Initial Growth of BN on Diamond Substrates: A Theoretical Approach

The prerequisites for an initial growth of c-BN (100) have been studied by adding the alternative B and N layers sequentially and calculating the resu...
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J. Phys. Chem. C 2010, 114, 11448–11455

Initial Growth of BN on Diamond Substrates: A Theoretical Approach Anna Pallas* and Karin Larsson Department of Materials Chemistry, Uppsala UniVersity, Box 538, Uppsala 751 21, Sweden ReceiVed: December 17, 2009; ReVised Manuscript ReceiVed: May 11, 2010

Cubic boron nitride, c-BN, is a very interesting material due to its extreme properties of which some are comparable, or even superior, to diamond. Unfortunately, there are severe problems with the vapor phase synthesis of c-BN, which makes it very important to investigate the possibility for new growth pathways. The choice of substrate has been experimentally found to be decisive for an ideal growth of c-BN. Diamond is a material that has been found to be a good substrate for growth of c-BN directly onto the substrate. By using quantum mechanical density functional theory (DFT) under periodic boundary conditions, the details in the layer-by-layer formation of BN onto diamond (100) has been investigated in the present study. The prerequisites for an initial growth of c-BN (100) have been studied by adding the alternative B and N layers sequentially and calculating the resulting interfacial binding strengths and geometrical structures. For the situation with one monatomic layer on diamond, the interfacial binding energy was calculated to be strongest for nitrogen heteroepitaxially positioned onto diamond (100). The individual atoms in a monatomic B adlayer did, however, not choose corresponding heteroepitaxial positions. When applying a second atomic layer of c-BN, two different models were initially constructed with different structural alignments with respect to the underlying diamond structure. One model was heterostructurally positioned on top of diamond (100), while the other model had the x-axis of the c-BN lattice aligned with the y-axis of the diamond lattice. For the situation with N attached to the diamond substrate, the heteroepitaxial adlayer structure stayed cubic as a result of the geometry optimization, while the other became amorphous-like. Both of these adlayer structures showed large interfacial binding strengths, but the amorphous-like structure became energetically the most stable one. On the contrary, a two-layer BN structure with B attached to the diamond surface did not show the same characteristics. It was only the initial heteroepitaxial BN lattice that resulted in a stable adlayer structure. It stayed cubic after the geometry optimization, with a large interfacial binding strength. The fourlayer BN structure on diamond showed similar features. Introduction Cubic boron nitride has been in focus for several years due to its interesting and extreme properties of which some are even superior to diamond. These important properties include extreme hardness, chemical stability, large bandgap, wear resistance, and chemical inertness.1-3 The usefulness as tool coatings for machining of steel, cast iron, and ferrous alloys is therefore obvious.3,4 The possibility for large area deposition of c-BN is a requirement for realization of these different properties in various applications. There are, however, at present severe problems in the vapor phase synthesis of c-BN, which makes the possibility to grow large-area c-BN considerably smaller. A mixture of BN phases (amorphous boron nitride (a-BN), turbostratic boron nitride (t-BN), and c-BN) is usually the result when trying to deposit c-BN by using methods based on surface bombardment with highly energetic ions.5 Ion bombardment will also cause problems with high film stresses (up to 20 GPa), poor crystalline quality, small grain sizes, and high defect density.6-8 The c-BN will peel off from the substrate even for low film thicknesses (about 0.2 µm).5-7 Also, when using conventional CVD, ion bombarding is essential for the formation of c-BN.9 The main question still remains: why is it so difficult to grow c-BN by using thermal diffusion of growth species to the growing surface? Cubic BN films have, however, recently been deposited without the presence of noncubic interlayer * To whom correspondence should be addressed. E-mail: anna.pallas@ mkem.uu.se.

phases like a-BN and t-BN closest to the substrate. This was made possible using fluorine-assisted plasma-enhanced chemical vapor deposition (PECVD) on diamond substrates.5 This process still uses low-energetic ion bombardment since it is believed that the ion bombardment is required to break the B-F bonds in order to allow further B-N bonding. Since the bias required in the process was so low (about 20 V), the obtained film stress was only about 2 GPa.5 It is at present an urgent need for a process development of gentler vapor phase deposition methods, where no bombardment of ions can detrimentally affect crystallinity and/or film stress content. The role by the substrate material is not only to improve the interfacial binding of the c-BN films but also to control the phase ratio within the BN film (in favor of the cubic phase).10 Two important factors have been found to be beneficial: a low lattice mismatch and strong chemical affinity between the film and the substrate. The most common substrates of today have been sorted into categories like hard (diamond, β-SiC, Si),11-15 soft (metals),16 and ionic (KBr, KI). The search for an optimal substrate material is hereby regarded to be one of the most important research directions for a successful c-BN growth to occur. The purpose with the present study was to investigate theoretically, by using density functional theory under periodic boundary conditions, the initial growth process of c-BN (100) on a diamond (100) substrate. The diamond surface was not only used as a substrate due to its similarity with the diamond

10.1021/jp911924g  2010 American Chemical Society Published on Web 06/16/2010

Initial Growth of BN on Diamond Substrates

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lattice (i.e., small lattice mismatch) but also because of the fact that a successful growth of the cubic phase of BN directly onto this substrate has recently been obtained.5-7 When using vapor phase deposition methods, the resulting quality of the films will be completely dependent on the initial nucleation and growth process. A careful layer-by-layer study could bring some light in the search for a successful recipe for c-BN growth. A lot of questions still remain in this specific area.17-19 Therefore, a careful geometrical and energetically study of this layer-bylayer growth of c-BN (100) onto diamond (100) has here been theoretically performed. This has been done by studying an interface involving either B or N attached to the diamond surface (as one monolayer), up to a maximum number of four atomic layers (i.e., alternate layers of 2 B and 2 N). In this paper, neither H nor F has been used with the purpose to terminate the BN surface. Many PVD processes (like ion-beam-assisted evaporation) use growth precursors free from these types of terminating species in UHV environment.20,21 Boron carbide and elemental boron are examples of precursors used in these experimental setups.20,21 The main goal with this investigation has been twofold: (i) to get a deeper knowledge about the atomic-level factors that lead to a more or less perfect c-BN growth on diamond and (ii) to use this knowledge in the design and development of novel c-BN vapor phase deposition setups. Methods The interfacial binding energy between diamond (100) and the BN adlayer has been calculated using eq 1:

∆Ebinding ) Etot - Ediamond - EBN

(1)

where Etot is the calculated total energy for the whole interface, and Ediamond and EBN are the calculated total energy for the diamond substrate and the BN adlayer, respectively. Geometry optimization was performed when calculating Etot, while singlepoint calculations where used in calculating Ediamond and EBN. The geometry-optimized interfaces were used as starting geometries for the single-point calculations. By using this methodology, the interfacial bond strengths will be carefully estimated. With the purpose to further support and validate these binding energy results, the electron bond population within the interfacial C-B(or N) bonds was also calculated. The underlying reason is the fact that a strong correlation between bond energy and electron population is expected for (polar) covalent bonds like those in the present investigation. Degree of electron transfer and atomic charges were estimated to further analyze the structural evolution in the interfacial region. The geometryoptimized interfaces were used for these latter analyses. Density functional theory (DFT), using the program package CASTEP from Accelrys, Inc., was used for the energy and geometry optimization calculations above.22,23 The generalized gradient approximation (GGA-PW91) developed by Perdew and Wang was used in describing the electronic exchange and correlation interactions.24 GGA-PW91 introduces inhomogeneity by using an electron density gradient expansion. This method is in this sense more accurate than the local density approximation (LDA) method.25-27 As a result, the GGA method gives more correct total energies and structural energy differences. The LDA method tends to overbind electrons within the bonds in a molecule or solid.26,28 In the present investigation, the kinetic energy cutoff was set to 240 eV in the plane wave function description. A Monkhorst-Pack generated 2 × 3 × 2 k-point mesh was used for all calculations (yielding 6 k-points). This

Figure 1. Periodic slabs containing the upper five layers of C in a diamond (100)-2 × 1 reconstructed surface. The bottom C layer is hydrogen terminated, and all structures are geometry optimized. The figure demonstrates (a) an adlayer of (heteroepitaxial) N and (b) an adlayer of B (side views). The corresponding upper views are shown in (c) and (d).

scheme produces a uniform mesh of k-points in the reciprocal space, which has been found to be more reliable than linear or quadratic methods.29 The degree of electron transfer between the diamond substrate and the BN structure as a whole, and between individual atoms, has been estimated by calculating the individual atomic charges. In addition, the covalent bond strengths within the bonds were estimated by calculating the electron bond populations. The atomic charges and bond populations were calculated by projecting the plane wave states onto the localized basis set by means of Mulliken analysis.30 The geometry optimization procedure was based on the BFGS algorithm (BroydenFletcher-Goldfarb-Sharmo).31 The calculations were based on periodic boundary conditions, where the interfacial models were constructed as periodically repeated super cells. The diamond substrate within the interfacial structures was in the present investigation modeled as a (2 × 1) reconstructed diamond surface comprised of a 5-layer slab of 12 atoms per layer (see Figure 1). The BN structure within the here modeled diamond//BN interfaces consisted of alternate layers of B and N (with 12 atoms in each layer). The bottom C layer in diamond was hydrogen-terminated with the purpose to saturate the dangling bonds and to maintain the sp3 hybridization of the carbon atoms. This hydrogenated carbon layer was held fixed to simulate the crystalline bulk structure in the calculations. The other atoms were allowed to fully relax. When increasing the thickness of the BN adlayer to four atomic layers, two bottom carbon layers, with its terminating hydrogen’s, where held fixed in the calculations. As a result of test calculations, the difference in total energy for a model with one or two fixed carbon layers was less than 0.002%. Hence, it was found adequate for the present calculations to fix the two bottom C layers. Careful test calculations regarding the choice of vacuum adlayer thickness have earlier been conducted and resulted in a 7.5 Å thick vacuum layer.32 This is a strong indication that the effect of slab dipole moment has been eliminated for a 7.3 Å

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Figure 2. Two-atomic c-BN adlayers on diamond (100)-2 × 1 with N attached to the diamond substrate. The x-axis of the c-BN layer is either (a) in parallel with the x-axis of the diamond substrate or (b) in parallel with the y-axis of the substrate. These model structures are initial ones, prior to geometry optimization.

thick vacuum layer, which was therefore found adequate to use in the present calculations. Two different types of interfaces have been included in the present investigation; with either a N or B layer attached to the (2 × 1) reconstructed diamond (100) substrate. In studying the initial process of a layer-by-layer growth of BN, 1, 2, and 4 atomic layers of BN were modeled. Moreover, different possibilities for two and four atomic layer growth of BN on diamond (100) were investigated by using either an aligned x-axis for the overlayer BN structure and the diamond substrate or by rotating the BN structure with respect to diamond so that the overlayer x-axis will be aligned with the y-axis of the substrate (i.e., a 90° rotation) (see Figure 2b). Hence, one type of interface was initially built as a perfect heteroepitaxial growth of c-BN on diamond (100), while the other was not built heteroepitaxial but still cubic with respect to BN. Results and Discussion A. General. The effect of the diamond (100) substrate on a layer-by-layer growth of BN has in the present study been investigated theoretically using DFT calculations under periodic boundary conditions. The main purpose was to achieve a better understanding about the underlying causes to the general observation made for the “brutal force” deposition of c-BN (i.e., using methods based on surface bombardment with highly energetic ions), namely that this deposition often results in noncubic forms of BN closest to the substrate.5 Both interfacial binding energies and geometrical structures have carefully been investigated with the purpose to find, and relate, stable structures of the initial films of BN grown on diamond (100). In this sense, 1, 2, and 4 atomic layers of BN onto diamond (100) have been modeled. Either a nitrogen layer, or a boron layer, was attached to the diamond surface in the interfaces. In analyzing the causes to formation of the respective interfaces obtained in the geometry optimization procedures, different types of parameters/indicators have been used: electron bond populations for bonds within the interface and degree of electron transfer between the surface carbon atoms (within diamond) and the surface-binding atoms in BN (nitrogen or boron atoms). This analysis is expected to be of great help in the tailoring and development of novel vapor phase deposition setups for phase pure c-BN growth of thin films on diamondlike substrates. B. Structural Geometries and Energetic Surface Stabilization. The interfacial binding energy, as calculated using eq 1, is here regarded to be a measure of the interfacial strength

between the diamond (100) surface and the growing BN adlayer. The numerical value of this binding energy is dependent not only on type of atom (B or N) attached to the diamond substrate and thickness of BN adlayer but also on the geometrical structure of the interface. Hence, the first atomic layer (B or N) attached to diamond has here been geometry optimized to find its lowest energetic value. The second atomic layer, forming a BN adlayer on diamond, has thereafter been added on the optimized firstlayer structure, followed by a geometry optimization of the whole interface. In a similar way, two BN layers have been modeled by adding a BN layer to an already optimized BN adlayer. In this way, the structural evolution of a layer-by-layer growth of BN on diamond (100) will here be modeled. B.1. Monolayer N or B on Diamond (100). As can be seen in Figure 5, a monolayer of N atoms directly attached to the diamond (100) surface shows the strongest interfacial binding energy (7.8 eV per N atom) and, hence, binds most strongly to the diamond surface. The corresponding geometrical structure of this N monolayer has the form of a heterostructural continuation of the underlying diamond (100)-2 × 1 structure (see Figure 1a,c). For the situation with a monolayer of B atoms onto diamond (100), the most stable B layer formation was found to be with B atoms in bridge formation along the C-C dimer chain (see Figure 1b,d). Compared to the situation with a B monolayer as a heterostructural continuation of the underlying diamond (100)-2 × 1 structure, the interstitial binding energy was calculated to be larger by 0.8 eV per monolayer B atom (see Figure 5). The calculated interfacial binding energy will be smaller than for a N monolayer (5.4 vs 7.8 eV per monolayer atom). This lower interfacial bond strength is further visualized in the structural geometry of the interface in the sense that the weaker C-B bond does not have the capacity to counteract the 2 × 1 reconstruction of the diamond (100) surface. In addition, the B atoms will bind in bridge formations to two C atoms along the reconstructed carbon dimer rows (see Figure 1b,d). B.2. One BN Layer on Diamond (100). As presented above, the most stable surface configurations of one monolayer of N (or B) on the diamond (100) substrate was used as starting structures onto which one additional layer of B (or N) was added. As described in the Methods section, two different interfacial structures were initially constructed for the situation with N attached to the surface: one with a cubic phase of BN heterostructurally positioned on diamond (100) (i.e., with aligned x-axes) (see Figure 2a) and another where the x axis of c-BN is aligned with the y-axis of the diamond lattice (see Figure 2b).

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Figure 4. Interfaces of BN/diamond, showing structures obtained from geometry optimization. (a) and (b) show the geometrical results for the initially heteroepitaxially constructed four-atomic adlayer, with N attached to diamond, using two different side views (either along the y-axis (a) or along the x-axis (b)). The corresponding geometrical structures for the initially constructed nonheteroepitaxial structures are shown in (c) and (d).

Figure 3. Interfaces of BN/diamond, showing structures obtained from geometry optimization. (a) and (b) give the side views of the twoatomic BN layer (with N attached to diamond) for (a) initially heteroepitaxially adlayer structure and (b) the initially nonheteroepitaxially (but still cubic) adlayer structure (to be compared with Figure 4). (c) and (d) show the corresponding top views. The geometrical structure for the initially heteroepitaxially constructed adlayer with B attached to the diamond substrate is shown both as a (e) side view and (f) top view.

As a result of the geometrical relaxation, the heteroepitaxially modeled c-BN layer stayed perfectly cubic while the other c-BN structure, which was rotated with respect to diamond, became more amorphous-like. Both BN adlayer structures showed relatively strong interfacial binding energies to the underlying diamond substrate (3.9 and 5.8 eV per binding N atom). However, the amorphous-like BN structure was found to be much more energetically favorable with a difference of 1.9 eV per binding N atom (see Figure 3b,d). When adding a second layer of N to the first attached B layer on diamond, the BN adlayer was found not to bind to the substrate. It must be stressed that the starting geometry for the B atoms were not heterostructural with diamond since that type of structure does not correspond to the most stable monatomic layer (see section B.1). In order to check the possibility for an on top layer of N to be able to transform the geometrical structure of the underlying B layer to a heteroepitaxial one, an initially heteroepitaxial BN layer was built on top of diamond (100). As a result of the following geometry optimization, this interfacial structure stayed heteroepitaxially cubic with a surface reconstructed N layer (see Figure 3e,f) and with an interfacial

Figure 5. Interfacial binding energies (∆E (eV) per binding adlayer atom) for geometry-optimized structures. The suffix e (in e.g. Be) means that the adlayer is heteroepitaxial to diamond (100). The values for the thicker BN adlayers are inserted as a reference lines. The lower and upper horizontal lines are for the adlayer with N (lower) vs B (upper) closest to the diamond substrate.

binding energy of 5.3 eV per binding B atom. This interfacial binding energy is very similar to the situation with a thicker c-BN adlayer, with B closest to the diamond substrate (5.5 eV per binding B atom). The difference in total energy for the two different B monolayers is only about 0.8 eV per binding adlayer atom (in favor of the nonheterostructural adlayer) (see Figure 5). During a layer-by-layer growth of BN, and starting from the most stable nonheterostructural configuration of B atoms, an energy barrier of ∼0.8 eV per binding adlayer atom has, hence, to be overcome in order to grow a heteroepitaxial adlayer of c-BN. This is possible to occur, especially at higher deposition temperatures. However, even though it is somewhat energetically feasible for a two-layer c-BN layer to form with B attached to

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a diamond (100) substrate, it is less stable than the situation with an amorphous-like BN adlayer with N attached to diamond (5.3 vs 5.8 eV per binding adlayer atom). Furthermore, it is interesting to note that the heteroepitaxial c-BN structure with B attached to the diamond substrate is much more stable than for the heteroepitaxial structure with N attached to diamond (5.3 vs 3.9 eV per binding atom) B.3. Two BN Layers on Diamond (100). A BN adlayer was finally built on top of the two-atomic-layer thick BN adlayer (forming a four-atomic-layer thick BN), with the purpose to see if the structure and interfacial binding strength will dramatically change in the continuation of the layer-by-layer growth of BN onto diamond (100). For the initially heteroepitaxial twoatomic-layer BN structure (from here on denoted as BN1), with nitrogen attached to the diamond surface, the B atoms became reconstructed when adding the second BN layer (see Figure 4a,b). Despite this tendency for reconstruction, an overall high degree of heteroepitaxy with the underlying diamond (100) structure was sustained. The resulting interfacial binding energy for the BN structure with four atom layers was improved when compared to the situation with a two-atomic-layer BN interface, 6.5 vs 3.9 eV per binding adlayer atom. For a structure where the adlayer was initially built as a cubic BN structure and rotated 90° with respect to the diamond lattice (from here on denoted as BN2), the addition of an extra BN layer resulted in an obvious amorphous structure (see Figure 4c,d). For this amorphous BN adlayer, the interfacial binding energy became somewhat less energetic favorable when compared to the heteroepitaxial fouratomic layer described above (5.8 vs 6.5 eV per binding adlayer atom). It is interesting to note that the interfacial binding energies for the amorphous two- and four-atomic BN layers are identical, namely 5.8 eV per binding N. The here-presented interfacial binding energies have been compared with two calculated models simulating thick heteroepitaxial c-BN adlayers on diamond (100): one adlayer with N closest to the diamond substrate and one adlayer with B closest the diamond substrate. As shown in Figure 5, oscillations in the interfacial binding energy are observed when initiating BN growth on diamond (100) by using a layer-by-layer growth starting from N attached to the substrate. The heterostructural N monolayer binds extremely strong to the substrate (with an interfacial binding energy of 7.8 vs 5.6 (thicker c-BN) eV per binding N). Depending on the following growth pathways, the next atomic layer (consisting of B atoms) will lead to either a heterogeneous c-BN structure or an amorphous BN structure. For the heterostructural two-atomic-layer structure, the addition of the B layer onto the N layer resulted in a marked weakening in the interfacial binding to the diamond substrate (from 7.8 to 3.9 eV per binding N). This energetic value of 3.9 eV per binding N is even appreciably smaller than the value obtained for the thicker c-BN film with N closest the diamond substrate (5.6 eV per binding N). A four-atomic layer of heteroepitaxial c-BN, on the other hand, was found to bind much stronger to diamond (100): 6.5 eV per binding N. In fact, this value is even stronger than for the thicker c-BN adlayer with N closest the diamond substrate (5.6 eV per binding N). On the other hand, the correspondingly amorphous two- and four-layer structures were found to bind strongly with almost identical interfacial binding energies (5.8 eV per binding N), which were also very similar to the interfacial binding energy for the thicker c-BN with N closest the diamond substrate. C. Electron Bond Populations. The electron bond population (i.e., electron density between two atoms) is generally regarded to be a measure of the (covalent) bond strength. The results of the

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Figure 6. Diagram over electron bond populations for the interfacial binding atoms. The suffix e (in e.g. Ne) means that the adlayer is heteroepitaxial to diamond (100). The suffix b (in e.g. NBNBb) means that it is a thicker heteroepitaxial BN adlayer.

calculated electron bond populations within the present study are shown in Figure 6. The presented bond populations are calculated values for the interfacial C(diamond)-N(BN) and C(diamond)B(BN) bonds and for the interatomic interactions within the first atomic layer within the adlayer (i.e., either B-B or N-N interactions). All interfaces that have been investigated in the present study showed a numerically large electron bond population for the bonds between the surface carbon atoms and the attached nitrogen (or boron) atoms in the adlayer (i.e., C-B or C-N). When building a BN adlayer sequentially, by starting from one monolayer of N and continuing to a thicker BN adlayer, no strict correlation between adlayer binding energy and C-N bond population was observed. The main reason for this observation is most probably the structural environment to the substrate-binding N atoms. It is possible to identify two different types of structural environments: (i) sp3 hybridization of N where no electron is filling antibonding states and (ii) sp3 hybridization where electrons occupy antibonding states (and thereby weaken the C-N bonds). Members of the first type of N structure are monatomic N and four-atomic BN adlayers. The interfacial binding energies for these adlayers (7.8 vs 6.5 eV per binding N), together with the C-N bonding populations (0.75 vs 0.78), are to be compared with the corresponding values for the latter type of N structural environment: two-atomic and thicker BN adlayers. On the basis of the interfacial binding energies for these adlayers (3.9 vs 5.5 eV per binding N), together with the C-N bonding populations (0.65 and 0.62), it is clear that these adlayer formations will form a separate group. The underlying reason for these observations is, as will be discussed in section D, most probably bond weakening effects within the latter group due to partial filling of antibonding N-C orbitals. The calculated bonding populations for the interfaces with boron closest to diamond show a much clearer trend for the heteroepitaxial interfaces. The following numerical order of interfacial binding energies was obtained: 4.6 eV (heteroepitaxial B monolayer), 5.3 eV (heteroepitaxial BN layer), and 5.2 eV (thicker c-BN adlayer) per binding B. The corresponding C-B bond populations are 0.59, 0.74, and 0.75. It is obvious that

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TABLE 1: Changes in Atomic Charge as a Result of Electron Transfer within C-N Bonds across the Interfacea atom layer

Ne

NB

NBepitax

NBNB

NBNBepitax

NBNBbulk

C charge [e] N charge [e] B charge [e]

0.25 -0.25-(-0.30)

0.22-0.24 -0.41-(-0.46) 0.14-0.24

0.21 -0.39 0.16

0.21-0.25 -0.37-(-0.46) 0.15-0.55

0.21 -0.40-(0.48) 0.54-0.72

0.19 -0.40 0.66

a

The electron transfer within N-B bonds across second atomic layer of the adlayer is also included.

when the bonding population is high, the interfacial binding energy is strong. D. Degree of Electron Transfer. The degree of electron transfer between atoms in the diamond/BN interface has mainly been used with the purpose to explain the underlying causes to geometrical structures and interfacial binding energies. In this sense, it is a complement to the calculations of electron bond population (as presented and discussed in section C). The degree of electron transfer was estimated from calculated atomic charges. This parameter is generally regarded to be a strong indication of interactions and hence bonding. The two material surfaces in an interface are usually interacting by forming overlapping orbitals. The factors that are governing the interaction strengths and bond types are (i) degree of spherical orbital overlap and (ii) orbital energy difference. Depending on these factors, the interaction will span all the way from perfectly covalent bonds over polar covalent bonds to ionic bonds. This is also the situation with degree of electron transfer. Perfect covalent bonds do not show any degree of electron transfer. However, the more polar the bond is, the larger the degree of electron transfer. For this specific compound system (i.e., diamond/BN), the electron transfer processes are also very much governed by the circumstance that N is a Lewis base and B is a Lewis acid. This means that for some of the B-N bonds (1/4 in the case of cubic BN) one of the overlapping orbitals is filled (for N) and the other is empty (for B). The nitrogen atoms will thereby contribute with one electron pair to the bond formed with the electron-deficient element B. However, and as stated above, the difference in electron negativity will induce withdraw of these binding electrons toward the N atom. D.1. N Attached to Diamond (100). For the situation with a monolayer of N in heteroepitaxy with the underlying diamond (100)-2 × 1 surface (being the energetically most preferred monatomic layer structure), all three indicators for interfacial bond strength show the same results. As is obvious from Table 1 and Figures 5 and 6, the energy of the interfacial bonds, the electron population within these bonds, and degree of electron transfer along the bonds indicate a very strong interfacial C-N bonding situation. As can be understood from Table 1, the degree of electron transfer is the highest (C donates ∼0.25e to N) of all interfaces in the present investigation, indicating a strong interaction between the diamond substrate and the adlayer. The driving force for this electron transfer is the difference in electronegativity between the elements C and N. The resulting “lone pairs” on N, which are each more than halffilled with electrons, will have the possibility to overlap with each other and thereby form very weak antibonding N-N interactions. Indeed, an indication of overlapping “lone-pair” orbitals among the N atoms in the heteroepitaxial adlayer was observed in the form of negative N-N electron bond populations (of ∼-0.12) (see Figure 1a,c). When adding a monatomic B layer on top of the first attached N adlayer, a strong correlation between interfacial bond strength, electron bond population, and degree of electron transfer was observed also here (both for the resulting heteroepitaxial BN adlayer and for the more amorphous BN adlayer). As can be seen in Table 1 and Figures 5 and 6, the somewhat weaker

interlayer bonding observed for the heteroepitaxial BN adlayer is accompanied by a smaller degree of electron transfer (of 0.22e) from C to N. However, the substrate-binding N layer will receive electrons from both the underlying diamond and from the upper B layer (i.e., due to differences in electronegativity). In addition, the N element has five valence electrons. As a consequence, antibinding states will be filled. This is to be observed as weaker C-N binding interactions (with an electron bond population of 0.66) and as a more pronounced tendency for antibinding N-N interactions (with an electron bond population of -0.12). A similar trend can be observed for the amorphous BN counterpart. However, larger variations in degree of electron transfer are observed due to the fact that there are for this structure larger variation in C-N and B-N bond lengths. It is, hence, for the BN adlayer obvious that boron prefers three valence electrons and nitrogen five valence electrons. As a consequence, the surface B layer will reconstruct and form pairwise B-B binding interactions. The situation with a four atomic BN adlayer on diamond (100) is very similar to the two-atomic BN scenario. However, for the situation with a heteroepitaxial interface, the preference for three valence electrons and a more planar structure is more apparent for the B atoms in the second atomic layer (i.e., positioned in between the attached N layer and the second N layer). As a result, the substrate-attached N atoms become bonded to only three other atoms, with no tendency for filling of C-N antibonding orbitals (see Figure 4a,b). The four-atomic BN adlayer interfacial binding energy will thereby become larger when compared to the corresponding scenario for the two-atomic BN adlayer (6.5 vs 3.9 eV per binding N atom). The more pronounced amorphous structure of the four-atomic BN adlayer, when compared to the two-atomic ditto, can be strongly correlated to the large variation in degree of electron transfer from B to its surrounding atoms (∼0.39e vs ∼0.17e). D.2. B Attached to Diamond (100). For the situation with a B monolayer attached to the diamond (100) surface, the direction of the electron transfer is the opposite. The boron atoms will partially donate electrons to the carbon atoms. For the most stable, nonheteroepitaxial boron adlayer, the electron transfer for each B is 0.32e. This value is high and correlates well with both the interfacial binding energy (see Figure 5) and the electron bonding populations (see Figure 6). As can also be seen in Figure 6, there are appreciate antibonding interactions between the B atoms. The predominant degree of electron transfer from the B atoms, in combination with the B-B antibonding interactions, speaks in favor of the formation of a three-electron bond formation over the C-B-C formation. This phenomenon is more common, although for electron-deficient atoms that are very similar with respect to electronegativity (identical to or less than 0.5).33 The difference in electronegativity for B and C is 0.5. Hence, one of the B electrons will be involved in the bonds with the substrate, and the rest of the electrons will form a lone pair which overlaps with a neighboring lone pair. For the heteroepitaxially built diamond/B interface, there is a larger spread in the electron transfer from the B atoms to the C atoms: 0.15e-0.35e. The major explanation is the variation

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TABLE 2: Changes in Atomic Charge as a Result of Electron Transfer within C-B Bonds across the Interfacea

a

atom layer

B

Be

BN

BNepitax

BNBNbulk

C charge [e] B charge [e] N charge [e]

-0.32 0.30-0.32

-0.15-(-0.35) 0.02-0.33

-0.01-(-0.03) 0.93-0.96 -0.93-(-0.96)

-0.14-(-0.39) 0.54 -0.35

-0.21 0.52 -0.63

The electron transfer within B-N bonds across second atomic layer of the adlayer is also included.

in orbital overlap as a result of the different bond lengths: 1.52-2.49 Å. In average, the degree of electron transfer within the interface is much lower compared to the energetically more stable nonheteroepitaxial structure (0.24e vs 0.32e). This lower value of electron transfer correlates strongly with the somewhat weaker interfacial binding energy (4.64 vs 5.42 eV per binding B; see Figure 5) and smaller electron bond populations 0.59 vs 0.80 (see Figure 6). As can also be seen in Figure 6, there are appreciate positive electron bond populations between the B atoms in the adlayer, which strongly support the pairwise binding observed in the structure. Hence, there is also for this interfacial structure a strong preference for three valence electrons within the B atoms. The heteroepitaxial BN adlayer obtained by adding a monatomic N layer on top of the first attached heteroepitaxial B layer shows an electron transfer of 0.54e from the B atoms to surrounding C and N atoms (see Table 2). Because of differences in electronegativity, the substrate-binding B atoms will partially donate electrons to both the underlying C atoms and the upper N atoms. As can be seen in Figure 3, the “capture” of the B atoms between the diamond substrate and the surface N atomic layer will force the B atoms to stay sp3-hybridized. Every B atom binds to four other atoms (two N and two C), with C-B and B-N bonds that are very strong (a bonding population of 0.74 and 0.73, respectively). Boron is an element that has only three valence electrons. However, from the obtained geometrical structure, in addition to the high electron bond population in each of the four bonds, it is obvious that N has donated an electron pair to form a fourth B-N bond (although strongly polarized) B. This can be explained by the fact that N is a Lewis base and B is a Lewis acid. The remaining valence electrons on N will, after the formation of two N-B bonds, have the possibility to form strong N-N bonds. Calculated N-N electron bond populations (0.77; see Figure 6) give evidence of strong N-N bond formations which will explain the observed surface reconstruction. Conclusion The initial growth of cubic boron nitride (100) on a diamond (100)-2 × 1 surface has in the present study been investigated theoretically using density functional theory (DFT) under periodic boundary conditions. The purpose with this study has been to outline the possibility (from an energetic point of view) for a layer-by-layer growth of cubic BN when using a diamond (100) surface as a substrate. Therefore, diamond/BN interfaces with varying number of BN atomic layers have been used as models in the calculations, with either B (or N) directly attached to the diamond substrate and as either a heteroepitaxial or a nonheteroepitaxial continuation of the diamond lattice. One, two, and four atomic layers were built and geometry optimized. Deposition of BN using methods like ion-beam-assisted evaporation PVD has here been regarded, and therefore, surface terminating species like H and F has been omitted. These results and conclusions presented in this paper will strongly support the experimental observations made for a c-BN growth onto monocrystalline diamond substrates. With N

forming the first atomic layer on top of diamond (100), the most energetic favorable position is as a heterostructural continuation of the underlying diamond structure. This structure is also the most energetically favorable one among all interfacial structures included in the present study. When applying a second atomic layer of B on top of the heteroepitaxial N monolayer, different results were obtained depending on the initial positions of the B atoms in this second atomic layer. For the situation where the cubic BN adlayer was rotated 90° with respect to the underlying diamond lattice (i.e., the x-axis of c-BN was aligned with the y-axis of the diamond lattice) and followed by geometry optimization, an amorphous-like BN structure was obtained. On the contrary, the initially heteroepitaxially modeled c-BN adlayer stayed perfectly cubic as a result of the geometry optimization. What is most interesting in this context is that the amorphouslike BN structure was found to be the most energetically favorable one (as compared with the cubic BN structure). For the situation with a four-atomic BN adlayer, a totally different result was obtained. As was the situation with the two-atomic BN adlayer, either a heteroepitaxially cubic BN structure (although reconstructed) or an amorphous BN structure was obtained, depending on the initially constructed diamond/BN interface. The main difference for this thicker adlayer is, however, that the cubic BN adlayer was now found to be the most energetically favorable one. The interfacial binding energies for the cubic BN was calculated to 6.5 eV per binding adlayer atom, which is to be compared with 5.8 eV per binding adlayer atom for the amorphous BN structure. Hence, it is from these calculations confirmed that there is a clear preference for the noncubic phase of BN to become bonded directly to the diamond (100) substrate. However, there is a strong indication for a switch-over to the cubic phase of BN only two atomic layers away from the underlying substrate. Hence, the weak point in the deposition of c-BN onto diamond (100), and without using surface termination species, is to pass the formation of the second atomic layer when starting from N attached to the substrate. The obtained lowest energy structural evolution is cubic-amorphous-cubic-cubic. To overcome this structural/ energetically bottleneck, addition of energy seems to be needed. With B forming the first atomic layer on top of diamond (100), the most energetic favorable position for the B atoms was found to be in bridge formations to two C atoms along the reconstructed carbon dimer rows. The interfacial binding energy for this structural formation is somewhat more energetically preferred when comparing with a B monolayer in a heterostructural continuation of the diamond lattice (5.4 vs 4.6 eV per binding adlayer atom). When a second atomic layer of N is added on top of the first nonheteroepitaxial B layer, and followed by geometry optimization, the total BN adlayer is found to be highly unstable and, hence, will not bind to the diamond substrate. For comparison, a second atomic layer of N was also added on top of the less stable heteroepitaxial B structure. As a result of the geometry optimization, this BN adlayer stayed perfectly cubic and strongly attached to the diamond substrate. The difference in total energy between the two different B monolayer’s (nonheterostructural and heterostructural adlayer)

Initial Growth of BN on Diamond Substrates is only about 0.8 eV per binding adlayer atom. Hence, if this energy barrier could be overcome during the growth process of BN, then there is a marked possibility for c-BN to be grown also with B attached to the diamond substrate. It has here been clarified that energy in e.g. the form of ion bombardment need to be introduced into the vapor phase deposition setup in order to be successful in the growth of c-BN directly onto diamond (100). Only a low-energy impact of ions seems to be necessary to use for the situation where B is directly attached to the substrate. Acknowledgment. The work was supported by the Swedish Research Council (VR), Go¨ran Gustafsson Foundation and the Swedish Foundation for Strategic Research (SSF); MS2E “Materials Science for Nanoscale Engineering”. The computational results were obtained using the software programs from Accelrys, Inc. (first principle calculations were done with the CASTEP program within the Cerius2 program package). References and Notes (1) Olander, J.; Larsson, K. Diamond Relat. Mater. 2002, 11, 1286. (2) Sachdev, H. Diamond Relat. Mater. 2001, 10, 1390. (3) Larsson, K. Diamond Relat. Mater. 2002, 11, 1300. (4) Olander, J.; Larsson, K. Surf. Coat. Technol. Phys. ReV. B 1995, 68, 075411. (5) Zhang, W.; Bello, I.; Lifshitz, Y.; Chan, K.; Wu, Y.; Chan, C.; Meng, X.; Lee, S. Appl. Phys. Lett. 2004, 85, 1344. (6) Zhang, W.; Bello, I.; Lifshitz, Y.; Chan, K.; Meng, X.; Wu, Y.; Chan, C.; Lee, S. AdV. Mater. 2004, 16. (7) Zhang, W.; Meng, X.; Chan, C.; Chan, K.; Wu, Y.; Bello, I.; Lee, S. J. Phys. Chem. B 2005, 109, 16005. (8) Chong, Y.; Ma, K.; Leung, K.; Chan, C.; Ye, Q.; Bello, I.; Zhang, W.; Lee, S. Chem. Vap. Deposition 2006, 12. (9) Bello, I.; Chan, C.; Zhang, W.; Chong, Y.; Leung, K.; Lee, S.; Lifshitz, Y. Diamond Relat. Mater. 2005, 14, 1154. (10) Zhang, F.; Guo, Y.; Song, Z.; Chen, G. Appl. Phys. Lett. 1994, 65, 971.

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