationship is still a matter of debate. The second issue is related to subplantation processes believed to produce densification and compressive stress generation and to promote sp 3 bonding as well. One is interested to know how the amorphous network responds to the incorporation of incoming C atoms during deposition. Subplantation models have been proposed by Robertson w2x and Davis w3x. In the following, we outline the method used in our calculations, we give the results regarding the surface microstructure, atomic stresses and defect energies, and discuss the implications of these results with respect to possible growth models.
0022-3093r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 Ž 9 8 . 0 0 1 4 3 - 4
598
P.C. Keliresr Journal of Non-Crystalline Solids 227–230 (1998) 597–601
2. Theoretical methods The investigations are based on Monte Carlo ŽMC. simulations within the empirical potential approach. Two types of cells are used. One is a standing free slab geometry with 480 atoms periodically repeated in two dimensions Žsix cells generated.. The other type of cell has 550 atoms with the lateral dimensions constrained to be those of the diamond lattice, while the vertical dimension is allowed to vary Žfour cells generated.. Results from these two types of cells give a full account of the surface properties. The amorphous networks are MC generated by quenching the liquid under pressure within the constant pressure–temperature Ž N, P, T . ensemble, as done previously w1,4x. The liquid is equilibrated at ; 9000 K and then cooled to 300 K under various pressures up to 300 GPa and cooling rates up to ; 25 ŽMC steps.ratom-K. After removing the pressure, the cell density is equilibrated and the atomic positions are thoroughly relaxed to avoid local energy minima due to artificial surface geometries. The empirical potential of Tersoff w5x is used to model the interactions. It is tested extensively and found to describe reasonably well the properties of ta-C. Though in principle less accurate than ab initio methods, this approach is appealing because it permits extraction of atomic leÕel properties, otherwise inaccessible. This kind of analysis already gave valuable information, generally confirmed by experiment, regarding the metastability w4x and elastic properties w1x of ta-C networks. The potential also describes strain conditions quite well, as recent work by Kelires and Kaxiras w6x shows.
3. Results 3.1. Surface microstructure The resulting microstructure Žaverage atomic positions. in a typical 550-atom cell constrained on a diamond lattice is shown in Fig. 1. Atoms are indicated according to their coordination. The average coordination, z, of this cell is 3.6, so the bulk regions of the film, especially close to the interface with the substrate, are sp 3 rich. Note the increased
Fig. 1. Atomic positions in a 550-atom cell, constrained on a diamond substrate, projected on a vertical plane along the nonperiodic direction of the cell. Filled and open circles denote sp 2 and sp 3 atoms, respectively.
ordering Žreduced degree of amorphicity. as we approach the interface, which is attributed to the lattice match of the film with the substrate. ŽThis ordering does not occur when there is a lattice mismatch, as in the case of a-C on Si substrates.. The sp 2 sites in the film are largely clustered Žpairs and small chains.. Only few sp 2 sites are isolated. The degree of clustering increases as we approach the surface region, which at the top is enhanced with threefold coordinated atoms. Such inhomogeneous distribution of sp 2 atoms as a function of depth from the surface Žor the interface. is observed in every cell studied, so we may conclude that this is a generic behavior of ta-C networks. Further details are given in a top view of the surface structure, illustrated in Fig. 2 Žonly top atoms are shown., for two characteristic cases: Ža. a cell with z , 3.5 and Žb. a cell with z , 3.75. The enrichment of the top layer with sp 2 atoms is profound, especially for the more diamond-like film in panel Žb., in which the bulk content of sp 2 sites is only ; 25%. Perhaps, the most interesting finding is the specific reconstruction of the amorphous surface in the form of distorted sixfold-ring patterns of sp 2 sites. ‘Defects’ in this structure are odd-membered rings and sp 3 atoms. The graphite-like, in a large extent, nature of the surface in ta-C is in contrast to its bulk topology, for which researchers w4,6x have reached a consensus about the clustering of sp 2 sites: they are found in pairs, chains and small clusters rather than in aromatic rings. Experimental work w7x has observed sp 2 rich ta-C surfaces, but did not infer the atomic structure at the top.
P.C. Keliresr Journal of Non-Crystalline Solids 227–230 (1998) 597–601
Fig. 2. Top view of the surface layer in two typical slab cells. Filled and open circles denote sp 2 and sp 3 atoms, respectively. Ža. ˚ Žb. z , 3.75; cell width,10.2 A. ˚ z , 3.5; cell width,12.9 A, Lines are guide to the eye.
599
w1x.. The majority of atoms are under compression, but the two surfaces are under tensile stress. To show more quantitatively how the atomic stresses vary as a function of depth, we cut the slabs into amorphous layers Žslices. either of equal width Žs aamorp r4, 0 typically ; 0.1 nm. and varying number of atoms, or with fixed number of atoms Žequal to that in the respective crystalline layer. and varying layer width. The average of the atomic stresses within each layer is then calculated. A characteristic case is depicted in Fig. 4a. I find large tensile stresses in the surface layer Ždenoted as layer 1.. In the layer below the stresses become compressive, and subsequently they vary in a complex oscillatory way. These oscillations are larger near the surface and tend to diminish deep in the bulk, where stresses approach the average stress of the film Ž; 8 GPa in this case.. This complex behavior is present in every cell studied. We suggest that these anomalous oscillations are induced by the reconstructed amorphous surface, an effect which is reminiscent of stress oscillations near
3.2. Atomic leÕel stresses The graphite-like nature of ta-C surfaces has an effect on the local atomic stresses nearby. ŽThese were previously defined w1x.. We show in Fig. 3 a slab cell Ž z , 3.7. with atoms identified as being under compressive or tensile stress. The inhomogeneous distribution of stresses is clear Žsee also Ref.
Fig. 3. Atomic positions in a slab cell Ž z , 3.7., projected on a vertical plane as in Fig. 1, with atoms distinguished according to their local atomic stress. Filled and open circles denote atoms under tensile and compressive local stress, respectively.
Fig. 4. Depth profile of local atomic stresses in a slab cell with z , 3.7. Values shown are averages over the respective layers in the two halves of the slab. Layer 1 is the surface layer. Compressive stresses are positive. Lines are guide to the eye. Ža. Total average local stress. Žb. Decomposition into contributions from sp 2 atoms Žtriangles. and sp 3 atoms Žsquares..
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P.C. Keliresr Journal of Non-Crystalline Solids 227–230 (1998) 597–601
crystalline reconstructed surfaces w8x. So, the layers just below the surface tend to compensate for the stress conditions above, because in the overall structure the total strain is minimized and the effect propagates deeper. The separate contributions from threefold and fourfold atoms to the variation of stresses are given in Fig. 4b. We see that both contributions exhibit the same kind of oscillation, while compensating each other in some layers. Note that in most layers fourfold geometries are on the average under compression, while threefold ones are under tension. 3.3. Defect energetics Information about defect formation energies in amorphous materials is either rare or lacking. This lack of information arises because reliable amorphous geometries of adequate size, and the statistical accuracy needed, are difficult to achieve. Owing to the simplicity and statistical accuracy of our approach, we have been able to extract for the first time defect formation energies in ta-C, especially in the near-surface region. These are very useful for understanding the incorporation processes of energetic atoms Žions. impinging on the surface. The relevant defects to our investigations are vacancies, interstitials, and Frenkel pairs. The significant outcome of our calculations is that all formation energies Žaverages over about twenty configurations for each cell and over four cells of varying z . are considerably less than in the crystal Žeither diamond or graphite.. For example, the vacancy in the graphite-like top layer has a formation energy of ; 4 eV, compared to ; 7 eV in the graphite plane. The interstitial costs ; 7 eV, compared to the tetrahedral interstitial in diamond or the in plane hexagonal interstitial in graphite which both cost more than 20 eV. Subsequently, Frenkel pairs Ža surface vacancy–deep interstitial pair. also cost much less than in the crystal. A careful analysis of the insertion process reveals that this difference is a result of significant rebonding in the region around the incorporated atom, which partly compensates for the energy expense. We also find that insertion and rebonding do not always lead to the formation of sp 3 geometries, but to sp 2 sites as well, depending on the local stress conditions.
4. Discussion The above results lead to a number of interesting observations regarding the structure and growth of thick ta-C films, which I discuss below. Ži. Surface topology; intrinsic or not: It has been argued w7x that the sp 2-rich surface layer is intrinsic to the growth process and that it does not form by a surface relaxation after deposition. The energetic ions with high kinetic energies and thus large subplantation depth are incorporated deep into the film, and so they do not densify the surface layer. Our simulations, on the other hand, show that the sp 2 layer always forms because the surface environment relaxes the compression. Samples generated ultrahigh larger pressure conditions, with all atoms artificially overcoordinated before allowing relaxation, always end up with sp 2 surfaces and sp 3-like bulk after relaxation. I should take into account, however, that the thickness of the sp 2 layer seen experimentally is ; 1.3 nm Žlarger than it is possible at present to simulate with our cells.. This indicates that probably the inner regions of this layer are indeed formed due to deep subplantation, rather than surface relaxation. There is another issue related to the above: Do the incoming energetic ions penetrate the surface Žsubplantation model., or do they just stick on the growing surface, as suggested recently w9x, distorting locally the surface and producing compressively stressed geometries, which are ‘locked-in’ as growth proceeds? Based on our finding of spontaneous relaxation of compressive stress and the dominance of tensile conditions in the surface region, we conclude that the latter mechanism has much less chance to operate, at least for deposition methods with energetic ions. We can not exclude it, however, in other than energetic ion methods such as magnetron sputtering with intense argon bombardment, which do not allow for sufficient surface relaxation. Žii. Low defect formation energies: This result not only suggests that subplantation events are possible, but that they have a smaller penetration threshold than previously estimated using defect energies appropriate for the crystal. In the subplantation models w2x, the penetration threshold, Ep , depends on the displacement threshold, Ed , the energy needed to create a permanent Frenkel pair by displacement.
P.C. Keliresr Journal of Non-Crystalline Solids 227–230 (1998) 597–601
This energy equals the Frenkel formation energy plus the migration energy for sufficient separation of the vacancy and the interstitial to prevent recombination. According to our calculations for the Frenkel energies, we suggest that the values for Ed and Ep should be reduced by ; 12 eV from the crystal-based values, and so model predictions should be reexamined. A reasonable value for Ep would be ; 16 eV. Žiii. Subplantation Õs. compressiÕe stress model: From our work, present and previous w1x, it has become clear that compressive stress generation is a local process extending over few atomic volumes for every ion impact event. Densification is also a local process, and from this point of view the two concepts, and thus the two models, are interrelated and equivalent: The incorporation of an atom which densifies a small region produces most likely compressive conditions over the region. Thinking the other way around, an atom entering into a compressively stressed area will rather become an sp 3 site and increase the density. In the incorporation process, however, tensile conditions may also arise and sp 2 sites may be formed w1x. This rather complicated procedure gives rise to an inhomogeneous stress distribution, such as the one shown in Fig. 3. Whether the film is finally under compression or tension is determined by summing up the individual local atomic contributions. So, the final metastable state of the film is produced by quenching continuously during growth the non-equilibrium local structures, resulting from densification and compressive stress generation. The initial interpretation of the compressive stress model as proposed by McKenzie et al. w10x, which supports the idea of a transition from sp 2 ™ sp 3 phase at a critical average intrinsic stress of the film, being a theory at pure thermodynamic equilibrium, seems not to be valid. Finally, the finding of extensive rebonding around interstitials suggests that accumulation of incorpo-
601
rated atoms in small regions makes the above mechanisms more effective, because it prevents relaxation of density and stress. Shallow subplantation near the surface is rather ineffective because of the tensile conditions and the driving force for surface relaxation. Deeper subplantation is more effective because the amorphous network is more constrained.
5. Conclusion Monte Carlo simulations revealed the graphite-like nature of the surface in ta-C networks. Characteristic ingredient of the surface structure are distorted sixfold-ring patterns of sp 2 sites. The profile of local stresses varies with depth in a complex oscillatory way, driven by the tensile stresses found on the surface. The defect formation energies in the nearsurface region are considerably less than either diamond or graphite, supporting the likelihood of subplantation events. Rebonding occurs in the region of interstitial insertions, not always leading to sp 3 bonding, pointing out the importance of accumulation processes.
References w1x w2x w3x w4x w5x w6x w7x
P.C. Kelires, Phys. Rev. Lett. 73 Ž1994. 2460. J. Robertson, Diam. Relat. Mater. 2 Ž1993. 984. C.A. Davis, Thin Solid Films 226 Ž1993. 30. P.C. Kelires, Phys. Rev. Lett. 68 Ž1992. 1854. J. Tersoff, Phys. Rev. Lett. 61 Ž1988. 2879. P.C. Kelires, E. Kaxiras, Phys. Rev. Lett. 78 Ž1997. 3479. C.A. Davis, K.M. Knowles, G.A.J. Amaratunga, Surf. Coat. Technol. 76–77 Ž1995. 316. w8x P.C. Kelires, J. Tersoff, Phys. Rev. Lett. 63 Ž1989. 1164. w9x N.A. Marks, D.R. McKenzie, B.A. Pailthorpe, Phys. Rev. B 53 Ž1996. 4117. w10x D.R. McKenzie, D. Muller, B.A. Pailthorpe, Phys. Rev. Lett. 67 Ž1991. 773.